Exponential decay for binary time-varying covariates in Cox models

Cox models are commonly used in the analysis of time to event data. One advantage of Cox models is the ability to include time-varying covariates, often a binary covariate that codes for the occurrence of an event that affects an individual subject. A common assumption in this case is that the effect of the event on the outcome of interest is constant and permanent for each subject. In this paper, we propose a modification to the Cox model to allow the influence of an event to exponentially decay over time. Methods for generating data using the inverse cumulative density function for the proposed model are developed. Likelihood ratio tests and AIC are investigated as methods for comparing the proposed model to the commonly used permanent exposure model. A simulation study is performed, and 3 different data sets are presented as examples.