Robust methodology for predicting and evaluating prognosis in right censored time to event data

For censored time to event data, it is important to develop flexible regression models that can be used to accurately predict future risk. A common goal in medical studies with survival data is to stratify patients according to their predicted risk. Using the traditional methodology, it is difficult to assess the predictive accuracy in an intuitive and interpretable manner. We frame the problem in terms of prediction error, and develop methodology using working survival models to make predictions in terms of failure time intervals. We propose two measures of prediction error which are consistently estimated even when the survival model is misspecified. We demonstrate a resampling technique that approximates the large sample distribution of the error statistics, and can be used to differentiate between two models on the basis of prediction error.;In the second part of the thesis, we extend our methodology to include ordered risk categories defined as a function of a study's marginal survival quantiles. A robust classification scheme is developed via a working survival model, which may be directly evaluated either through a loss based metric or time dependent ROC methodology. The regression coefficient estimates and corresponding loss based error statistics are demonstrated to be consistent, asymptotically normal, and free of the nuisance censoring distribution. We demonstrate a data adaptive procedure designed to aid practitioners in selecting survival quantiles.;In the final part of the thesis, we develop robust prediction models for event time outcomes by generalizing Cai's estimating equation approach for the linear transformation model (Cai et al., 2000), which includes the proportional odds and proportional hazards model. This allows for prediction of survival probabilities at any given timepoint for multiple timepoints. We demonstrate that under mild regularity conditions, the solution of the estimating equations possess a stability property which allows for valid predictive inference under possible model misspecification. The proposed procedures are applied to a multiple myeloma dataset to derive a flexible regression model for predicting patient survival based on traditional clinical factors with and without the addition of genetic information. The finite sample properties of the procedures are evaluated through a simulation study.