Marginal and Conditional Models for the Analysis of Multivariate Failure Time Data

Abstract

Failure time problems are considered in which individual study subjects may experience multiple failures, or in which failure times among study subjects in the same ‘block’ may be dependent. Overall intensity process models, which describe the failure rate for a subject as a function of the preceding failure experience of the entire sample, are briefly reviewed and critiqued. Frailty models, on the other hand, presume failure times in a block to be independent given a multiplicative random effect, or frailty, for the block. Hence parameters in these models have a marginal interpretation given their hypothetical frailty value. An alternative attractive approach involves the direct modeling and estimation of marginal hazard functions and corresponding covariance functions. Though related work is very recent and somewhat preliminary, the approach appears to hold considerable promise for the development of flexible and interpretable regression methods for multivariate failure time data.