Regression on median residual life function for censored survival data

In the analysis of time-to-event data, the median residual life (MERL) function has been promoted by many researchers as a practically relevant summary of the residual life distribution. Formally the MERL function at a time point is defined as the median of the remaining lifetimes among survivors beyond that particular time point. Despite its widely recognized usefulness, there is no commonly accepted approach to model the median residual life function.In this dissertation we introduce two novel regression techniques that model the relationship between the MERL function and covariates of interest at multiple time points simultaneously; proportional median residual life model and accelerated median residual life model. These models have a conceptual similarity to the well-known proportional hazards and accelerated failure time (AFT) models. Inference procedures that we propose for these models permit the data to be right censored.For the semiparametric analysis under the proportional MERL model, we propose an estimating equation for the regression coefficients. The bootstrap resampling technique is utilized to evaluate the standard errors of the regression coefficient estimates. A simulation study is performed to investigate the proposed inferential approach. The developed method is applied to a real data example from a breast cancer study conducted by the National Surgical Adjuvant Breast and Bowel Project (NSABP).We also propose parametric and semiparametric (under the AFT assumption) inference procedures under the accelerated MERL model. The maximum likelihood inference is considered for the parametric inference and the Buckley and James method is used to estimate the median residual lifetimes semiparametrically under the AFT assumption. A simulation study is performed to validate the proposed maximum likelihood inference procedure. A generated dataset is used to illustrate statistical analysis via both estimation approaches.It is very important from a public health perspective to be able to identify the risk factors for a specific disease or condition. The regression techniques presented in this work enable researchers to identify the patients characteristics that affect their survival experience and describe advantages of a preventive or therapeutic intervention by means of median residual life function in a clinically relevant and intuitively appealing way.