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A step-wise guide to performing survival analysis

Chakraborty, Santam

Tata Medical Centre, Kolkata, West Bengal, India

Address for correspondence: Dr. Santam Chakraborty, Tata Medical Centre, 14, MAR (E-W), New Town, Rajarhat, Kolkata - 700 160, West Bengal, India. E-mail: [email protected]

This is an open access journal, and articles are distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License, which allows others to remix, tweak, and build upon the work non-commercially, as long as appropriate credit is given and the new creations are licensed under the identical terms.

Survival analysis refers to statistical techniques which have been designed to circumvent the issues arising out of incomplete information regarding the time until which a desired event or endpoint occurs. The reasons for this may be manifold, for example, lost to follow-up, dropouts from the study, lack of sufficient research budget, and short follow-up period. It is one of the common but complicated analysis done in trials. The current article provides a step-wise guide toward understanding survival functions and performing it.

SURVIVAL ANALYSIS DEFINITION

Survival analysis refers to statistical techniques which have been designed to circumvent the issues arising out of incomplete information regarding the time until which a desired event or end point occurs. Synonyms include reliability analysis, duration analysis, and event history analysis. While duration and proportion survived are the most common outcomes of interest that are estimated using these methods, the analytical techniques can be applied to other end points when we are interested in the time taken for an event to occur, for example, duration of time stayed at a hotel and recidivism after incarceration.

WHY DO SURVIVAL ANALYSIS?

Continuous variables such as height, weight, and blood pressure can be measured objectively, and hence measures of central tendency (e.g., mean, median, and mode) and dispersion (range and standard deviation) are easy to understand and calculate in these situations. While it may be tempting to consider time to an event as a continuous variable, it is important to remember that in most cases, we cannot wait long enough for the entire population to experience the specific event of interest. Of course, if the entire population were to experience the event that is of interest, then time could be considered as a continuous variable, and routine measures of central tendency could be used to describe it. For example, if the event of interest were the duration of survival in fruit flies (irrespective of the cause of death) kept in a jar, while being unable to reproduce, the time to death would be recorded in all individual fruit flies within a practical time span of 60 days (as the lifespan is approximately 30 days). On the other hand, doing the same in a population of humans would certainly not be practical.

UNDERSTANDING CENSORING

The key issue that these analytical techniques attempt to circumvent is that all members of the population do not get to experience the event of interest within the time frame of the period of observation. The reasons for this may be manifold (e.g., lost to follow-up, dropouts from the study, lack of sufficient research budget, and short follow-up period), but all these are situations in which the events could be observed if the observation time and resources were further extended. The way these analytical techniques deal with this situation is referred as censoring. Censoring is of several types, but the most common type of censoring done is also known as right censoring, where the event may occur after the duration of observation. For example, if we wished to estimate the duration of time taken to finish a marathon race but have only 2–3 h to record the timings before we go home. In this case, some runners would have finished the marathon, some would be just finishing, and some would still be struggling at various distances or would have given up. In this case, the people who did not complete the marathon within 3 h would be censored. Note here that in a marathon, the people usually start at the same time, but survival analytic techniques deal with staggered entries typically seen in clinical trials and studies (i.e., all patients do not enter in the study at the same time point) [ Figure 1 ].

One of the key concepts to remember is that most survival techniques are designed to work with “noninformative” censoring.[ 1 ] The seemingly innocuous term means that censoring should not be determined by the event under consideration, i.e., the reasons that patients drop out of a study should be unrelated to the study question. If patients in a study were to drop out only if they experienced a recurrence, then censoring would be informative, and an accurate estimate of the recurrence-free survival could not be obtained. Noninformative censoring is necessary as traditional survival analytic methods like the Kaplan–Meier method assume that the population that remains after censoring is representative of the entire population.

PREPARING THE DATASET

Before starting out with survival analysis, there are certain basic data points that should be recorded in your dataset:

• The date/time of start of observation: This is usually the time at which you start observing your patients. This time point should be available for all patients and should be chosen such that there is minimal ambiguity. For randomized studies, the date of randomization is usually chosen as the start date, while in retrospective studies, a good choice is the date of registration or diagnosis. The key is to have a consistent way to record this date
• Date/time to event: This is basically the time at which your patient has experienced the event in question. The best practice is to record this as a date. The actual duration of survival is calculated from the date of start of observation to the date of event. Patients who do not experience an event should have the last date of follow-up noted in this column
• Event indicator: An indicator column which indicates whether the event of interest has happened. The best practice is to record the event as Yes or 1 and the absence of event as 0 or No.

Note here that if you are interested in multiple events of interest, then it is best to record these events separately in your dataset. It is also important to maintain consistency in encoding events in such a scenario. Figure 2 depicts an example on how to arrange your datasheet prior to the analysis.

Note that in the example, patients who have been lost to follow-up have not been coded as dead even if they had a recurrence. Instead, these have been censored at the last date of follow-up known for the patient. This is because while this patient may have subsequently died, we do not have concrete information on the same. If, on the other hand, we had known that this patient had died (e.g., by making a phone call/looking at the death certificate), then this patient would have been recorded as dead and the date of death would have been noted appropriately. Survival analytic methods are useful because they incorporate information on censoring and as such do not use subjective “data juggling” to account for what is not known about the patient's actual outcome. The corollary of this is that the figures obtained from this are not actual figures but always an estimate and therefore associated with a degree of uncertainty. How to quantify this uncertainty has been discussed in the subsequent sections. Note that for patients who have not died, the date of last known follow-up is recorded. In several situations in developing nations, where follow-up is not perfect, phone calls, letters, and mails are important tools to obtain survival information. In this setting, while objective events like death can be recorded accurately, endpoints like recurrence should not be recorded via these modes of communication if exact details are not available.

Prior to the actual analysis, the duration of survival-/recurrence-free survival needs to be calculated. As shown in Figure 3 , the duration was calculated using the available spreadsheet functions. These functions differ depending on the specific software utilized but for Statistical Package for the Social Sciences (SPSS), a good resource can be found online:

UNDERSTANDING HAZARD

One of the oft-repeated terms used in survival analysis is hazard. Semantically, the term “hazard” refers to an agent that may cause harm, while “risk” is the probability of the hazardous event occurring. In case of survival analysis, the term hazard is often used to imply risk. The term hazard refers to the probability that an individual who is under observation at a time t has an event at that time.[ 2 ] Plotting this instantaneous hazard against time gives the hazard function, and the rate at which this instantaneous hazard changes with respect to time is called the hazard rate. The ratio of two hazard rates is also referred to as hazard ratio.

CONDUCTING THE ANALYSIS

Prior to conducting the analysis, it is important to understand what estimate you desire and which analytical techniques you will need. Survival analytic methods can be broadly grouped into the following three categories:

• Nonparametric: These techniques do not make any assumptions about the distribution of the survival times. As such, these are very versatile and can be used for any survival distributions. However, these techniques are not ideal if you are attempting to generate predictive models. In the current manuscript, we will be dealing with an example of this form of analysis
• Semi-parametric: The most popular technique of this method is the Cox proportional hazards model, which is considered semi-parametric as it does not make an assumption about the baseline hazard. However, it is assumed that the factors influencing the survival are linearly related to the survival. This is useful when you desire to obtain a predictive model without wanting to “guess” the actual distribution of hazard[ 3 ]
• Parametric: These models assume that the hazard function follows a specific distribution. This is particularly useful when you want to calculate the hazard of the event for a specific person in your population and therefore is a technique used for advanced survival modeling.

BASIC SURVIVAL ANALYSIS: KAPLAN–MEIER METHOD

We will start with the simplest and practically the most (ab) used method for survival analysis, the Kaplan–Meier product limit estimator.[ 4 ] This technique,first described in a collaborative article in 1958, has become immensely popular owing to its simplicity and ease of interpretation. The complete details of how the calculation is done will not be presented here owing to space limitations, but a good description has been previously provided by Rich et al .[ 5 ]

In order to analyze the survival using this method, the basic requirements are the time and event descriptors. This page gives step-wise details on how to perform this analysis in SPSS (). The output of the analysis comprises a survival curve and a survival table. Note that for calculation of the survival time, the event is death and vice versa. Similarly, for calculation of the recurrence-free survival, the event of interest is the development of recurrence.

The Kaplan–Meier curve as depicted in Figure 4 consists of the survival probability on the Y-axis and the time duration on the X-axis. The curve itself comprises a series of steps with tick marks. The steps are indicative of an event, while the tick marks indicate censoring. We can obtain the cumulative survival probability at any point of time by reading the corresponding value on the Y-axis at the corresponding time point on the X-axis.

The survival table obtained from this analysis can provide us with the mean and median estimates of survival. Reporting of mean times is noninformative in general as they are affected by extremes. Median times are usually reported along with the 95% confidence intervals of the estimate. Note that median times may not be “reached” in cases where less than half of the patients have experienced an event. As a matter of practice, it is usual to report the proportion of patients who survive at the median follow-up duration. The stock Kaplan–Meier curves obtained in SPSS often fail to highlight important aspects of the survival distribution. Figure 5 depicts a more enhanced version of the Kaplan–Meier curve which has been generated using R software (Vienna, Austria). The important additions are as follows:

• 95% confidence intervals of the estimated cumulative survival at any point of time depicted by translucent bands
• Number at risk below the Y-axis which denotes the number of patients at risk for the event at any point of time
• Censoring plot: This shows the distribution of censoring and can be useful in special situations to understand if techniques to deal with informative or unequal censoring are required.

It should be noted that the 95% confidence intervals widen appreciably toward the end of the curve when the number of patients at risk is low. Therefore, estimates of the survival should be reported only from the time points when there is an adequate number of patients at risk (typically considered more than 10–15 patients).

The survival table provided in the output [ Figure 6 ] also allows us to estimate the cumulative survival probability at a given time point. It is a good practice to report the 95% confidence intervals of this estimate which can also be calculated from the same table using the standard error.

COMPARING THE SURVIVAL OF TWO (OR MORE) GROUPS

While obtaining survival estimates of the population is often adequate, we are usually interested in comparing the survival times between two populations. The Kaplan–Meier method also permits this form of analysis [ Figure 7 ]. The key to this analysis is to have a separate column indicative of the groups that you want to compare. For example, the group column can be gender. The key issue is that the data should be in a categorical format. For example, it is acceptable to have Stages I, II, III, and IV, but not height in centimeter. This is because the method estimates the cumulative survival probability for each group separately. In SPSS, the compare groups option must be checked to get the output. While the plot provides a visual indication, a formal statistical comparison is also possible. The most common technique for this formal comparison is the log-rank test which has been used to derive the Pvalue shown in the plot.[ 6 ] The test computes the Chi-square value for the two groups at each time point and summates the result. The summated Chi-square value for each group is compared using a standard Chi-square test.

