ABSTRACT
This chapter considers semiparametric Cox-type regression models for each of the hazard rates in, and a plug-in estimating equation approach for parameter estimation. In contrast, nearly all of the multivariate failure time literature uses a likelihood-based approach for regression modeling and estimation. Ross L. Prentice and Hsu consider a mean and covariance parameter estimating equation approach for marginal hazard ratio and corresponding dependency parameters. Specifically Cox model estimating equations, expressed in terms of marginal martingales as in, were considered for two or more failure time variates. The elements of these equations were weighted according to the inverse of the estimated covariance matrix for the set of marginal martingales for each study subject, with a corresponding set of unbiased estimating equations for marginal martingale covariance parameters. Simulation studies under pairwise Clayton–Oakes models indicated that the estimated cross ratio parameters approximately target an average cross ratio value over the study follow-up period, under departure from a cross ratio model that is time-independent.
