Joint regression modeling of two cumulative incidence functions under an additivity constraint and statistical analyses of pill-monitoring data

In the first part of this dissertation, we propose a parametric regression model for cumulative incidence functions (CIFs) which are commonly used for competing risks data. Our parametric model adopts several parametric functions as baseline CIFs and a proportional hazard or a generalized odds rate model for covariate effects. This parametric model explicitly takes into account the additivity constraint that a subject should eventually fail from one of the causes so the asymptotes of the CIFs should add up to one. Our primary goal is to propose a parametric regression model that provides regression parameters for the CIFs of both the primary and secondary risks. Moreover, we introduce a modified Weibull baseline distribution. The inference procedure is straightforward. Parameters are estimated via the maximization of the likelihood. Standard errors are obtained via the Hessian of the log-likelihood. We demonstrate the good practical performance of this parametric model. We simulate the underlying processes for cause 1 and cause 2, and compare our models with some existing methods. In the second part of this dissertation, we propose several approaches for the modeling and analysis of medication bottle opening events data, and focus on frailty models, in both parametric and semiparametric forms. This approach provides regression coefficients which are of great interest to investigators and clinicians. A time effect can also be estimated. We apply our approaches to the analysis of a medication bottle opening event data set. To our knowledge, this is the first study of prescription bottle opening events which focuses on time between medication administrations through frailty models. We discuss the interpretation of the random effect of a subject, and how it can help characterize the adherence of that individual relative to that of the other subjects. We then present an exploratory cluster analysis of the survival curves of the participants