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• Published: 15 July 2003

Survival Analysis Part I: Basic concepts and first analyses

• T G Clark 1 ,
• M J Bradburn 1 ,
• S B Love 1 &
• D G Altman 1  

British Journal of Cancer volume  89 ,  pages 232–238 ( 2003 ) Cite this article

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Introduction

In many cancer studies, the main outcome under assessment is the time to an event of interest. The generic name for the time is survival time , although it may be applied to the time ‘survived’ from complete remission to relapse or progression as equally as to the time from diagnosis to death. If the event occurred in all individuals, many methods of analysis would be applicable. However, it is usual that at the end of follow-up some of the individuals have not had the event of interest, and thus their true time to event is unknown. Further, survival data are rarely Normally distributed, but are skewed and comprise typically of many early events and relatively few late ones. It is these features of the data that make the special methods called survival analysis necessary.

This paper is the first of a series of four articles that aim to introduce and explain the basic concepts of survival analysis. Most survival analyses in cancer journals use some or all of Kaplan–Meier (KM) plots, logrank tests, and Cox (proportional hazards) regression. We will discuss the background to, and interpretation of, each of these methods but also other approaches to analysis that deserve to be used more often. In this first article, we will present the basic concepts of survival analysis, including how to produce and interpret survival curves, and how to quantify and test survival differences between two or more groups of patients. Future papers in the series cover multivariate analysis and the last paper introduces some more advanced concepts in a brief question and answer format. More detailed accounts of these methods can be found in books written specifically about survival analysis, for example, Collett (1994) , Parmar and Machin (1995) and Kleinbaum (1996) . In addition, individual references for the methods are presented throughout the series. Several introductory texts also describe the basis of survival analysis, for example, Altman (2003) and Piantadosi (1997) .

Types of ‘event’ in cancer studies

In many medical studies, time to death is the event of interest. However, in cancer, another important measure is the time between response to treatment and recurrence or relapse-free survival time (also called disease-free survival time). It is important to state what the event is and when the period of observation starts and finishes. For example, we may be interested in relapse in the time period between a confirmed response and the first relapse of cancer.

Censoring makes survival analysis different

The specific difficulties relating to survival analysis arise largely from the fact that only some individuals have experienced the event and, subsequently, survival times will be unknown for a subset of the study group. This phenomenon is called censoring and it may arise in the following ways: (a) a patient has not (yet) experienced the relevant outcome, such as relapse or death, by the time of the close of the study; (b) a patient is lost to follow-up during the study period; (c) a patient experiences a different event that makes further follow-up impossible. Such censored survival times underestimate the true (but unknown) time to event. Visualising the survival process of an individual as a time-line, their event (assuming it were to occur) is beyond the end of the follow-up period. This situation is often called right censoring . Censoring can also occur if we observe the presence of a state or condition but do not know where it began. For example, consider a study investigating the time to recurrence of a cancer following surgical removal of the primary tumour. If the patients were examined 3 months after surgery to determine recurrence, then those who had a recurrence would have a survival time that was left censored because the actual time of recurrence occurred less than 3 months after surgery. Event time data may also be interval censored , meaning that individuals come in and out of observation. If we consider the previous example and patients are also examined at 6 months, then those who are disease free at 3 months and lost to follow-up between 3 and 6 months are considered interval censored. Most survival data include right censored observations, but methods for interval and left censored data are available ( Hosmer and Lemeshow, 1999 ). In the remainder of this paper, we will consider right censored data only.

In general, the feature of censoring means that special methods of analysis are needed, and standard graphical methods of data exploration and presentation, notably scatter diagrams, cannot be used.

Illustrative studies

Ovarian cancer data.

This data set relates to 825 patients diagnosed with primary epithelial ovarian carcinoma between January 1990 and December 1999 at the Western General Hospital in Edinburgh. Follow-up data were available up until the end of December 2000, by which time 550 (75.9%) had died ( Clark et al, 2001 ). Figure 1 shows data from 10 patients diagnosed in the early 1990s and illustrates how patient profiles in calendar time are converted to time to event (death) data. Figure 1 (left) shows that four patients had a nonfatal relapse, one was lost to follow-up, and seven patients died (five from ovarian cancer). In the other plot, the data are presented in the format for a survival analysis where all-cause mortality is the event of interest. Each patient's ‘survival’ time has been plotted as the time from diagnosis. It is important to note that because overall mortality is the event of interest, nonfatal relapses are ignored, and those who have not died are considered (right) censored. Figure 1 (right) is specific to the outcome or event of interest. Here, death from any cause, often called overall survival, was the outcome of interest. If we were interested solely in ovarian cancer deaths, then patients 5 and 6 – those who died from nonovarian causes – would be censored. In general, it is good practice to choose an end-point that cannot be misclassified. All-cause mortality is a more robust end-point than a specific cause of death. If we were interested in time to relapse, those who did not have a relapse (fatal or nonfatal) would be censored at either the date of death or the date of last follow-up.

Converting calendar time in the ovarian cancer study to a survival analysis format. Dashed vertical line is the date of the last follow-up, R=relapse, D=death from ovarian cancer, Do=death from other cause, A=attended last clinic visit (alive), L=loss to follow-up, X=death, □=censored.

Lung cancer clinical trial data

These data originate from a phase III clinical trial of 164 patients with surgically resected (non-small cell) lung cancer, randomised between 1979 and 1985 to receive radiotherapy either with or without adjuvant combination platinum-based chemotherapy ( Lung Cancer Study Group, 1988 ; Piantadosi, 1997 ). For the purposes of this series, we will focus on the time to first relapse (including death from lung cancer). Table 1 gives the time of the earliest 15 and latest five relapses for each treatment group, where it can be seen that some patients were alive and relapse-free at the end of the study. The relapse proportions in the radiotherapy and combination arms were 81.4% (70 out of 86) and 69.2% (54 out of 78), respectively. However, these figures are potentially misleading as they ignore the duration spent in remission before these events occurred.

Survival and hazard

Survival data are generally described and modelled in terms of two related probabilities, namely survival and hazard . The survival probability (which is also called the survivor function) S ( t ) is the probability that an individual survives from the time origin (e.g. diagnosis of cancer) to a specified future time t . It is fundamental to a survival analysis because survival probabilities for different values of t provide crucial summary information from time to event data. These values describe directly the survival experience of a study cohort.

The hazard is usually denoted by h ( t ) or λ ( t ) and is the probability that an individual who is under observation at a time t has an event at that time. Put another way, it represents the instantaneous event rate for an individual who has already survived to time t . Note that, in contrast to the survivor function, which focuses on not having an event, the hazard function focuses on the event occurring. It is of interest because it provides insight into the conditional failure rates and provides a vehicle for specifying a survival model. In summary, the hazard relates to the incident (current) event rate, while survival reflects the cumulative non-occurrence.

Kaplan–Meier survival estimate

The survival probability can be estimated nonparametrically from observed survival times, both censored and uncensored, using the KM (or product-limit) method ( Kaplan and Meier, 1958 ). Suppose that k patients have events in the period of follow-up at distinct times t 1 < t 2 < t 3 < t 4 < t 5 < ⋯ < t k . As events are assumed to occur independently of one another, the probabilities of surviving from one interval to the next may be multiplied together to give the cumulative survival probability. More formally, the probability of being alive at time t j , S ( t j ), is calculated from S ( t j − 1 ) the probability of being alive at t j − 1 , n j the number of patients alive just before t j , and d j the number of events at t j , by

where t 0 =0 and S (0)=1. The value of S ( t ) is constant between times of events, and therefore the estimated probability is a step function that changes value only at the time of each event. This estimator allows each patient to contribute information to the calculations for as long as they are known to be event-free. Were every individual to experience the event (i.e. no censoring), this estimator would simply reduce to the ratio of the number of individuals events free at time t divided by the number of people who entered the study.

Confidence intervals for the survival probability can also be calculated. The KM survival curve , a plot of the KM survival probability against time, provides a useful summary of the data that can be used to estimate measures such as median survival time. The large skew encountered in the distribution of most survival data is the reason that the mean is not often used.

Survival analysis of the lung cancer trial

Table 2 shows the essential features of the KM survival probability. The estimator at any point in time is obtained by multiplying a sequence of conditional survival probabilities, with the estimate being unchanged between subsequent event times. For example, the probability of a member of the radiotherapy alone treatment group surviving (relapse-free) 45 days is the probability of surviving the first 36 days multiplied by the probability of then surviving the interval between 36 and 45 days. The latter is a conditional probability as the patient needs to have survived the first period of time in order to remain in the study for the second. The KM estimator utilises this fact by dividing the time axis up according to event times and estimating the event probability in each division, from which the overall estimate of the survivorship is drawn.

Figure 2 shows the survival probabilities for the two treatment groups in the conventional KM graphical display. The median survival times for each group are shown and represent the time at which S ( t ) is 0.5. The combination group has a median survival time of 402 days (1.10 years), as opposed to 232 days (0.64 years) in the radiotherapy alone arm, providing some evidence of a chemotherapy treatment benefit. Other survival time percentiles may be read directly from the plot or (more accurately) from a full version of Table 2 . There appears to be a survival advantage in the combination therapy group, but whether this difference is statistically significant requires a formal statistical test, a subject that is discussed later.

Relapse-free survival curves for the lung cancer trial. * Median relapse-free survival time for each arm, + censoring times, CAP=cytoxan, doxorubicin and platinum-based chemotherapy.

Survival function of the ovarian data

The KM survival curve of the ovarian cancer data is shown in Figure 3A . The steep decline in the early years indicates poor prognosis from the disease. This is also indicated by changes in the cumulative number of events and number at risk. Specifically, of the 825 women diagnosed with ovarian cancer, about a third had died within the first year, accounting for 43% of the total deaths as recorded by the last date of follow-up. The number lost to follow-up can be deduced from the total number in the cohort and the cumulative number of events and number at risk.

