Models for survival and longitudinal data in cancer research

In the field of survival analysis, we often encounter the situation where a fraction of the study subjects will never experience an event. Cure models have been formulated to address this issue. We developed a family of cure models, indexed by a Box-Cox type transformation parameter, such that different formulations of cure models can be obtained by varying the index parameter. A profile likelihood approach was used for parameter estimation. Simulation studies were conducted to show unbiasedness. This model was applied to bone marrow transplant data and tonsil cancer data.;Along with survival information, medical studies also often collect longitudinal biomarkers. Joint models have been proposed to analyze these data simultaneously. We developed a non-parametric joint model of longitudinal biomarker and survival data where the longitudinal trajectories are modeled based on penalized B-splines and linked with the risk of failure by the Cox proportional hazard model. This model can accommodate nonlinearity in the longitudinal trajectories with a large degree of flexibility. A Bayesian approach was used for parameter estimation, and the Metropolis-Hastings algorithm was implemented to construct the MCMC chains. This model was applied to prostate cancer data, and a validation set was fit to evaluate the model performance.;Furthermore, we evaluated our joint model in terms of its prognostic power by focusing on the predicted conditional survival probabilities. We proposed absolute distance based measures to assess the predictive accuracy. We carried out simulation studies to evaluate the predictive accuracy of our joint model by comparing it with three alternative approaches. The simulation results showed that our joint model yielded consistently lower average prediction errors, and hence out-performed the other three approaches in terms of its prognostic power.