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

Abstract

Publisher Summary This chapter addresses the survival function estimation in a general data structure that includes time independent and/or dependent covariate processes that are subject to right censoring. It describes the methods to estimate the censoring mechanism in a way that allows dependent censoring and reviews a general methodology of constructing mappings from full data estimating functions to observed data estimating functions along with a new way of obtaining such mappings by using the influence curve of a given regular asymptotically linear (RAL) estimator. RAL is a powerful method, and its application in general bivariate right censored data structure resulted in a generalized estimator of Dabrowska's estimator. This proposed generalized estimator overcomes the deficiencies of the commonly used Dabrowska's estimator by allowing informative censoring and incorporating covariate processes. An orthogonalized estimating function and its corresponding estimator are discussed along with a demonstration of the practical performances of the proposed estimators with a simulation study.