Survival and cumulative hazard curves with 95% CIs for the ovarian cancer study. Std.Err=standard error. ( A ) Kaplan–Meier survivor function, ( B ) cumulative incidence curve, ( C ) cumulative hazard function, ( D ) hazard function (smoothed).

The 95% confidence limits of the survivor function are shown. In practice, there are usually patients who are lost to follow-up or alive at the end of follow-up, and confidence limits are often wide at the tail of the curve, making meaningful interpretations difficult. Thus, it may be sensible to curtail plots before the end of follow-up on the x -axis ( Pocock et al, 2002 ). Curtailing of the y -axis, a common practice for diseases or events of low incidence, should not be performed. Instead, the incidence of death curve, or 1− S ( t ), ( Figure 3B ) may be presented ( Pocock et al, 2002 ). The cumulative incidence at a time point is simply one minus the survival probability. For example, Figure 3A shows how the 5-year survival of 0.29 (29%) is calculated, and could also be read from Figure 3B as a cumulative incidence of 71% for the first 5 years.

Hazard and cumulative hazard

There is a clearly defined relationship between S ( t ) and h ( t ), which is given by the calculus formula:

The formula is unimportant for routine survival analyses as it is incorporated into most statistical computer packages. The point here is simply that if either S ( t ) or h ( t ) is known, the other is automatically determined. Consequently, either can be the basis of statistical analysis.

Unfortunately, unlike S ( t ) there is no simple way to estimate h ( t ). Instead, a quantity called the cumulative hazard H ( t ) is commonly used. This is defined as the integral of the hazard, or the area under the hazard function between times 0 and t , and differs from the log-survivor curve only by sign, that is H ( t )=−log[ S ( t )]. The interpretation of H ( t ) is difficult, but perhaps the easiest way to think of H ( t ) is as the cumulative force of mortality, or the number of events that would be expected for each individual by time t if the event were a repeatable process. H ( t ) is used an intermediary measure for estimating h ( t ) and as a diagnostic tool in assessing model validity. A simple nonparametric method for estimating H ( t ) is the Nelson-Aalen estimator ( Hosmer, 1999 ), from which it is possible to derive an estimate of h ( t ) by applying a kernel smoother to the increments ( Ramlau-Hansen, 1983 ). Cox (1979) suggests another method to estimate the hazard based on order statistics but similar in spirit to the previous method.

Another approach to estimating the hazard is to assume that the survival times follow a specific mathematical distribution. Figure 4 shows the relationship between four parametrically specified hazards and the corresponding survival probabilities. It illustrates a constant hazard rate over time (which is analogous to an exponential distribution of survival times), strictly increasing/decreasing hazard rates based on a Weibull model, and a combination of decreasing and increasing hazard rates using a log-Normal model. These curves are illustrative examples and other shapes are possible. The specification of hazards using fully parametric distributions is an important and under-utilised modelling technique that will be discussed in subsequent papers.

Relationships between (parametric) hazard and survival curves: (a) constant hazard (e.g. healthy persons), (b) increasing Weibull (e.g. leukaemia patients), (c) decreasing Weibull (e.g. patients recovering from surgery), (d) increasing and then decreasing log-normal (e.g. tuberculosis patients).

Hazard function in the ovarian data

Figure 3C shows the cumulative hazard for the ovarian cancer data. The hazard is shown in Figure 3D . As the hazard function is generally very erratic, it is customary to fit a smooth curve to enable the underlying shape to be seen. Figure 3D shows that the (instantaneous) risk of death appears to be high in the first year after diagnosis and decreases afterwards. This observation corresponds to the steeply descending survival probability ( Figure 3A ) and marked increase in cumulative incidence ( Figure 3B ) in the first year. The y -axis is difficult to interpret for the hazard and the cumulative hazard, but the decreasing shape of the hazard may be consistent with a decreasing Weibull's model (see Figure 4 ).

Nonparametric tests comparing survival

Survival in two or more groups of patients can be compared using a nonparametric test. The logrank test ( Peto et al, 1977 ) is the most widely used method of comparing two or more survival curves. The groups may be treatment arms or prognostic groups (e.g. FIGO stage). The method calculates at each event time, for each group, the number of events one would expect since the previous event if there were no difference between the groups. These values are then summed over all event times to give the total expected number of events in each group, say E i for group i . The logrank test compares observed number of events, say O i for treatment group i , to the expected number by calculating the test statistic

This value is compared to a χ 2 distribution with ( g −1) degrees of freedom, where g is the number of groups. In this manner, a P -value may be computed to calculate the statistical significance of the differences between the complete survival curves.

If the groups are naturally ordered, a more appropriate test is to consider the possibility that there is a trend in survival across them, for example, age groups or stages of cancer. Calculating O i and E i for each group on the basis that survival may increase or decrease across the groups results in a more powerful test. For the new O i and E i , the test statistic for trend is compared with the χ 2 distribution with one degree of freedom ( Collett, 1994 ).

When only two groups are compared, the logrank test is testing the null hypothesis that the ratio of the hazard rates in the two groups is equal to 1. The hazard ratio (HR) is a measure of the relative survival experience in the two groups and may be estimated by

where O i /E i is the estimated relative (excess) hazard in group i . A confidence interval (CI) for the HR can be calculated ( Collett, 1994 ). The HR has a similar interpretation of the strength of effect as a risk ratio. An HR of 1 indicates no difference in survival. In practice, it is better to estimate HRs using a regression modelling technique, such as Cox regression, as described in the next article.

Other nonparametric tests may be used to compare groups in terms of survival ( Collett, 1994 ). The logrank test is so widely used that the reason for any other method should be stated in the protocol of the study. Alternatives include methods to compare median survival times, but comparing confidence intervals for each group is not recommended ( Altman and Bland, 2003 ). The logrank method is considered more robust ( Hosmer and Lemeshow, 1999 ), but the lack of an accompanying effect size to compliment the P -value it provides is a limitation.

Survival differences in the lung cancer trial

We have already seen that median survival is greater in the combination treatment arm. Table 3 provides information about (relapse-free) survival differences between the trial arms. A test of differences between median survival times in the groups is indicative of a difference in survival ( P <0.01). The number of relapses observed among patients treated with radiotherapy+CAP (cytoxan, doxorubin and platinum-based chemotherapy) and radiotherapy alone were 54 and 70, respectively. Using the logrank method, the expected number of relapses for each group were 70.6 and 53.4, respectively. Thus, the logrank test yields a χ 2 value of 9.1 on 1 degree of freedom ( P <0.002). The HR of 0.58 indicates that there is 42% less risk of relapse at any point in time among patients surviving in the combination treatment group compared with those treated with radiotherapy alone. Overall, there is an indication that the combination treatment is more efficacious than radiotherapy treatment, and may be preventing or delaying relapse.

Survival differences in the ovarian study

In the ovarian study, we wished to compare the survival between patients with different FIGO stages–an ordinal variable. Figure 5 shows overall survival by FIGO stage. A logrank test of trend is statistically significant ( P <0.0001), and reinforces the visual impression of prognostic separation and a trend towards better survival when the disease is less advanced.

FIGO stage and prognosis in the ovarian study. Chisq= χ 2 .

Some key requirements for the analysis of survival data

Uninformative censoring.

Standard methods used to analyse survival data with censored observations are valid only if the censoring is ‘noninformative’. In practical terms, this means that censoring carries no prognostic information about subsequent survival experience; in other words, those who are censored because of loss to follow-up at a given point in time should be as likely to have a subsequent event as those individuals who remain in the study. Informative censoring may occur when patients withdraw from a clinical trial because of drug toxicity or worsening clinical condition. Standard methods for survival analysis are not valid when there is informative censoring. However, when the number of patients lost to follow-up is small, very little bias is likely to result from applying methods based on noninformative censoring.

Length of follow-up

In general, the design of a study will influence how it is analysed. Time to event studies must have sufficient follow-up to capture enough events and thereby ensure there is sufficient power to perform appropriate statistical tests. The proposed length of follow-up for a prospective study will be based primarily on the severity of the disease or prognosis of the participants. For example, for a lung cancer trial a 5-year follow-up would be more than adequate, but this follow-up duration will only give a short- to-medium-term indication of survivorship among breast cancer patients.

An indicator of length of follow-up is the median follow-up time. While this could in theory be given as the median follow-up time of all patients, it is better calculated from follow-up among the individuals with censored data. However, both these methods tend to underestimate follow-up, and a more robust measure is based on the reverse KM estimator ( Schemper and Smith, 1996 ), that is the KM method with the event indicator reversed so that the outcome of interest becomes being censored. In the ovarian cohort example, the median follow-up time of all the patients is 1.7 years, although is influenced by the survival times which were early deaths. The median survival of the censored patients was 3.2 years, but the reverse KM estimate of the median follow-up is 5.3 years (95% CI: 4.7–6.0 years).

Completeness of follow-up

Each patient who does not have an event can be included in a survival analysis for the period up to the time at which they are censored, but completeness of follow-up is still important. Unequal follow-up between different groups, such as treatment arms, may bias the analysis. A simple count of participants lost to follow-up is one indicator of data incompleteness, but it does not inform us about time lost and another measure has been proposed ( Clark et al, 2002 ). In general, disparities in follow-up caused by differential drop-out between arms of a trial or different subgroups in a cohort study need to investigated.

Cohort effect on survival

In survival analysis, there is an assumption of homogeneity of treatment and other factors during the follow-up period. However, in a long-term observational study of patients of cancer, the case mix may change over the period of recruitment, or there may be an innovation in ancillary treatment. The KM method assumes that the survival probabilities are the same for subjects recruited early and late in the study. On average, subjects with longer survival times would have been diagnosed before those with shorter times, and changes in treatments, earlier diagnosis or some other change over time may lead to spurious results. The assumption may be tested, provided we have enough data to estimate survival probabilities in different subsets of the data and, if necessary, adjusted for by further analyses (see next section).

Between-centre differences

In a multicentre study, it is important that there is a consistency between the study methods in each centre. For example, diagnostic instruments, such as staging classification, and treatments should be identical. Heterogeneity in case mix among centres can be adjusted for in an analysis (see next section).

