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Multistate models are widely used in health research to analyze life history processes in which each individual is assumed to occupy one of a finite number of states at any given point in time. Models allowing for back transitions are necessary when considering recurrent events or disease states from which recovery is possible along with subsequent return to illness. The objective of this dissertation is to consider current challenges in the statistical analyses of multistate models arising in public health. Applications to the fields of HIV/AIDS and dementia are considered.To assess the effect of concurrent or overlapping partnership patterns on the trajectory of the HIV epidemic in a population, it is necessary to estimate both the extent and the magnitude of concurrency. Data are typically available in the form of retrospective sexual history reports. We introduce a joint multistate and point process model in which states are defined as the number of ongoing partnerships an individual is engaged in at a given time. Sexual partnerships starting and ending on the same date are referred to as one-offs and modeled as discrete events. The proposed method treats each individual's continuation in and transition through various numbers of ongoing partnerships as a separate stochastic process and allows the occurrence of one-offs to impact subsequent rates of partnership formation and dissolution. Among a sample of men having sex with men and seeking HIV testing at a Los Angeles clinic, the estimated point prevalence of concurrency was higher among men later diagnosed HIV positive. One-offs were associated with increased rates of subsequent partnership dissolution.In constructing a disease progression multistate model, panel data consisting of the states occupied by an individual at a series of discrete time points are often used to to estimate transition intensities of the underlying continuous-time process. When transition intensities depend on the time elapsed in the current state and back transitions between states are possible, this intermittent observation process leads to intractability of the likelihood function. We present an iterative stochastic expectation-maximization (SEM) algorithm that relies on a simulation-based approximation to the likelihood function and implement this algorithm using rejection sampling. In a simulation study, we demonstrate the feasibility and performance of the proposed procedure. We then demonstrate application of the algorithm to a study of dementia, the Nun Study, consisting of intermittently-observed elderly subjects in one of four possible states corresponding to intact cognition, impaired cognition, dementia, and death. We show that the proposed SEM algorithm substantially reduces bias in model parameter estimates compared to an alternative naive approach. We then extend the utility of this disease progression model to settings in which healthy individuals have a non-negligible probability of being misclassified into a disease state. The proposed model accomplishes unbiased estimation of the semi-Markov model parameters associated with transition rates and probabilities while simultaneously estimating the true underlying misclassification rate without requiring information from a gold standard. In applying this SEM algorithm addressing misclassification to the Nun Study, findings suggest that the rate of misclassification may be relatively high among this sample and that true back transitions from impaired to intact cognition are somewhat rare.By describing and addressing statistical challenges in multistate modeling, we demonstrate the utility of and reduce existing barriers to the implementation of such models across a wide range of applications in the field of public health and in situations where imperfect data are available.