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The Role of the Design, Analysis, and Computation in Addressing Etiology in Three Types of studies in Public Health

 Ravi Varadhan, PhD Candidate, Johns Hopkins Department of Biostatistics

This dissertation research comprises three distinct papers. In the first paper, we highlight two important methodological issues in the case-crossover design, a novel epidemiological study design. It only uses the cases, and 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. We show that the standard analysis can suffer from length bias, and also makes inefficient use of available information. We propose a method to eliminate length bias, and also develop a new modeling approach, based on fully utilizing the gap times, to increase the efficiency of the design.

The second paper addresses model uncertainty in model based low-dose extrapolation for microbial risk assessment. Inference on low-dose risk estimates is highly sensitive to model choice, and, hence, can be overly optimistic, if model uncertainty is ignored. We propose a new approach called profiled Bayesian model averaging (PBMA), that uses the profile likelihood in Bayesian model averaging, and that only requires prior distribution on the target of inference. PBMA is justified based on both practical and theoretical (asymptotic) arguments, and possesses major computational advantage by reducing all the Bayesian computations to that of evaluating one-dimensional integrals. We also demonstrate using simulations that PBMA performs better than the widely used competing method.

In the third paper, we present a new class of computationally efficient, yet simple, numerical schemes, called the SQUAREM, which significantly improve the rate of convergence of the EM. These new schemes are based on extrapolation techniques from the numerical analysis literature. They can be applied very broadly to any nonlinear fixed point iterative scheme, and to the EM, in particular. When applied to the EM, they do not require any auxiliary quantities such as the complete- or incomplete-data log-likelihood, and/or their derivatives. The new schemes have potential utility in important scientific problems such as causal inference in longitudinal studies, latent variable regression models, mixed effects models, image reconstruction, and population genetics models.


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