Need for survival analysis adjusting for covariates

When comparing treatments in terms of survival, it is often sensible to adjust for patient-related factors, known as covariates or confounders, which could potentially affect the survival time of a patient. For example, suppose that despite the treatment being randomised in the lung cancer trial, older patients were assigned more often to the radiotherapy alone group. This group would have a worse baseline prognosis and so the simple analysis may have underestimated its efficacy compared to the combination treatment, referred to as confounding between treatment and age. Also, we sometimes want to determine the prognostic ability of various factors on overall survival, as in the ovarian study. Figure 5 shows overall survival by FIGO stage, and there is a significant decrease in overall survival with more advanced disease.

Multiple prognostic factors can be adjusted for using multivariate modelling. For example, if those women with early stage disease were younger than those with advanced disease, then the FIGO I and II groups might be surviving longer because of lower age and not because of the effect of FIGO stage. In this case, the FIGO effect is confounded by the effect of age, and a multivariate analysis is required to adjust for the differences in the age distribution. The appropriate analysis is a form of multiple regression, and is the subject of the next paper in this series.

Survival analysis is a collection of statistical procedures for data analysis where the outcome variable of interest is time until an event occurs . Because of censoring–the nonobservation of the event of interest after a period of follow-up–a proportion of the survival times of interest will often be unknown. It is assumed that those patients who are censored have the same survival prospects as those who continue to be followed, that is, the censoring is uninformative. Survival data are generally described and modelled in terms of two related functions, the survivor function and the hazard function. The survivor function represents the probability that an individual survives from the time of origin to some time beyond time t . It directly describes the survival experience of a study cohort, and is usually estimated by the KM method. The logrank test may be used to test for differences between survival curves for groups, such as treatment arms. The hazard function gives the instantaneous potential of having an event at a time, given survival up to that time. It is used primarily as a diagnostic tool or for specifying a mathematical model for survival analysis. In comparing treatments or prognostic groups in terms of survival, it is often necessary to adjust for patient-related factors that could potentially affect the survival time of a patient. Failure to adjust for confounders may result in spurious effects. Multivariate survival analysis, a form of multiple regression, provides a way of doing this adjustment, and is the subject the next paper in this series.

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Acknowledgements

We thank John Smyth for providing the ovarian cancer data, and Victoria Cornelius and Peter Sasieni for invaluable comments on an earlier manuscript. Cancer Research UK supported all the authors. Taane Clark holds a National Health Service (UK) Research Training Fellowship.

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Clark, T., Bradburn, M., Love, S. et al. Survival Analysis Part I: Basic concepts and first analyses. Br J Cancer 89 , 232–238 (2003). https://doi.org/10.1038/sj.bjc.6601118

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Issue Date : 21 July 2003

DOI : https://doi.org/10.1038/sj.bjc.6601118

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Survival analysis in clinical trials: Basics and must know areas

Ritesh singh.

Department of Community Medicine, College of Medicine and JNM Hospital, Kalyani, West Bengal, India

Keshab Mukhopadhyay

1 Department of Pharmacology, College of Medicine and JNM Hospital, Kalyani, West Bengal, India

Many clinical trials involve following patients for a long time. The primary event of interest in those studies is death, relapse, adverse drug reaction or development of a new disease. The follow-up time for the study may range from few weeks to many years. A different set of statistical procedures are employed to analyze the data, which involves time to event an analysis. It is a very useful tool in clinical research and provides invaluable information about an intervention. This article introduces the researcher to the different tools of survival analysis.

INTRODUCTION

Clinical trials are conducted to assess the efficacy of new treatment regimens. The major events that the trial subjects suffer are death, development of an adverse reaction, relapse from remission, and development of a new disease entity.[ 1 ] Medical articles dealing with survival analysis often use Cox's proportional hazards regression model. These statistical models takes into consideration time until an event of interest occurs and compare the cumulative probability of events over time for two or more cohorts, while adjusting other influential covariates. This article outlines the must know areas of survival analysis and introduces the reader to often-used terms in the survival analysis.

HISTORY OF SURVIVAL ANALYSIS

Survival analysis is a collection of statistical procedures for data analysis, for which the outcome variable of interest is time until an event occurs. It is the study of time between entry into observation and a subsequent event. The term ‘Survival analysis’ came into being from initial studies, where the event of interest was death. Now the scope of the survival analysis has become wide. Today scientists are using it for time until onset of disease, time until stock market crash, time until equipment failure, time until earthquake, and so on.[ 2 ] Common events studied are death, disease, relapse, and recovery. Few examples of studies where tools of survival analysis are used are: leukemia patients and time in remission, time to develop a heart disease for normal individuals, elderly population and time until death, and heart transplants and time until death.[ 3 ]

No one is sure of the birth of this statistical procedure. Probably it originated centuries ago, but only after World War II a new era of survival analysis has emerged, being stimulated by an interest in the reliability of military equipment. At the end of the war these newly developed statistical methods, emerging from strict mortality data research to failure time research, quickly spread through the private industry as customers became more demanding of safer, more reliable products.

LIFE TABLE ANALYSIS

In longitudinal studies it is often of interest to estimate a ‘survival’ curve for the population. What proportion of the population survive beyond a specified time interval without a particular event happening?[ 4 ] The most straightforward way to describe the survival in a sample is to compute the Life Table. The life table technique is one of the oldest methods for analyzing survival data. The distribution of survival times is divided into a certain number of intervals. For each interval we can then compute the number and proportion of cases or objects that entered the respective interval ‘alive,’ the number and proportion of cases that failed in the respective interval (number of terminal events, or number of cases that died), and the number of cases that were lost or censored (will be described later) in the respective interval. Based on those numbers and proportions, several additional statistics can be computed, such as, the number of cases at risk, proportion failing, proportion surviving, survival function, hazard rate, and median survival time. This procedure is used for larger samples where the time intervals are large enough to be broken down into smaller units.[ 5 ] By using the life table analysis we can find out the probability of whether a woman who retained an IUD for the first six months will still have it by the end of the twentieth month. Similarly we can find out if Mrs. A, who has retained her IUD until now (the beginning of the eleventh month) and Mrs. B, who has also retained her IUD until now (the beginning of the thirteenth month) will both lose their IUDs within the next six months.

SOME COMMON TERMS USED IN SURVIVAL ANALYSIS

Most survival analyses consider a key analytical problem called censoring. It occurs when we have some information about individual survival time, but we do not know the survival time exactly. Three reasons of censoring are: When a person does not experience the event before the study ends, when a person is lost to follow-up during the study period, and when a person withdraws from the study because of death (if death is not the event of the interest) or some other reason like adverse drug reaction. Censoring is of two types, right and left.[ 6 ] We generally encounter right-censored data. Left-censored data can occur when a person's survival time becomes incomplete on the left side of the follow-up period for the person. As an example, we may follow up a patient for any infectious disorder from the time of his or her being tested positive for the infection. We may never know the exact time of exposure to the infectious agent.

Survival function

Survival function, S (t) gives the probability that a person survives longer than some specified time t . It gives the probability that the random variable T exceeds the specified time t . The survival function is fundamental to a survival analysis. The survivor function is often expressed as a Kaplan-Meier curve. The name is a misnomer as in the actual data case scenario we get the step functions rather than smooth curves. Vertical drop in a Kaplan-Meir curve indicates an event.

Hazard function

The hazard function h (t) gives the instantaneous potential per unit time for the event to occur, given the individual has survived up to time t . It is the probability of failure in an infinitesimally small time period between y and y + Δy given that the subject has survived up till time y. In this sense, the hazard is a measure of risk: The greater the hazard between times y1 and y2, the greater the risk of failure in this time interval. The hazard function has its own importance, as it provides an insight into the conditional failure rates; it may be used to identify a specific model form and it is the vehicle by which mathematical modeling of survival data is carried out.

Hazard ratio

Hazard ratio (HR) is akin to relative risk. It has been used to describe the outcome of therapeutic trials where the question is, to what extent can treatment shorten the duration of an illness.[ 7 ] The hazard ratio is an estimate of the ratio of the hazard rate in the treated versus the control group. For example if there are two groups, group 1 and group 2, HR = 4.5 for treatment means that the risk (of relapse) for group 2 is 4.5 times that of group 1. If HR = 1 then Group 1 h (t) = Group 2 h (t).

COX PROPORTIONAL HAZARDS MODEL

Clinical trials commonly record the length of time from study entry to a disease endpoint for a treatment and a control group. These data are commonly depicted with a Kaplan-Meier curve, from which the median (time at which, in 50% of cases, an event of interest has occurred) and the mean (average time for the event) can be derived. There are several methods available to analyze time-to-event curves, such as Cox proportional hazards, log-rank, and Wilcoxon two sample tests. The Cox proportional hazards model has been the most widely used because of its applicability to a wide variety of clinical studies.[ 8 ] The Cox model was introduced by Cox, in 1972, for analysis of survival data with and without censoring, for identifying differences in survival due to treatment and prognostic factors (covariates or predictors or independent variables) in clinical trials. The Cox model is a regression method for survival data. It provides an estimate of the hazard ratio and its confidence interval. Cox regression is considered a ‘semi-parametric’ procedure because the baseline hazard function, h 0 ( t ), does not have to be specified. There are two assumptions about the Cox proportional hazard model: The hazard ratios of two people are independent of time, and are valid only for time-independent covariates. This means that the hazard functions for any two individuals at any point in time are proportional. In other words, if an individual has a risk of death at some initial point in time that is twice as high as that of another individual, then at all later times the risk of death remains twice as high.

In a survival study, one should ensure that patients are not removed from the study just before they die. Survival studies often recruit patients over a long period of time and so it is also important to verify that other factors remain constant over the period, such as, the way patients are recruited into a study, and the diagnosis of the disease. The Cox model is popular as it is robust, the estimated hazards are always non-negative and the hazard ratio can be calculated.

Logistic regression is applied when the investigators examine the relationship between risk factors and various disease events. The ability to consider the time element of event occurrences by proportional hazards models has meant that logistic regression has played a less important role in the analysis of survival data.[ 9 ] The Cox model is preferred over the logistic model, which ignores survival time and censoring information.[ 10 ] Given a Cox model and the coefficients, we can subsequently estimate the baseline hazard function and the survival curves.

