A nonparametric analysis of waiting times from a multistate model using a novel linear hazards model approach

Abstract

Traditional methods for the analysis of failure time data are often employed in the analysis of waiting times of transient states from multistate models. However, such methods can exhibit bias when waiting times among model states are dependent, even when censoring is random. Furthermore, right-censoring can occur prior to entry into the transient state of interest, preventing the observation of transitions from the state and providing another potential source of bias. We introduce a nonparametric linear hazards model for waiting times from multistate models, analogous to Aalen’s linear hazards model for failure time data, where proper estimation can be carried out via reweighting, a method flexible enough to incorporate general forms of induced and other dependent censoring. We illustrate the approximate unbiasedness of the proposed regression coefficient estimators through a simulation study, while also demonstrating the bias arising from traditional Aalen’s linear hazards model estimators obtained from correlated waiting time data. Theoretical results for the parameter estimators are provided. The reweighted estimators are used in the analysis of two data sets, to identify predictors of ambulatory recovery in a data set of spinal cord injury patients receiving activity-based rehabilitation and to identify prognostic indicators for patients receiving bone marrow transplant.