Bayesian Methods in Nutrition Epidemiology and Regression-based Predictive Models in Healthcare

This dissertation has mainly two parts. In the first part, we propose a bivariate nonlinear multivariate measurement error model to understand the distribution of dietary intake and extend it to a multivariate model to capture dietary patterns in nutrition epidemiology. In the second part, we propose regression-based predictive models to accurately predict surgery duration in healthcare.

Understanding the distribution of episodically consumed dietary components is an important problem in public health. Short-term measurements of episodically consumed dietary components are zero-inflated skewed distributions. So-called two-part models have been developed for such data. However, there is much greater public health interest in the usual intake adjusted for caloric intake. Recently a nonlinear mixed effects model has been developed and fit by maximum likelihood using nonlinear mixed effects programs. However, the fitting is slow and unstable. We develop a Monte-Carlo-based fitting method in Chapter II. We demonstrate numerically that our methods lead to increased speed of computation, converge to reasonable solutions, and have the flexibility to be used in either a frequentist or a Bayesian manner. Diet consists of numerous foods, nutrients and other components, each of which have distinctive attributes. Increasingly nutritionists are interested in exploring them collectively to capture overall dietary patterns. We thus extend the bivariate model described in Chapter III to multivariate level. We use survey-weighted MCMC computations to fit the model, with uncertainty estimation coming from balanced repeated replication. The methodology is illustrated through an application of estimating the population distribution of the Healthy Eating Index-2005 (HEI-2005), a multi-component dietary quality index , among children aged 2-8 in the United States.

The second part of this dissertation is to accurately predict surgery duration. Prior research has identified the current procedural terminology (CPT) codes as the most important factor when predicting surgical case durations but there has been little reporting of a general predictive methodology using it effectively. In Chapter IV, we propose two regression-based predictive models. However, the naively constructed design matrix is singular. We thus devise a systematic procedure to construct a fullranked design matrix. Using surgical data from a central Texas hospital, we compare the proposed models with a few benchmark methods and demonstrate that our models lead to a remarkable reduction in prediction errors.