Mean residual life cure models for right-censored data with and without length-biased sampling

We propose a semiparametric mean residual life mixture cure model for right-censored survival data with a cured fraction. The model employs the proportional mean residual life model to describe the effects of covariates on the mean residual time of uncured subjects and the logistic regression model to describe the effects of covariates on the cure rate. We develop estimating equations to estimate the proposed cure model for the right-censored data with and without length-biased sampling, the latter is often found in prevalent cohort studies. In particular, we propose two estimating equations to estimate the effects of covariates in the cure rate and a method to combine them to improve the estimation efficiency. The consistency and asymptotic normality of the proposed estimates are established. The finite sample performance of the estimates is confirmed with simulations. The proposed estimation methods are applied to a clinical trial study on melanoma and a prevalent cohort study on early-onset type 2 diabetes mellitus.