LOG RANK TEST

The log rank test (also known as the Mantel log-rank test, the Cox Mantel log-rank test, or the Mantel-Haenszel test) is a form of Chi-square test.[ 11 ] It calculates a test statistic for testing a null hypothesis that the survival curves are the same for all groups, in other words, to test a null hypothesis where there is no difference between the populations in the probability of an event at any time point. For each time point the observed number of deaths in each group and the number expected if there has been no difference, are calculated. The number of expected is calculated as the proportion of subjects who are at risk at a given time point multiplied by the total number of events at that point. The log rank test is based on the same assumptions as the hazard ratio that the survival probabilities are the same for subjects early and late in the study, and the events happen at the time specified. The test is more likely to detect a difference between groups when the risk of an event is consistently greater for one group than another. It is unlikely to detect a difference when survival curves cross. Hence it is useful to plot survival curves when analyzing survival data. Under the null hypothesis, the log-rank statistic is approximately chi-square with one degree of freedom. Thus, a P -value for the log-rank test is determined from tables of the chi-square distribution.

There are other tests for survival data. One of the important one is the ‘Peto test’. It is an alternative to the log-rank test. In contrast to the log-rank test, the Pito test uses a weighted average of the observed minus expected score. It places more emphasis on the information at the beginning of the survival curve where the number at risk is large.

Survival analysis is a very good tool when a researcher takes into account the time till an event occurs and the censored data. There are some common mistakes performed by researchers when applying tools of survival analysis for their research.[ 12 ] The first being, only data related to an event of interest occurring is reported. The time of the event is not mentioned. How long patients were observed with no events occurring is not considered. It is evident that events would be observed more frequently in patients with longer follow-up times than in patients with a short follow-up. Evaluation of raw event frequencies without mention of time will produce biased results. Similarly, when we get biased results, no distinction is made as to whether a patient suffered an event or was censored. The third error is not including the censored data in the analysis. If we take a specific proportion of events from both the groups, without taking into account the censoring, a different method of statistics should be employed, and not the survival analysis technique.

There are three primary goals of survival analysis, to estimate and interpret survival and / or hazard functions from the survival data; to compare survival and / or hazard functions, and to assess the relationship of explanatory variables to survival time. Survival analysis provides a great tool for analyzing the time to an event type of data, which is very common in any clinical trial. Researchers are not using it frequently because they are not confident in the theory of its application and its interpretation. There are books available that provide the basic knowledge on survival analysis. They should not make common mistakes while applying these tools to their data.

Source of Support: Nil.

Conflict of Interest: None declared.

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Survival analysis in public health research

Affiliation.

• 1 College of Public Health, University of Oklahoma Health Sciences Center, Oklahoma City 73190, USA. [email protected]
• PMID: 9143714
• DOI: 10.1146/annurev.publhealth.18.1.105

This paper reviews the common statistical techniques employed to analyze survival data in public health research. Due to the presence of censoring, the data are not amenable to the usual method of analysis. The improvement in statistical computing and wide accessibility of personal computers led to the rapid development and popularity of nonparametric over parametric procedures. The former required less stringent conditions. But, if the assumptions for parametric methods hold, the resulting estimates have smaller standard errors and are easier to interpret. Nonparametric techniques include the Kaplan-Meier method for estimating the survival function and the Cox proportional hazards model to identify risk factors and to obtain adjusted risk ratios. In cases where the assumption of proportional hazards is not tenable, the data can be stratified and a model fitted with different baseline functions in each stratum. Parametric modeling such as the accelerated failure time model also may be used. Hazard functions for the exponential, Weibull, gamma, Gompertz, lognormal, and log-logistic distributions are described. Examples from published literature are given to illustrate the various methods. The paper is intended for public health professionals who are interested in survival data analysis.

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Biologic brachytherapy: genetically modified surgical flap as a therapeutic tool—a systematic review of animal studies.

1. Introduction

2. materials and methods, 2.1. study selection, 2.2. search, 2.3. data extraction.

• Interventions focusing on affecting surrounding tissue or the whole organism using the flap and achieving additional therapeutic activity;
• Preconditioning interventions directed towards affecting surroundings and the flap;
• Interventions focusing on improving flap survival and managing flap surgery-related complications;
• Studies that described the safety and efficacy of surgical flap gene therapy.

3.1. Local or Systemic Tissue Therapy Using Genetically Modified Surgical Flaps

3.2. genetic flap preconditioning affecting surrounding tissue and the flap, 3.3. genetically modifie surgical flap for flap-surgery related complications management.

• Vascular endothelial growth factor (VEGF), a signalling molecule that belongs to the PDGF supergene family and, as a homodimer, regulates angiogenesis and vascular permeability (VEGF-A) [ 99 ].
• Platelet-derived growth factor (PDGF), a heterodimer cytokine, which promotes angiogenesis [ 100 ].
• Fibroblast growth factors (FGFs), with leading member FGF-2, which belong to heparin-binding growth factors, contributing to angiogenesis via regulation of the SRSF1/SRSF3/SRPK1 network, leading to VEGFR-1 alternative splicing [ 101 ].
• Hepatocyte growth factor (HGF), which acts through the Met receptor and induces the expression of VEGF leading to an angiogenic response [ 102 ].
• Angiopoietin 1 (Ang-1), a cytokine required for vessel maturation, which mediates the migration, adhesion and survival of endothelial cells [ 103 ].
• Hypoxia-inducible factor 1α (HIF-1α), an important transcription factor regulating the transcription of genes associated with angiogenesis, primarily VEGF [ 38 ].
• Interleukin 10 (IL-10), an anti-inflammatory interleukin, with limited understanding regarding its influence on vessel development with potential pro- and anti-angiogenic actions [ 104 ].
• Transforming growth factor beta (TGF-β), a pleiotropic factor that participates both in vasculogenesis and angiogenesis, resulting in the promotion or suppression of endothelial cell migration and proliferation [ 105 ].

3.4. Genetically Modified Flaps Used for Optimization Studies

4. discussion, 5. conclusions.

• Biologic brachytherapy uses genetically modified surgical flaps to produce a chosen molecule and exert desired effects on the flap itself, local surroundings or in the whole organism.
• Biologic brachytherapy, in a preclinical setting, is a feasible therapeutic option for many ailments, including wounds, bone defects, cancer or protein-deficiency disorders. Additionally, they can be used to increase tissue survival in ischemic flaps, but also in other contexts, such as irradiation-damage management, and in allotransplants to reduce the immune response.
• Biologic brachytherapy of flaps with VEGF appears to be well-grounded for first-in-human studies. Other therapeutic aims require more research.
• New investigations should focus on high-quality data reporting, studying long-term side effects, expanding the use of genetically enhanced flaps for systemic therapies and determining the optimal transgene delivery method.

Supplementary Materials

Author contributions, institutional review board statement, informed consent statement, data availability statement, acknowledgments, conflicts of interest.

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Pascal, W.; Gotowiec, M.; Smoliński, A.; Suchecki, M.; Kopka, M.; Pascal, A.M.; Włodarski, P.K. Biologic Brachytherapy: Genetically Modified Surgical Flap as a Therapeutic Tool—A Systematic Review of Animal Studies. Int. J. Mol. Sci. 2024 , 25 , 10330. https://doi.org/10.3390/ijms251910330

Pascal W, Gotowiec M, Smoliński A, Suchecki M, Kopka M, Pascal AM, Włodarski PK. Biologic Brachytherapy: Genetically Modified Surgical Flap as a Therapeutic Tool—A Systematic Review of Animal Studies. International Journal of Molecular Sciences . 2024; 25(19):10330. https://doi.org/10.3390/ijms251910330

Pascal, Wiktor, Mateusz Gotowiec, Antoni Smoliński, Michał Suchecki, Michał Kopka, Adriana M. Pascal, and Paweł K. Włodarski. 2024. "Biologic Brachytherapy: Genetically Modified Surgical Flap as a Therapeutic Tool—A Systematic Review of Animal Studies" International Journal of Molecular Sciences 25, no. 19: 10330. https://doi.org/10.3390/ijms251910330

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Title: research reproducibility as a survival analysis.

Abstract: There has been increasing concern within the machine learning community that we are in a reproducibility crisis. As many have begun to work on this problem, all work we are aware of treat the issue of reproducibility as an intrinsic binary property: a paper is or is not reproducible. Instead, we consider modeling the reproducibility of a paper as a survival analysis problem. We argue that this perspective represents a more accurate model of the underlying meta-science question of reproducible research, and we show how a survival analysis allows us to draw new insights that better explain prior longitudinal data. The data and code can be found at this https URL

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• Lifetime effects and cost-effectiveness of statin therapy for older people in the United Kingdom: a modelling study
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• http://orcid.org/0000-0002-0951-1304 Borislava Mihaylova 1 , 2 ,
• Runguo Wu 2 ,
• Junwen Zhou 1 ,
• Claire Williams 1 ,
• http://orcid.org/0000-0002-4154-1431 Iryna Schlackow 1 ,
• Jonathan Emberson 3 ,
• Christina Reith 3 ,
• Anthony Keech 4 ,
• John Robson 5 ,
• Richard Parnell 6 ,
• Jane Armitage 3 ,
• http://orcid.org/0000-0003-0239-7278 Alastair Gray 1 ,
• John Simes 4 ,
• Colin Baigent 3
• 1 Health Economics Research Centre, Nuffield Department of Population Health , University of Oxford , Oxford , UK
• 2 Health Economics and Policy Research Unit, Wolfson Institute of Population Health , Queen Mary University of London , London , UK
• 3 Clinical Trial Service Unit and Epidemiological Studies Unit, Nuffield Department of Population Health , University of Oxford , Oxford , UK
• 4 NHMRC Clinical Trials Centre , The University of Sydney , Sydney , New South Wales , Australia
• 5 Clinical Effectiveness Group, Wolfson Institute of Population Health , Queen Mary University of London , London , UK
• 6 Patient and Public Representative , Havant , UK
• Correspondence to Dr Borislava Mihaylova; boby.mihaylova{at}dph.ox.ac.uk

Background Cardiovascular disease (CVD) risk increases with age. Statins reduce cardiovascular risk but their effects are less certain at older ages. We assessed the long-term effects and cost-effectiveness of statin therapy for older people in the contemporary UK population using a recent meta-analysis of randomised evidence of statin effects in older people and a new validated CVD model.

Methods The performance of the CVD microsimulation model, developed using the Cholesterol Treatment Trialists’ Collaboration (CTTC) and UK Biobank cohort, was assessed among participants ≥70 years old at (re)surveys in UK Biobank and the Whitehall II studies. The model projected participants’ cardiovascular risks, survival, quality-adjusted life years (QALYs) and healthcare costs (2021 UK£) with and without lifetime standard (35%–45% low-density lipoprotein cholesterol reduction) or higher intensity (≥45% reduction) statin therapy. CTTC individual participant data and other meta-analyses informed statins’ effects on cardiovascular risks, incident diabetes, myopathy and rhabdomyolysis. Sensitivity of findings to smaller CVD risk reductions and to hypothetical further adverse effects with statins were assessed.

