Bootstrap analysis of multivariate failure time data.

Multivariate failure time data often arise in research. Cox proportional hazards modelling is a widely used method of analysing failure time data for independent observations. However, when failure times are correlated the Cox proportional hazards model does not yield valid estimates of standard errors or significance tests. Many methods for the analysis of multivariate failure time data have been proposed. These methods commonly test hypotheses about the regression parameters, a practice which averages the treatment effect across time. The purpose of this paper is to examine the bootstrap method for obtaining standard errors in the multivariate failure time case, particularly when the focus is the survival probability or the treatment effect at a single time point such as in a surgical trial. Our motivating example comes from the Asymptomatic Carotid and Atherosclerosis Study (ACAS) in which the outcome of stroke or perioperative complications could be observed for either or both carotid arteries within each patient. Extensive simulation studies were conducted to examine the bootstrap procedure for analysing correlated failure time data under a variety of conditions including a range of treatment effects, cluster sizes, intercluster correlation values and for both proportional and non-proportional data. We found that the bootstrap method was able to estimate the standard error adequately for survival probabilities at a specific time and the standard error for the survival difference and the relative risk at a specific time. We illustrated the bootstrap method for calculating the standard error for the survival probability and statistical testing at a specific time value by analysing the two arteries per patient from the ACAS study.