Application of the Wei-Lachin multivariate one-directional test to multiple event-time outcomes.

Abstract

Cardiovascular outcome trials, among others, aim to assess the beneficial effects of a treatment on multiple event-time outcomes, such as the time to a myocardial infarction and the time to a stroke. The traditional approach is to conduct a simple analysis of a composite outcome defined as the time to the first component event using a logrank test or the Cox Proportional Hazards regression model. This ignores information from other component events after the first. The composite outcome analysis also treats all initial outcome events as equally important, for example, non-fatal myocardial infarction is as important as cardiovascular death. Herein, we describe the application of the Wei-Lachin multivariate one-sided (or one-directional) test to the analysis of multiple event-time outcomes. The test is based on the unweighted mean of the treatment group coefficients from individual Cox proportional hazards models fit to the outcomes, where the covariance of the set of coefficients is obtained from a partitioning of the information sandwich estimate. A weighted test is also described, weighing the outcomes by a scoring of their clinical importance. These and other methods are compared with application to the Prevention of Events with Angiotensin-Converting Enzyme Inhibition cardiovascular outcome study. The Wei-Lachin test provides an inference with strong control of the type 1 error probability on the difference between groups for the set of outcomes considered. However, it does not provide an inference on the individual components specifically with control of the overall type 1 error probability. By direct computation of relative efficiency and by simulation, we show that the power of the Wei-Lachin one-directional test can be greater than that of the traditional composite outcome analysis based on the time to the first observed component event. The Wei-Lachin multivariate one-directional test may be more powerful than the traditional analysis of a composite outcome defined as the time to the first component outcomes experienced by each subject.