Results In categories of men and women ≥70 years old without (15,019) and with (5,103) prior CVD, lifetime use of a standard statin increased QALYs by 0.24–0.70 and a higher intensity statin by a further 0.04–0.13 QALYs per person. Statin therapies were cost-effective with an incremental cost per QALY gained below £3502/QALY for standard and below £11778/QALY for higher intensity therapy and with high probability of being cost-effective. In sensitivity analyses, statins remained cost-effective although with larger uncertainty in cost-effectiveness among older people without prior CVD.

Conclusions Based on current evidence for the effects of statin therapy and modelling analysis, statin therapy improved health outcomes cost-effectively for men and women ≥70 years old.

• Health Care Economics and Organizations
• Computer Simulation
• Cardiovascular Diseases
• Outcome Assessment, Health Care

Data availability statement

Data may be obtained from a third party and are not publicly available. The datasets used in the current study may be obtained from third parties (UK Biobank https://www.ukbiobank.ac.uk/ ; Whitehall II study www.ucl.ac.uk/epidemiology-health-care/research/epidemiology-and-public-health/research/whitehall-ii ) and are not publicly available. Researchers can apply to use the UK Biobank resource and Whitehall II study data.

This is an open access article distributed in accordance with the Creative Commons Attribution 4.0 Unported (CC BY 4.0) license, which permits others to copy, redistribute, remix, transform and build upon this work for any purpose, provided the original work is properly cited, a link to the licence is given, and indication of whether changes were made. See:  https://creativecommons.org/licenses/by/4.0/ .

https://doi.org/10.1136/heartjnl-2024-324052

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WHAT IS ALREADY KNOWN ON THIS TOPIC

Randomised studies showed that statins reduce the incidence of myocardial infarction and ischaemic stroke by about one quarter for every 1 mmol/L reduction in low-density lipoprotein cholesterol but direct evidence among older people without prior cardiovascular disease (CVD) is limited.

In previous studies, statin therapy has been shown to be cost-effective in older people, but it has been suggested that a small further adverse effect would offset its cardiovascular benefit.

Despite markedly increased CVD risks with advancing age, lower statin use is reported among older people.

WHAT THIS STUDY ADDS

The value of statin therapy was reassessed using a contemporary UK CVD model validated in older people together with the synthesised evidence of statins’ beneficial effects on CVD events and adverse effects on myopathy, rhabdomyolysis and incident diabetes.

The study reported that both standard and higher intensity statin therapies enhanced health outcomes, with higher intensity therapy achieving larger benefits, and were cost-effective in people ≥70 years old in the UK. These findings remained robust in scenarios with smaller CVD risk reductions and further hypothetical adverse effects with statin therapy, though with increased uncertainty among older people without CVD.

HOW THIS STUDY MIGHT AFFECT RESEARCH, PRACTICE OR POLICY

While ongoing statin trials in older people without CVD will add valuable data, particularly in those over the age of 75 years, statin treatment of individuals should not be delayed while awaiting their findings.

Increasing statin uptake and adherence among older people will reduce CVD risks.

Introduction

Statins are widely available generically and a cornerstone in cardiovascular disease (CVD) prevention. High-quality randomised evidence has shown that statins reduce the incidence of myocardial infarction (MI) and ischaemic stroke by about one quarter for every 1 mmol/L reduction in low-density lipoprotein cholesterol (LDL-C). More intensive statin regimens achieve larger reductions in LDL-C and prevent more atherosclerotic cardiovascular events. 1 However, there is less definitive evidence for statin benefit among older patients without CVD history 2 and guidelines stop short of making specific recommendations on initiating statins for primary CVD prevention in older people. 3 4 Despite the growing proportion of older people (people ≥70 years old make up about 30% of those over the age of 40 years in the UK) and the markedly higher cardiovascular risk with increasing age, lower statin use is reported. 5 6

Evidence for treatments’ long-term effects and cost-effectiveness guides healthcare decisions in many countries and healthcare systems, including in the UK. Such evidence ensures that by implementing cost-effective treatments, healthcare systems efficiently use their resources to maximise population health. Previous evidence has indicated that statin therapy is likely to be cost-effective for older people, but the estimates were sensitive to further adverse effects of statins or lower statin effectiveness. 7–9 A recent individual participant data meta-analysis of large statin trials strengthened the evidence for efficacy and safety of statins in older people. 2 Therefore, we set out to reassess the lifetime effects and cost-effectiveness of statin therapy in people ≥70 years old in the contemporary UK population, in categories by prior CVD, sex and LDL-C level, using this evidence 2 and a new UK CVD microsimulation model. 10

Study population

The lifetime effects and cost-effectiveness of statin therapy were assessed in categories of UK adults ≥70 years old in the UK Biobank and the Whitehall II cohort studies. All UK Biobank participants ≥70 years old at recruitment into the study (2006–2010), and those who reached this age by subsequent resurveys, were included in the present study from their earliest eligible attendance. All Whitehall II participants ≥70 years old at phase 9 (2007–2009) in Whitehall II were also included. Information on the derivation of participants’ baseline characteristics is presented in the online supplemental methods . To assess the lifetime effects of statin therapy, a model is required that reliably projects individual participant’s morbidity, mortality, quality of life (QoL) and healthcare costs over their lifetimes without and with statin therapy.

Supplemental material

Cvd microsimulation model.

The CVD microsimulation model has been reported elsewhere. 10 Briefly, the model was developed using the individual participant data of large statin clinical trials, and calibrated using the UK Biobank’s participant data. The model employs a broad range of socio-demographic and clinical characteristics to project annually the first occurrence of MI, stroke, coronary revascularisation, vascular death, incident diabetes, incident cancer and non-vascular death. Participant characteristics and incident events determined health-related QoL 10 and primary care and hospital admission costs 11 in the model. The model was validated in UK Biobank and Whitehall II studies and against national data.

CVD microsimulation model validation in older people

In the present study, the model performance was further assessed among participants ≥70 years old during follow-up in the UK Biobank and Whitehall II studies using their linked electronic hospital admissions, primary care records (UK Biobank only), cancer registrations and death records to identify MIs, strokes, coronary revascularisations (UK Biobank only), incident diabetes (UK Biobank only), cancers and deaths during follow-up.

Effects and costs of statin therapy

The Cholesterol Treatment Trialists’ Collaboration (CTTC) individual participant data meta-analysis of large randomised statin trials informed the relative reductions in the risks of cardiovascular events per 1 mmol/L in LDL-C with statin therapy ( table 1 ) of 24% in MI risk, 16% in stroke, 25% in coronary revascularisation and 12% in cardiovascular death. 2 We assessed the effects of standard (eg, achieving 35%–45% LDL-C reduction: atorvastatin 20 mg/day, rosuvastatin 5–10 mg/day or simvastatin 40–80 mg/day) and higher intensity statin therapy (eg, achieving ≥45% LDL-C reduction: atorvastatin 40–80 mg/day, rosuvastatin 20–40 mg/day) ( online supplemental table 1 ). 12 The reduction in LDL-C achieved with each level of statin intensity was derived using the therapy’s proportional reduction and participant’s untreated LDL-C level (with the effects of any ongoing statin therapy removed). Meta-analyses of statin therapies informed 9% excess odds of new-onset diabetes with standard 13 and further 12% excess odds with higher intensity 14 statin therapy. An overview of cohort studies informed excess rates of myopathy (11 cases per 100 000 treated per year) and rhabdomyolysis (3.4 cases per 100 000 treated per year; 10% case fatality) with statin therapy 15 ; with myopathy and rhabdomyolysis effects on QoL informed from a modelling study. 16 Generic statin medication costs, 17 costs of consultations 18 and blood lipids tests 19 for initiation and monitoring of statin prescribing in the UK National Health Service were included ( table 1 ).

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Statin treatment effects and statin treatment costs

Cost-effectiveness of statin therapy

We employed the model to project event risks and survival and summarise life years, quality-adjusted life years (QALYs) and primary and hospital care costs over individuals’ remaining lifetimes (ie, death or 110 years of age) without and with statin therapy and to assess the cost-effectiveness of different statin therapies in categories of older individuals.

Base-case analysis

In our base-case analysis, we assessed the cost-effectiveness of lifetime statin therapy from the perspective of the UK National Health Service under a number of key assumptions based on current evidence. First, the reductions in individuals’ LDL-C levels with a particular statin therapy were assumed to correspond to the average proportional reduction achieved with the therapy. Second, we assumed that the relative effects of a particular statin therapy on event risks were independent of duration of therapy or individual person characteristics including age (ie, the overall effects reported in meta-analyses were employed). Third, disease events were assumed not to differ in severity or otherwise, irrespective of statin treatment status. Finally, statin therapy was assumed not to affect the risks of cancer or other non-vascular events, 20 nor confer any discomfort or disutility beyond the adverse events specified above.

Assessment of uncertainty

We ran 500 microsimulations per individual for each set of parameters. We summarised the parameter uncertainty, including uncertainty in effects of statin therapy on vascular and non-vascular events, all event risk equations, QoL and healthcare cost equations in the decision-analytic model using 1000 sets of parameter values, derived using a bootstrap approach, employing sampling with replacement from respective populations. 21 Values for treatment effects were sampled from lognormal distributions corresponding to the natural logarithm of relative risk reductions with statin therapy.

We report life years and QALYs gained, the additional statin and other healthcare costs (2020/2021 UK£) and the incremental costs per QALY with standard and higher-intensity statin therapies. We discounted future QALYs and costs at 3.5% per year in the summary measures for cost-effectiveness. 22 We present cost-effectiveness acceptability curves for willingness-to-pay values from £0-£40K/QALY.

