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Book Summary:
Joint modeling of longitudinal and survival data is becoming increasingly essential in most cancer and AIDS clinical trials. In this thesis, we first generalize the longitudinal component to be multivariate in the joint modeling framework. A multivariate mixed effects model is presented to explicitly capture two different sources of dependence among longitudinal measures over time and over different variables. A novel univariate survival model is also proposed to incorporate longitudinal trajectories, representing the true longitudinal measures, as well as other baseline covariates in the model. This survival model is novel with a sound biological meaning, and is capable of accommodating both zero and nonzero cure fractions. We then further generalize the survival component to be multidimensional to investigate the relationship between multivariate longitudinal markers and multivariate failure time random variables. The proposed multivariate survival model has a proportional hazards structure for the population hazard, conditionally as well as marginally, when the baseline covariates are specified through a specific mechanism. In addition, the model is capable of dealing with survival functions with different cure rate structures. In the third thesis paper, we develop a Bayesian hierarchical longitudinal model for time course microarray data to account for correlated gene expression measurements over time and over different genes. A new gene selection algorithm, based on a set of ratio-type statistics is also presented with the model to simultaneously identify genes that show changes in expression among biological conditions, in response to time and other experimental factors of interest. |
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