Computer-intensive approaches to four topics in biostatistics

My dissertation is composed of four distinct projects in Biostatistics that are related primarily through their dependence on a computer intensive approach towards estimation and inference. In the first paper, I present a method based on the profile likelihood function that allows for the estimation and inference of a parameter of interest in a complex differential equation model when the full parameter set may be effectively non-identified due to collinearity of the parameter estimates. This approach is then employed to study several parameters of interest in a model of the 1993 Milwaukee Cryptosporidium outbreak. In the second paper, I present a computer intensive method based on cross-validation that can be used to select a model for a nuisance parameter in semiparametric model. Unlike a standard model selection procedures that selects variables in an effort to improve predictive accuracy of a model, this method selects variables in the nuisance parameter model in an effort to minimize the MSE of a parameter of particular interest to the researcher. I study the performance of the proposed method through a simulation study and then demonstrate its application by estimating the marginal causal effect of boiled water use on diarrhea incidence among an HIV positive population. For the third paper, I propose a computer intensive procedure that can be used to implement a locally efficient estimator of a structural nested model. The performance of this method is examined through a pair of simulation studies. In the final paper, I introduce an event history model and associated sampling strategy that can be used to analyze state transitions in very large state administrative data sets containing longitudinal data on welfare participation.