"Event-time data are routinely obtained from longitudinal investigations to evaluate the time to onset and progression of chronic diseases. Such data are commonly referred to as disease life course data and have several nontrivial complications. In many longitudinal studies, disease life course data are subject to interval censoring, within-sampling-unit clustering, and multiplicity of event states. Moreover, because medical studies usually collect a large number of hypothesized risk factors for the disease, identifying pertinent determinants of the disease life course is of interest for disease prevention and prediction. In Chapter 1, we describe a dental caries data set from a unique longitudinal study of young low-income urban African-American children. This data set motivates the three statistical methodologies developed respectively in Chapters 2-4. In Chapter 2, we formulate a parametric frailty Markov model coupled with a likelihood-based inference to analyze the life course data with the complications of interval censoring, within-sampling-unit clustering and three event states. We also develop a Bayesian approach to predict observational-unit-level future transition probabilities. Such probabilities have implications for precision medicine. Albeit its ease of computations, the proposed parametric method in Chapter 2 has some limitations. An obvious limitation is the restrictive parametric model imposed on the baseline intensities. Thus, in Chapter 3, we propose a similar model but with unspecified baseline intensities and develop a penalized spline method for the model estimation. Numerical experiments demonstrate that the proposed methods perform very well in finite samples with moderate sizes. In Chapter 4, we propose a penalized variable selection method for interval censored data under the Cox proportional hazards model. It conducts a penalized nonparametric maximum likelihood estimation with an adaptive Lasso penalty, which can be implemented through a penalized EM algorithm. The method is proved to have the oracle property. We also extend it to left truncated and interval censored data. Our simulation studies show that the method demonstrates the oracle property in samples of modest sizes and outperforms existing approaches in terms of many operating characteristics. The practical utility of the approach is illustrated using the mouth-level dental caries data introduced in Chapter 1."--Abstract.
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