Sensitivity and scenario analyses

The following parameters were varied. First, in view of the higher uncertainty in the effects of statin therapy in older people, in scenario analyses, we applied relative risk reductions in cardiovascular endpoints per 1 mmol/L LDL-C, informed from data only among: (1) people >75 years old at randomisation and (2) people >75 years old and without prior CVD at randomisation in the individual participant data meta-analysis. 2 Second, to explore sensitivity to possible double counting of statin effects in the model through its direct effect on vascular death risk and indirect effects through MI and stroke risks, we studied the impact of smaller direct relative risk reduction in cardiovascular death with statin therapy (ie, 7% instead of 12% per 1 mmol/L in LDL-C reduction). Third, to assess sensitivity to variation in major non-vascular disease risk, we ran scenario analyses with a small detrimental or beneficial statin effect on incident cancer, informed by the 95% CI limits reported in a meta-analysis of randomised statin trials. 20 Fourth, in acknowledgement of substantial rates of statin discontinuation and reinitiation, a scenario analysis assessed statin cost-effectiveness using estimated real-world compliance with statin derived from routine UK data, 23 with statin effects and costs discontinued with therapy discontinuation. Fifth, to acknowledge the uncertainty concerning any further QoL disutility from taking a daily statin pill, we included analyses with yearly disutility equal to 0.001, 0.002 or 0.005. Sixth, we present scenarios with doubled risk of non-vascular death; with lower general QoL; and both together to assess sensitivity to further reduced potential in older people to benefit from preventive treatment. We also present scenario analyses with only healthcare costs for CVD and incident diabetes included; with higher costs of statin therapy and with 1.5% discount rate for costs and outcomes.

Further details are provided in the online supplemental methods .

Patient and public involvement

Three members of the public were involved in the study management and steering groups. Study methods and results were also discussed in separate sessions with our lay members who helped us refine the study methodology and approach to presenting study findings.

The baseline characteristics of participants ≥70 years old in the UK Biobank and Whitehall II studies in categories by prior CVD are presented in table 2 and online supplemental table 2 . There were 15 019 (52% men; mean age 72.5 years) participants without CVD and 5103 (66% men; mean age 72.9 years) with history of CVD. Among participants without and with prior CVD, 29% and 58%, respectively, were prescribed a statin at baseline and the derived untreated mean LDL-C levels were 4.2 mmol/L (SD 0.78 mmol/L) and 4.3mmol/L (SD 0.98 mmol/L), respectively.

Baseline characteristics of UK Biobank and Whitehall II participants 70 years and older

In model validation, the cumulative event rates predicted by the CVD microsimulation model, using the baseline characteristics of participants ≥70 years old, corresponded mostly well to the observed rates of cardiovascular and non-vascular events in categories of participants by prior CVD, respectively, though higher MI risks, but not cardiovascular death risks, were predicted among participants with prior CVD in UK Biobank but not in Whitehall II study ( figure 1 ).

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CVD microsimulation model validation among UK Biobank and Whitehall II participants 70 years and older.In the Whitehall II study, no linked data for CRV and diabetes were available and, therefore, no model validation performed for CRV and diabetes. CRV, coronary revascularisation; CVD, cardiovascular disease; MI, myocardial infarction; NVD, nonvascular death; VD, vascular disease.

In participant categories by sex, prior CVD and LDL-C level, standard statin therapy was projected to increase individual survival (undiscounted) by 0.37 to 1.05 life years (0.24 to 0.7 QALYs), and higher intensity statin therapy by a further 0.08 to 0.21 life years (0.04 to 0.13 QALYs) ( figure 2A , online supplemental tables 3 and 4 ). Across these categories, the incremental cost per QALY gained for standard statin therapy compared with no statin ranged from £116 to £3502 and that for higher intensity compared with standard statin from £2213 to £11 778 per QALY ( figure 2B ). The analyses of parameter uncertainty indicated that at £20 000/QALY willingness to pay threshold, higher intensity statin therapy had a very high probability of being cost-effective across all categories of men and women ≥70 years old ( figure 3 ). The probability that statin therapy was cost-effective for people ≥70 years old remained high even at a cost-effectiveness threshold of £5K/QALY. However, at this lower threshold, the standard statin therapy had the highest probability of being cost-effective among women with a pretreatment LDL-C lower than 4.1 mmol/L and among men with a pretreatment LDL-C lower than 3.4 mmol/L ( figure 3 ).

Life years and QALYs gained (A) and cost-effectiveness (B) of lifetime statin therapy in categories by prior cardiovascular disease, sex and pre-treatment LDL cholesterol level. Incremental Cost-Effectiveness Ratio (ICER) is the ratio of the incremental costs divided by the incremental QALYs with costs and QALYs discounted at 3.5% per year. CVD, cardiovascular disease; LDL, low density lipoprotein; QALY, quality-adjusted life years.

Probability that lifetime statin therapy is cost-effective in categories by prior cardiovascular disease, sex and pre-treatment LDL cholesterol level. The probability that the treatment scenario provides the highest QALYs gain at the particular threshold of cost-effectiveness plotted. CVD, cardiovascular disease; LDL-C, low-density lipoprotein cholesterol; QALY, quality-adjusted life years.

These cost-effectiveness results remained robust in a wide range of sensitivity analyses ( figure 4 , online supplemental table 5 ) with higher sensitivity noted for a higher intensity statin at a five times higher price. In particular, although reduced gains in QALYs were projected, standard statin therapy remained cost-effective in people ≥70 years old if relative risk reductions after age 75 were equal to those reported in the subgroup of participants >75 years old, or indeed in the subgroup of participants >75 years old without CVD at randomisation, in the CTTC meta-analysis ( figures 4 and 5 and online supplemental figure 1 ). Higher intensity statin therapy remained cost-effective among older people with pretreatment cholesterol levels 3.4 mmol/L or higher. In these scenario analyses with lower CVD risk reductions with statin therapy, the probability of standard or higher intensity statin therapy being cost-effective remained higher than no statin therapy in all categories of older people but was substantially reduced among older women with lower LDL-C levels.

Sensitivity analyses of cost-effectiveness of statin therapy for people 70 years or older. (A) Incremental cost (£) per QALY gained (standard statin vs no statin). (B) Incremental cost (£) per QALY gained (higher intensity vs standard statin). See online supplemental methods table 7 for description of sensitivity analyses. The * on the horizontal axes represent the base-case analysis. CVD, cardiovascular disease; LDL, low-density lipoprotein; NVD, nonvascular death; QALY, quality-adjusted life year; QoL, quality of life.

Life years and QALYs gained and cost-effectiveness of lifetime statin therapy in older people: scenario analyses with CVD reductions with statin therapy in people>75 years old informed from effects of statin therapy among participants>75 years old (Scenario 1) or >75 years old without CVD (Scenario 2) from Cholesterol Treatment Trialists’ collaborative meta-analysis. Statin effects up to age 75 as in base-case analysis; statin effect thereafter as per respective scenario analysis. CVD, cardiovascular disease; ICER, Incremental Cost-Effectiveness Ratio with costs and QALYs discounted at 3.5% per year; LDL, low-density lipoprotein; QALY, quality-adjusted life year.

This assessment of the lifetime effects and cost-effectiveness of statin therapy in people ≥70 years old in the UK used contemporary patient data, a validated CVD microsimulation model and a meta-analysis of the effects of statin treatment across age categories. It concluded that lifetime statin treatment increased quality-of-life-adjusted survival in older men and women and, at UK cost of generic statins, was highly cost-effective for all, irrespective of their CVD history or LDL-C level. Higher intensity statin therapy was the strategy likely to bring the highest health benefits cost-effectively, although standard statin regimens would achieve most of these benefits. These findings remained robust in sensitivity analyses with smaller cardiovascular risk reductions with statin therapy, though smaller benefits were projected and standard statin therapy became the preferred option for older people with LDL-C levels <3.4 mmol/L.

In this analysis, we used the overall relative risk reductions in cardiovascular events per 1 mmol/L LDL-C reduction with statin therapy given the similar relative risk reductions across age categories in the individual participant meta-analysis of statin trials. 2 The meta-analysis, however, noted trends towards smaller proportional reductions in major coronary events and vascular deaths in older people. Data were particularly limited among participants >75 years old without prior CVD, where there was no direct evidence for statistically significant cardiovascular risk reductions with statin therapy. In the present report, two scenario analyses assessed the sensitivity of findings to the size of statin effects using relative risk reductions in cardiovascular events in the meta-analysis (1) among participants >75 years old, and (2) among participants >75 years old without prior CVD at randomisation. 2 In both scenarios, despite smaller net health benefits, statin therapy remained cost-effective although with larger uncertainty.

We previously reported that statin therapy, at generic prices, is highly cost-effective in UK across patients 40–70 years old irrespective of their sex, age, CVD risk and LDL-C level. 21 Here, we extend this work to older people and indicate that, although the gains in QALYs are smaller, the additional costs are also lower, and the incremental cost per QALY remains highly attractive. Moreover, with a substantially higher CVD risk (99% of ≥70 years old UK Biobank participants without prior CVD had estimated 10 year CVD risk ≥10%; and 88% had 10-year CVD risk ≥15%, data not shown), the level of risk is irrelevant in guiding statin treatment decisions in older people.

This reassessment of statins’ value in the contemporary older UK population confirms findings of earlier cost-effectiveness studies 8 9 and reaffirms that, despite substantial reductions in CVD incidence and mortality over the last decades, statins remain a cornerstone in CVD prevention in this population. Our findings differ from an earlier study of cost-effectiveness of statin therapy for the primary prevention of CVD in people ≥75 years old, which reported that, although statin treatment was highly cost-effective, even a small hypothetical increase in a geriatric-specific adverse effect (ie, reducing disability-adjusted life years by 0.003–0.004) would offset its cardiovascular benefit. 7 In our study, the known small excesses of myopathy, rhabdomyolysis and incident diabetes with statin treatment were explicitly integrated, and our findings remained robust to hypothetical further statin-associated reductions in QoL up to 0.005 QALY/ year and to lower statin efficacy, suggesting that the value of statin therapy for older people is more certain than implied. It is important to also underline that high-quality randomised evidence indicate that the vast majority of adverse effects reported on statin therapy were also reported in the absence of statin therapy, 24 25 indicating serious misattribution of adverse effects in observational and uncontrolled studies.

Our results indicate that older people are likely to cost-effectively benefit from statin treatment. Statin treatment rates in our ≥70 years old cohort (29% among people without CVD to 58% among people with prior CVD) were similar to statin treatment rates reported by the Health Survey for England. 26 Hence, from the 9.1 million adults ≥70 years old in UK, 27 a third of them with prior CVD, 26 just over 40%, or less than 4 million, are receiving statin treatment. While further evidence for statins effects in older people will be helpful, the robustness of the findings to variations in key parameters suggests that delaying statin treatment in the millions of older people while awaiting new evidence is unjustifiable.

