THESIS DEFENSE ABSTRACT
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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