Estimation of the Bivariate Survival Function with Generalized Bivariate Right Censored Data Structures

Sunduz Keles, Department of Statistics, University of Wisconsin, Madison
Mark J. van der Laan, Division of Biostatistics, School of Public Health, University of California, Berkeley
James M. Robins, Department of Epidemiology, Harvard School of Public Health

Abstract

We propose a bivariate survival function estimator for a general right censored data structure that includes a time dependent covariate process. Firstly, an initial estimator that generalizes Dabrowska's (1988) estimator is introduced. We obtain this estimator by a general methodology of constructing estimating functions in censored data models. The initial estimator is guaranteed to improve on Dabrowska's estimator and remains consistent and asymptotically linear under informative censoring schemes if the censoring mechanism is estimated consistently. We then construct an orthogonalized estimating function which results in a more robust and efficient estimator than our initial estimator. A simulation study demonstrates the performance of the proposed estimators.