| Many diseases, especially cancer, are not static, but rather can be summarized by a series of events or stages (e.g. diagnosis, remission, recurrence, metastasis, death). Most available methods to analyze multi-stage data ignore intermediate events and focus on the terminal event or consider (time to) multiple events as independent. Competing-risk or semi-competing-risk models are often deficient in describing the complex relationship between disease progression events that are driven by a shared progression stochastic process. In the first chapter, we propose a semi-parametric joint model of diagnosis, latent metastasis, and cancer death and use nonparametric maximum likelihood to estimate covariate effects on the risks of intermediate events and death and the dependence between them. We illustrate the model using SEER prostate cancer data.;In the second chapter, we focus on the adverse effect of younger diagnosis age on cancer survival. We use a joint model with a shared gamma frailty term to interpret the effect as a consequence of correlation between diagnosis time and the post-diagnosis survival time. In the traditional analysis, diagnosis time is treated as the time origin for a model of overall survival that fails to utilize the full information leading up to diagnosis. Often the available covariates do not fully explain the correlation between time-to-diagnosis and time-to-death calling for use of joint modeling and frailties to extend the model. We show that the variance of the frailty term and covariate effects can be estimated by a nonparametric maximum likelihood method. Laplace transformation is used to derive likelihood contributions. The model is applied to Michigan SEER breast cancer data.;In the third chapter, we compare dynamic treatment regimens from clinical trials with multiple rounds of treatment randomization (sequential multiple assignment randomized trials, SMARTs). Previously proposed methods to analyze data with survival outcomes from a SMART use inverse probability weighting and provide non-parametric estimation of survival rates, but no other information. We apply a joint modeling approach here to provide unbiased survival estimates and as a mechanism to include auxiliary covariates, treatment effects and their interaction within regimens. We address the multiple comparisons problem using multiple-comparisons-with-the-best (MCB). |
