Semiparametric inference for the proportional mean residual life model with right-censored length-biased data

We propose a semiparametric inference approach for proportional mean residual life model with right-censored length-biased data, that arise frequently in observational studies, especially in epidemiological cohort studies. A challenge in the analysis of such data is the presence of informative censoring. Another challenge is that the distribution of the observed data is different from that of the underlying model. We develop an inverse probability weighted approach to estimation based on estimating equations. We establish large sample properties and study the semiparametric efficiency and double robustness property of the proposed estimators. We also propose an improved estimator that chooses the most efficient one in the class of augmented inverse probability weighted estimators. We use simulation studies to evaluate the proposed method, and illustrate its application using a data analysis.