The Use of a Binary Composite Endpoint and Sample Size Requirement: Influence of Endpoints Overlap

Applying Exercise Capacity and Physical Activity as Single vs Composite Endpoints for Trials of Cardiac Rehabilitation Interventions: Rationale, Use-case, and a Blueprint Method for Sample Size Calculation

OBJECTIVE

To conceptualize a composite primary endpoint for parallel-group RCTs of exercise-based cardiac rehabilitation (CR) interventions and to explore its application and statistical efficiency.

DESIGN

We conducted a statistical exploration of sample size requirements. We combined exercise capacity and physical activity for the composite endpoint (CE), both being directly related to reduced premature mortality in patients with cardiac diseases. Based on smallest detectable and minimal clinically important changes (change in exercise capacity of 15 W and change in physical activity of 10 min/day), the CE combines 2 dichotomous endpoints (achieved/not achieved). To examine statistical efficiency, we compared sample size requirements based on the CE to single endpoints using data from 2 completed CR trials.

SETTING

Cardiac rehabilitation phase III.

PARTICIPANTS

Patients in cardiac rehabilitation.

INTERVENTIONS

Not applicable.

MAIN OUTCOME MEASURE(S)

Exercise capacity (Pmax assessed by incremental cycle ergometry) and physical activity (daily minutes of moderate to vigorous physical activity assessed by accelerometry).

RESULTS

Expecting, for example, a 10% between-group difference and improvement in the clinical outcome, the CE would increase sample size by up to 21% or 61%, depending on the dataset. When expecting a 10% difference and designing an intervention with the aim of non-deterioration, the CE would allow to reduce the sample size by up to 55% or 70%.

CONCLUSIONS

Trialists may consider the utility of the CE for future studies in exercise-based CR to reduce sample size requirements. However, perhaps surprisingly at first, the CE could also lead to an increased sample size needed, depending on the observed baseline proportions in the trial population and the aim of the intervention.

Progression-free survival, disease-free survival and other composite end points in oncology: improved reporting is needed

Composite outcome measures such as progression-free survival and disease-free survival are increasingly used as surrogate end points in oncology research, frequently serving as the primary end point of pivotal trials that form the basis for FDA and EMA approvals. Such outcome measures combine two or more distinct events (for example, tumour (re)growth, new lesions and/or death) into a single, time-to-event end point. The use of a composite end point can increase the statistical power of a clinical trial and decrease the follow-up period required to demonstrate efficacy, thus lowering costs; however, these end points have a number of limitations. Composite outcomes are often vaguely defined, with definitions that vary greatly between studies, complicating comparisons of results across trials. Altering the makeup of events included in a composite outcome can alter study conclusions, including whether treatment effects are statistically significant. Moreover, the events included in a composite outcome often vary in clinical significance, reflect distinct biological pathways and/or are affected differently by treatment. Therefore, knowing the precise breakdown of the component events is essential to accurately interpret trial results and gauge the true benefit of an intervention. In oncology clinical trials, however, such information is rarely provided. In this Perspective, we emphasize this deficiency through a review of 50 studies with progression-free survival as an outcome published in five top oncology journals, discuss the advantages and challenges of using composite end points, and highlight the need for transparent reporting of the component events.

Sample size requirement in trials that use the composite endpoint major adverse cardiovascular events (MACE): new insights

BACKGROUND

The real impact of the degree of association (DoA) between endpoint components of a composite endpoint (CE) on sample size requirement (SSR) has not been explored. We estimate the impact of the DoA between death and acute myocardial infarction (AMI) on SSR of trials using use the CE of major adverse cardiac events (MACE).

METHODS

A systematic review and quantitative synthesis of trials that include MACE as the primary outcome through search strategies in MEDLINE and EMBASE electronic databases. We limited to articles published in journals indexed in the first quartile of the Cardiac & Cardiovascular Systems category (Journal Citation Reports, 2015-2020). The authors were contacted to estimate the DoA between death and AMI using joint probability and correlation. We analyzed the SSR variation using the DoA estimated from RCTs.

