Abstract: The mean residual life model is vital for its ability to investigate the association between covariates and patient life expectancy. In certain circumstances, a patient's lifespan may change when a covariate exceeds a particular threshold value, which is critical to predicting the patient's life expectancy and preventing diseases. This study considers a threshold regression analysis of a proportional mean residual life model with a continuous thresholding variable. We construct martingale-based smoothed estimating equations to obtain parameter estimators, and establish the large-sample properties of the proposed estimators. Furthermore, we propose a supremum test to examine the existence of the threshold. Finally, we assess the finite-sample performance of the proposed method using simulation studies, and then apply the methodology to data from colorectal and breast cancer studies.

Key words and phrases: Proportional mean residual model, smoothed estimation equation, subgroup identification, threshold test.