Institute of Medical Biometry and Epidemiology, University Medical Center Hamburg-Eppendorf, Martinistraße 52, Hamburg, 20246, Germany.
Charité - Universitätsmedizin Berlin, corporate member of Freie Universität Berlin, Humboldt-Universität zu Berlin, Institute of Biometry and Clinical Epidemiology, Charitéplatz 1, Berlin, 10117, Germany.
BMC Med Res Methodol. 2022 Feb 5;22(1):38. doi: 10.1186/s12874-022-01511-1.
In 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.
Within 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.
For 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.
The 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.
在临床试验中，研究兴趣通常在于比较治疗组与对照组的时间事件终点。复合终点可以同时考虑多个时间事件终点。通常，仅对患者的第一个发生事件的时间进行分析。然而，一个人可能会经历不止一次非致命事件。将所有观察到的事件纳入分析可以提高统计效能，并更全面地了解疾病。因此，需要使用分析复发性事件的方法。一个挑战是，属于复合终点的不同事件类型通常具有不同的临床相关性。在这种情况下，根据其临床相关性对事件类型进行加权是一种选择。已经提出了用于复合时间事件终点的不同基于权重的方法。到目前为止，这些方法之间还没有进行系统的比较。
在这项工作中，我们在考虑非致命和致命事件具有不同临床相关性的复发性事件背景下，对三种用于加权复合终点的方法进行了系统比较。我们考虑了 Wei 和 Lachin 提出的方法的扩展、Rauch 等人提出的方法和 Bakal 等人提出的方法。比较是基于模拟研究和临床研究示例进行的。
对于所有三种方法，都有封闭公式的检验统计量。Wei-Lachin 方法和 Rauch 等人的方法在均方误差方面表现相似。对于 Wei 和 Lachin 的方法，提供了置信区间。Bakal 等人的方法与可量化的估计量无关。不同方法的相关权重作用于不同的水平，即因果风险比或事件计数。
提供的比较和模拟可以帮助指导应用研究人员选择适当的方法来分析具有不同临床相关性的（复发性）事件的复合终点。当复合效应与时间无关时，推荐使用 Wei 和 Lachin 以及 Rauch 等人的方法。Bakal 等人的方法应谨慎使用。