RESULTS

Sixty-three of 134 publications that reported event rates and the therapy effect in all component endpoints were included in the quantitative synthesis. The most frequent combination was death, AMI, and revascularization (n = 20; 31.8%). The correlation between death and AMI, estimated from 5 trials¸ oscillated between - 0.02 and 0.31. SSR varied from 14,602 in the scenario with the strongest correlation to 12,259 in the scenario with the weakest correlation; the relative impact was 16%.

CONCLUSIONS

The DoA between death and AMI is highly variable and may lead to a considerable SSR variation in a trial including MACE.

Sample size estimation using a latent variable model for mixed outcome co-primary, multiple primary and composite endpoints

Mixed outcome endpoints that combine multiple continuous and discrete components are often employed as primary outcome measures in clinical trials. These may be in the form of co-primary endpoints, which conclude effectiveness overall if an effect occurs in all of the components, or multiple primary endpoints, which require an effect in at least one of the components. Alternatively, they may be combined to form composite endpoints, which reduce the outcomes to a one-dimensional endpoint. There are many advantages to joint modeling the individual outcomes, however in order to do this in practice we require techniques for sample size estimation. In this article we show how the latent variable model can be used to estimate the joint endpoints and propose hypotheses, power calculations and sample size estimation methods for each. We illustrate the techniques using a numerical example based on a four-dimensional endpoint and find that the sample size required for the co-primary endpoint is larger than that required for the individual endpoint with the smallest effect size. Conversely, the sample size required in the multiple primary case is similar to that needed for the outcome with the largest effect size. We show that the empirical power is achieved for each endpoint and that the FWER can be sufficiently controlled using a Bonferroni correction if the correlations between endpoints are less than 0.5. Otherwise, less conservative adjustments may be needed. We further illustrate empirically the efficiency gains that may be achieved in the composite endpoint setting.

A new approach for sizing trials with composite binary endpoints using anticipated marginal values and accounting for the correlation between components

Composite binary endpoints are increasingly used as primary endpoints in clinical trials. When designing a trial, it is crucial to determine the appropriate sample size for testing the statistical differences between treatment groups for the primary endpoint. As shown in this work, when using a composite binary endpoint to size a trial, one needs to specify the event rates and the effect sizes of the composite components as well as the correlation between them. In practice, the marginal parameters of the components can be obtained from previous studies or pilot trials; however, the correlation is often not previously reported and thus usually unknown. We first show that the sample size for composite binary endpoints is strongly dependent on the correlation and, second, that slight deviations in the prior information on the marginal parameters may result in underpowered trials for achieving the study objectives at a pre-specified significance level. We propose a general strategy for calculating the required sample size when the correlation is not specified and accounting for uncertainty in the marginal parameter values. We present the web platform CompARE to characterize composite endpoints and to calculate the sample size just as we propose in this paper. We evaluate the performance of the proposal with a simulation study and illustrate it by means of a real case study using CompARE.

Bin-CE: A comprehensive web application to decide upon the best set of outcomes to be combined in a binary composite endpoint

The estimation of the Sample Size Requirement (SSR) when using a binary composite endpoint (i.e. two or more outcomes combined in a unique primary endpoint) is not trivial. Besides information about the rate of events for each outcome, information about the strength of association between the outcomes is crucial, since it can determine an increase or decrease of the SSR. Specifically, the greater the strength of association between outcomes the higher the SSR. We present Bin-CE, a free tool to assist clinicians for computing the SSR for binary composite endpoints. In a first step, the user enters a set of candidate outcomes, the assumed rate of events for each outcome and the assumed effect of therapy on each outcome. Since the strength of the association between outcomes is usually unknown, a semi-parametric approach linking the a priori clinical knowledge of the potential degree of association between outcomes with the exact values of these parameters was programmed with Bin-CE. Bin-CE works with a recursive algorithm to choose the best combination of outcomes that minimizes the SSR. In addition, Bin-CE computes the sample size using different algorithms and shows different figures plotting the magnitude of the sample size reduction, and the effect of different combinations of outcomes on the rate of the primary endpoint. Finally, Bin-CE is programmed to perform sensitivity analyses. This manuscript presents the mathematic bases and introduces the reader to the use of Bin-CE using a real example.