Statistical methods for multivariate survival data

Multivariate survival analysis involves the study of failure times, including the influence of covariates, in the presence of dependence. A general method for constructing multivariate distributions, which allows for a different association parameter for each pair of variables, is used to specify multivariate survivor functions with specific univariate marginal survival functions. A particular form of the multivariate survivor function is applied to data from a toxicological study to make inferences about effects of treatments and other explanatory variables on three development times monitored on each animal in the study. Likelihood based inferences for the regression coefficients, using marginal proportional hazards models, and for the parameters governing the associations are considered for this fully parametric model.;This method of construction also provides a convenient way to simulate data for multivariate survival distributions with specific univariate margins. A simple algorithm is presented. This provides a valuable method for performing simulation studies to examine the efficiency and accuracy of various estimation methods for multivariate survival data.;In the presence of associations among survival times, it is usually difficult to identify an appropriate model for a multivariate survival data set. When inferences about marginal parameters are of primary interest, methods that do not require complete specification of the joint survival function can be used. These methods, independent marginal models and a semi-parametric approach using a robust covariance estimator, ignore dependence among survival times and estimate marginal parameters using marginal likelihood functions. These estimation methods are easier to apply than joint parametric methods, but they ignore associations among survival times and the resulting estimators are generally not efficient. The loss of efficiency depends on the levels of the associations among the survival times, the sample size, and the type of parameters. For the regression parameters in the Weibull regression model considered in Chapter 4, these losses are observed to be as large as 63% in cases involving moderately strong associations relative to maximum likelihood estimates computed from the true joint likelihood. In the two weak association cases where values of the Kendall Tau rank correlation coefficients are all less than 0.15, the loss of efficiency is less than 3% even for sample sizes as large as 512.;In the presence of weak association among survival times, tests of equal treatment effects based on the fully parametric model and the semi-parametric model with the robust covariance matrix provide almost the same power. For higher levels of association and larger sample sizes, tests of equal treatment effects based on the parametric model can have substantially greater power than tests based on the semi-parametric model.