Estimation and Inference for the Additive Mean Residual Life Model With Change Point in the Continuous Covariate

The mean residual life model offers comprehensive insights into the relationship between a patient's remaining life expectancy and various covariates. In cancer research, a patient's lifespan may dramatically change when a covariate exceeds a threshold. Accurately detecting and estimating this change-point is crucial for predicting the patient's life expectancy and preventing diseases. To address these challenges, we investigate the additive mean residual life model with an unknown change-point in the continuous covariate. The martingale-based smoothed estimating equations are used to estimate the baseline mean residual life function, regression parameters, and the unknown change-point. Furthermore, we establish the large sample properties of the estimator under mild conditions, and propose a maximal Wald test statistic to test the existence of the change-point. Finally, we assess the finite sample performance of our proposed method through extensive simulation studies and apply it to two real data examples from studies on stomach cancer and primary biliary cirrhosis. Supplementary materials for this article are available online.