Our study has a number of strengths. We used a contemporary UK CVD model, developed using a large and rich population biobank with demonstrable ability to predict cardiovascular and mortality risks in older people. We used the baseline characteristics of more than 20 000 people ≥70 years old to evaluate lifetime benefits and cost-effectiveness of statin therapy. A further strength of our analysis is the use of synthesised randomised evidence for the effects of statin therapy by age that allowed us to study the robustness of our findings to somewhat smaller reductions in cardiovascular risks in older people. Finally, the reported excesses in myopathy, rhabdomyolysis and incident diabetes with standard and higher intensity statin therapy were integrated allowing the net effects of treatment to be fully assessed.

The study has some limitations. First, the majority of our data is among people aged 70 to early 80s. Our findings, however, were very similar in participants 70–75 and ≥75 years old (results not shown), which suggest that they are generalisable to much older people. Second, our model and results are based on population cohorts, in which the healthy volunteer effect may limit generalisability. To address this limitation, the model used a broad range of socioeconomic, lifestyle and clinical characteristics that allow generalisations to populations with different distributions of these characteristics. Moreover, statin therapy remained cost-effective in scenario analyses with substantially higher risk of non-vascular death and lower QoL. Third, a small excess in milder muscle symptoms was recently reported with statin treatment across randomised studies with excess confined to the first year of treatment. 28 The sensitivity analyses suggest that this adverse effect is unlikely to materially alter statin’s cost-effectiveness. Fourth, two ongoing large statin trials, scheduled to complete in 2026, will add valuable further data to the direct evidence of effects of statin therapy in people aged ≥75 years without atherosclerotic CVD. 29 30 Fifth, missing baseline data were imputed using a single imputation. Moreover, while the model performance was good for most participant categories, endpoints and across the two datasets, there were some deviations. Therefore, it is possible that the uncertainty may be larger than reported by the model. However, the consistency of cost-effectiveness results across categories of participants and across a broad range of sensitivity analyses for key parameters indicate that our general findings are robust.

In conclusion, this study reports that statin therapy is highly likely to be cost-effective in older people, although there was greater uncertainty among older people without CVD in scenario analysis with substantially smaller CVD risk reductions with statin therapy. While further randomised evidence will be helpful, the robustness of these findings indicates that older people are likely to benefit cost-effectively from statin therapy and should be considered for treatment.

Ethics statements

Patient consent for publication.

Not applicable.

Ethics approval

This work used data of participants in research studies (UK Biobank, Whitehall II) who have consented to collection and use of their data for research. Ethics committee approval was not required for this secondary research study. Participants gave informed consent to participate in the study before taking part.

Acknowledgments

This research has been conducted using data from Cholesterol Treatment Trialists’ Collaboration https://www.cttcollaboration.org/ , UK Biobank Resource under Application Number 56757 www.ukbiobank.ac.uk , and Whitehall II study www.ucl.ac.uk/epidemiology-health-care/research/epidemiology-and-public-health/research/whitehall-ii . We thank all the participants, staff and other contributors to these resources. Project Oversight Group: Colin Baigent, Alison Gater, Borislava Mihaylova, Stephen Morris, Paul Roderick (Chair), Natalie Rowland, Peter Sever, Liam Smeeth. We also thank further members of the public with whom we discussed the project and emerging results.

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Supplementary materials

Supplementary data.

This web only file has been produced by the BMJ Publishing Group from an electronic file supplied by the author(s) and has not been edited for content.

• Data supplement 1

BM and RW are joint first authors.

Correction notice This article has been corrected since it was first published. Missing panel and axes titles have been added to Figure 1.

Collaborators Cholesterol Treatment Trialists’ Collaborators: CTT secretariat: J Armitage, C Baigent, E Barnes, L Blackwell, R Collins, K Davies, J Emberson, J Fulcher, H Halls, WG Herrington, L Holland, A Keech, A Kirby, B Mihaylova, R O’Connell, D Preiss, C Reith, J Simes, K Wilson. CTT Collaborating trialists: A to Z trial (phase Z): M Blazing, E Braunwald, J de Lemos, S Murphy; TR Pedersen, M Pfeffer, H White, S Wiviott; AFCAPS/TEXCAPS (AirForce/Texas Coronary Atherosclerosis Prevention Study) M Clearfield, JR Downs, A Gotto Jr, S Weis; ALERT (Assessment of Lescol in Renal Transplantation) B Fellström, H Holdaas (deceased), A Jardine, TR Pedersen; ALLHAT (Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial) D Gordon, B Davis; C Furberg, R Grimm, S Pressel, JL Probstfield, M Rahman, L Simpson; ALLIANCE (Aggressive Lipid-Lowering Initiation Abates New Cardiac Events) M Koren; ASCOT (Anglo-Scandinavian Cardiac Outcomes Trial) B Dahlöf, A Gupta, N Poulter, P Sever, H Wedel; ASPEN (Atorvastatin Study for the Prevention of Coronary Heart Disease Endpoints in Non-Insulin Dependent Diabetes Mellitus) RH Knopp (deceased); AURORA (A study to evaluate the Use of Rosuvastatin in subjects On Regular haemodialysis: an Assessment of survival and cardiovascular events) S Cobbe, B Fellström, H Holdaas (deceased), A Jardine, R Schmieder, F Zannad; CARDS (Collaborative Atorvastatin Diabetes Study) DJ Betteridge (deceased), HM Colhoun, PN Durrington, J Fuller (deceased), GA Hitman, A Neil; CARE (Cholesterol And Recurrent Events Study) E Braunwald, B Davis, CM Hawkins, L Moyé, M Pfeffer, F Sacks; CORONA (Controlled Rosuvastatin Multinational Trial in Heart Failure) J Kjekshus, H Wedel, J Wikstrand; 4D (Die Deutsche Diabetes Dialyse Studie): C Wanner, V Krane; GISSI (Gruppo Italiano per lo Studio della Sopravvivenza nell’Infarto miocardico) Heart Failure and Prevention trials: MG Franzosi, R Latini, D Lucci, A Maggioni;, R Marchioli, EB Nicolis, L Tavazzi, G Tognoni; HOPE-3: J Bosch, E Lonn, S Yusuf; HPS (Heart Protection Study): J Armitage, L Bowman, R Collins, A Keech, M Landray, S Parish, R Peto, P Sleight (deceased); IDEAL (Incremental Decrease in Endpoints through Aggressive Lipid-lowering) JJP Kastelein, TR Pedersen; JUPITER (Justification for the Use of Statins in Prevention: an Intervention Trial Evaluating Rosuvastatin) R Glynn, A Gotto Jr, JJP Kastelein, W Koenig, J MacFadyen, PM Ridker; LIPID (Long-term Intervention with Pravastatin in Ischaemic Disease) A Keech, S MacMahon, I Marschner, A Tonkin, J Shaw (deceased), J Simes, H White; LIPS (Lescol Intervention Prevention Study) PW Serruys; Post-CABG (Post-Coronary Artery Bypass Graft Study) G Knatterud (deceased); PROSPER (Prospective Study of Pravastatin in the Elderly at Risk) GJ Blauw, S Cobbe, I Ford, P Macfarlane, C Packard, N Sattar, J Shepherd (deceased), S Trompet; PROVE-IT (Pravastatin or Atorvastatin Evaluation and Infection Therapy) E Braunwald, CP Cannon, S Murphy; SEARCH (Study of Effectiveness of Additional Reductions in Cholesterol and Homocysteine): R Collins, J Armitage, L Bowman, R Bulbulia, R Haynes, S Parish, R Peto, P Sleight (deceased); SPARCL (Stroke Prevention by Aggressive Reduction in Cholesterol Levels): P Amarenco, KM Welch; (4S Scandinavian Simvastatin Survival Study) J Kjekshus, TR Pedersen, L Wilhelmsen; TNT (Treating to New Targets) P Barter, A Gotto Jr, J LaRosa, JJP Kastelein, J Shepherd (deceased); WOSCOPS (West of Scotland Coronary Prevention Study) S Cobbe, I Ford, S Kean, P Macfarlane, C Packard, M Roberston, N Sattar, J Shepherd (deceased), R Young, Other CTT Members: H Arashi, R Clarke, M Flather, S Goto, U Goldbourt, J Hopewell, GK Hovingh, G Kitas, C Newman, MS Sabatine, GG Schwartz, L Smeeth, J Tobert, J Varigos, J Yamamguchi.

Contributors BM and CB conceived the study. BM, IS, JE, CR, JR, AG, JA, CB secured funding. All authors contributed to study design. BM, RW, JZ, CW, IS performed the analyses. BM drafted the paper with support from RW. All authors provided comments on the paper. BM acts as guarantor. The corresponding author attests that all listed authors meet authorship criteria and that no others meeting the criteria have been omitted.

Funding This study was funded by the UK NIHR Health Technology Assessment (HTA) Programme (17/140/02). Further support from the British Heart Foundation (PG/18/16/33570 and CH/1996001/9454), the UK Medical Research Council (MC_UU_00017/4), the National Institute for Health Research Barts Biomedical Research Centre (NIHR203330) and NHMRC, Australia is acknowledged. The study was designed and analysed independently of all funders and the views expressed are those of the authors and not necessarily those of the NIHR, the Department of Health and Social Care or any other funder. For the purpose of Open Access, the author has applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission.

Competing interests AK reports research support from Abbott, Amgen, ASPEN, Bayer, Mylan, Novartis, Sanofi, Viatris; speaker fees from Novartis; and is a Data Safety Monitoring Board member for Kowa. JR reports funding from North East London Integrated Care Service. JA reports receiving a grant to their research institution from Novartis for the ORION 4 trial of inclisiran. JS reports receiving grants for his institution from Amgen, Bayer, BMS, MSD, Pfizer and Roche; consulting fees from FivepHusion, and is a chair (unpaid) of STAREE DSMB. CB reports research grants from Boehringer Ingelheim and Health Data Research UK and is a chair (unpaid) of a Data Safety Monitoring Board for Merck. All other authors declare no competing interests.

Patient and public involvement Patients and/or the public were involved in the design, or conduct, or reporting, or dissemination plans of this research. Refer to the Methods section for further details.

Provenance and peer review Not commissioned; externally peer-reviewed.

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