Robust inference for multivariate survival data

Multivariate survival data arise when an individual records multiple survival events or when individuals recording single survival events are grouped into clusters. In this paper we propose a new method for the analysis of multivariate survival data. The technique is a synthesis of the Poisson regression formulation for univariate censored survival analysis and the generalized estimating equation approach for obtaining valid variance estimates for generalized linear models in the presence of clustering. When the survival data are clustered, combining the methods provides not only valid estimates for the variances of regression parameters but also estimates of the dependence between survival times. The approach entails specifying parametric models for the marginal hazards and a dependence structure, but does not require specification of the joint multivariate survival distribution. Properties of the methodology are investigated by simulation and through an illustrative example.