Determination of the composition of failure time models with long-term survivors

Abstract

Failure-time data with long-term survivors are frequently encountered in clinical in vestigations. A standard approach for analyzing such data is to add a logistic regres sion component to the traditional proportional hazard models for accommodation of the individuals that are not at risk of the event. One such formulation is the cure rate model; other formulations with similar structures are also used in prac tice. Increased complexity presents a great challenge for determination of the model composition. Importantly, no existing model selection tools are directly applicable for determination of the composition of such models. This dissertation focuses on two key questions concerning the construction of complex survival models with long term survivors: (1) what independent variables should be included in which modeling components? (2) what functional form should each variable assume? I address these questions by proposing a set of regularized estimation procedures using the Least Absolute Shrinkage and Selection Operators (LASSO). Specifically, I present vari able selection and structural discovery procedures for a broad class of survival models with long-term survivors. Selection performance of the proposed methods is evaluated through carefully designed simulation studies.