Bootstrap analysis of multivariate failure-time data

Multivariate failure times occur when more than one event can occur per experimental unit. Marginal models (Lee, Wei and Amato (1992), Wei, Lin and Weissfeld (1989)) have been proposed for the analysis of correlated failure-time data. We used marginal models to analyze correlated failure-time data and investigated the bootstrap method for calculating the standard error for several quantities including the survival probability at a particular time, the survival difference at a particular time and the log-rank statistic. The existing methods for calculating the variance for these multivariate statistics are difficult. The bootstrap method is a well-known flexible method whose properties have not been investigated with multivariate survival data.; The bootstrap method was adequately able to estimate the standard error for these quantities for sufficient sample size across a range of within cluster correlations, censoring, treatment effects and for both proportional and non-proportional hazards. The asymptotic approximation (Spiekerman and Lin (1998)) and the bootstrap method gave similar results. Valid results were obtained with as few as 50 bootstrap samples. The bootstrap method is easy to program and well adapted to available high-speed computers.; The Asymptomatic Carotid Atherosclerosis Study was our motivating example. The ACAS study was a randomized clinical trial designed to determine if the addition of carotid endarterectomy to standard therapy would reduce the risk of cerebral infarction on the side of surgical intervention among patients with asymptomatic carotid stenosis. Our reanalysis using two arteries per patient with the bootstrap method for calculation of standard errors showed the same results as the original analysis with those arteries receiving surgical intervention having significantly reduced risk of stroke at five years. We also investigated the relationship between asymptomatic carotid artery stenosis and stroke using two arteries per patient. Arteries with asymptomatic carotid artery stenosis greater than 60% (with the exception of those with occlusion) had a significantly greater risk of stroke at five years compared with those with less than 60% stenosis.; The bootstrap method was shown to be a powerful and straightforward method for the analysis of multivariate failure-time data.