Density ratio model for multiple types of survival data with empirical likelihood

Abstract The density ratio model (DRM) is a semiparametric model that relates the distributions from multiple samples to a nonparametrically defined reference distribution via exponential tilting, with finite‐dimensional parameters governing their differences in shape. When multiple types of partially observed (censored/truncated) failure time data are collected in an observational study, the DRM can be utilized to conduct a single unified analysis of the combined data. In this paper, we extend the methodology for censored length‐biased/truncated data to the DRM framework and formulate the inference using empirical likelihood. We develop an EM algorithm to compute the DRM‐based maximum empirical likelihood estimators of the model parameters and survival function, and assess its performance through extensive simulations under correct model specification, overspecification, and misspecification, across a range of failure‐time distributions and censoring proportions. We also illustrate the efficacy of our method by analyzing the duration of time spent from admission to discharge in a Montreal‐area hospital in Canada. The R code that implements our method is available on GitHub at DRM‐combined‐survival .