Regression Analysis of Mean Residual Life Function

Abstract The mean residual life function (mrlf) of a subject is defined as the expected remaining lifetime of the subject given that the subject has survived up to a given time. The commonly used regression models as proportional mean residual life (PMRL) and linear mean residual life (LMRL) have limited applications due to adhoc restriction on the parameter space. The regression model we propose does not have any constraints. It turns out that the proposed proportional scaled mean residual life (PSMRL) model is equivalent to the accelerated failure time (AFT) model, which provides an alternative way to estimate the regression parameters of the AFT model and to interpret the regression parameters estimated from the AFT model in terms of the mrlf instead of the survival function. We use full likelihood by nonparametrically estimating the baseline mrlf using the smooth scale mixture estimator of the mrlf based on a single sample of iid observations to develop the statistical inference for the regression parameters, which are estimated using an iterative procedure. A simulation study is carried out to assess the properties of the estimators of the regression coefficients. We illustrate our regression model by applying it to the well-known Veteran’s Administration lung cancer data.