This thesis comprises three distinct research papers. The first paper focuses on two important methodological issues pertaining to the design and analysis in a relatively new epidemiological study design, called the case-crossover design. This design, which only uses the cases, can be useful in developing hypotheses regarding the etiology of an acute event by examining the association between a recurrent exposure and the acute event. The second paper addresses model uncertainty in model-based low dose extrapolation for microbial risk assessment. Here, inference on low-dose risk estimates is highly sensitive to model choice. We propose a new approach called profiled Bayesian model averaging (PBMA) to account for model uncertainty. PBMA only requires prior distribution on the target of inference, and can be justified based on practical and theoretical (asymptotic) arguments. The third paper presents simple and globally convergent numerical methods for accelerating the convergence of the Expectation-Maximization (EM) algorithm, a popular approach in computational statistics for finding maximum likelihood estimates of parameters.

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