Title: Joint modeling of longitudinal and state-change processes
Description: Joint modeling of continuous repeated measures and stochastic processes involving state changes has the potential to improve estimation, account for measurement error, and accommodate missing data. This dissertation considers likelihood methods for the joint modeling of longitudinal and state-change processes as well as longitudinal and discrete failure time processes when the longitudinal response is censored. The first chapter explores an approach to modeling the impact of resistance mutations on the longitudinal trajectory of HIV-1 RNA for patients receiving antiretroviral therapy when the time of occurrence and the nature of these mutations are known with error. The second chapter considers a maximum likelihood method for fitting autoregressive models of arbitrary order and covariance structure to response variables that may be censored or missing, and extends the method to accommodate joint modeling with an unobserved failure time. This approach can be used to model the longitudinal trajectory of HIV-1 RNA with time of treatment failure as a covariate when the HIV-1 RNA measurements are subject to a lower limit of detection and the time of treatment failure is unknown. The third chapter investigates joint modeling of longitudinal and state-change processes in the presence of missing data when failure to observe a state at a fixed time can depend on the unobserved state. The method is used to model substance use in adolescence and parental monitoring as associated processes. The applications for Chapters 1, 2, and 3 are to data from Protocol 398 of the AIDS Clinical Trials Group, the Genotypic Antiretroviral Resistance Testing Study, and the National Longitudinal Surveys of Youth 1997 respectively.