Weighted composite time to event endpoints with recurrent events: comparison of three analytical approaches

Ann-Kathrin Ozga,Geraldine Rauch

doi:10.1186/s12874-022-01511-1

Abstract

BackgroundIn clinical trials the study interest often lies in the comparison of a treatment to a control regarding a time to event endpoint. A composite endpoint allows to consider several time to event endpoints at once. Usually, only the time to the first occurring event for a patient is thereby analyzed. However, an individual may experience more than one non-fatal event. Including all observed events in the analysis can increase the power and provides a more complete picture of the disease. Thus, analytical methods for recurrent events are required. A challenge is that the different event types belonging to the composite often are of different clinical relevance. In this case, weighting the event types according to their clinical relevance is an option. Different weight-based methods for composite time to event endpoints were proposed. So far, there exists no systematic comparison of these methods.MethodsWithin this work we provide a systematic comparison of three methods proposed for weighted composite endpoints in a recurrent event setting combining non-fatal and fatal events of different clinical relevance. We consider an extension of an approach proposed by Wei and Lachin, an approach by Rauch et al., and an approach by Bakal et al.. Comparison is done based on a simulation study and based on a clinical study example.ResultsFor all three approaches closed formula test statistics are available. The Wei-Lachin approach and the approach by Rauch et al. show similar results in mean squared error. For the approach by Wei and Lachin confidence intervals are provided. The approach by Bakal et al. is not related to a quantifiable estimand. The relevance weights of the different approaches work on different level, i.e. either on cause-specific hazard ratios or on event count.ConclusionThe provided comparison and simulations can help to guide applied researchers to choose an adequate method for the analysis of composite endpoints combining (recurrent) events of different clinical relevance. The approach by Wei and Lachin and Rauch et al. can be recommended in scenarios where the composite effect is time-independent. The approach by Bakal et al. should be applied carefully.

Highlights

In clinical trials the study interest often lies in the comparison of a treatment to a control regarding a time to event endpoint
The common idea of these approaches is that a relevance weight is assigned to each event type with the aim to make the comparison between different events more fair
We start by looking at the estimands, estimator, and corresponding root mean squared error for the Wei-Lachin approach and the approach by Rauch et al since the deviation from the true simulated values is of primary interest

Summary

Introduction

In clinical trials the study interest often lies in the comparison of a treatment to a control regarding a time to event endpoint. Including only one of those event types can result in a large number of patients that need to be observed to gain an effect with sufficient power To overcome this issue and decrease the required sample size, composite endpoints can be considered alternatively [1, 2]. Cox proportional hazards based models were introduced for the analysis of recurrent time to events like the Andersen-Gill model [4], the marginal model by Wei, Lin and Weissfeld [5], and conditional models by Prentice, Williams and Peterson [6] In those models only one event type is considered and when applied to a composite endpoint, it is implicitly assumed that a myocardial infarction has the same clinical relevance as death and the treatment effect is the same in both endpoints [7]. Most of these weighted approaches were only described for the time to first event endpoint analysis

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Discussion

Conclusion