Central to the goals of public health are obtaining and interpreting timely and relevant information for the benefit of humanity. In this dissertation, we propose methods to monitor and assess the spread HIV in a more rapid manner, as well as to improve decisions regarding patient treatment options. In Chapter 1, we propose a method, extending the previously proposed dual-testing algorithm and augmented cross-sectional design, for estimating the HIV incidence rate in a particular community. Compared to existing methods, our proposed estimator allows for shorter follow-up time and does not require estimation of the mean window period, a crucial, but often unknown, parameter. The estimator performs well in a wide range of simulation settings. We discuss when this estimator would be expected to perform well and offer design considerations for the implementation of such a study. Chapters 2 and 3 are concerned with obtaining a more complete understanding of the impact of treatment in randomized clinical trials in which multiple patient outcomes are recorded. Chapter 2 provides an illustration of methods that may be used to address concerns of both risk-benefit analysis and personalized medicine simultaneously, with a goal of successfully identifying patients who will be ideal candidates for future treatment. Riskbenefit analysis is intended to address the multivariate nature of patient outcomes, while “personalized medicine” is concerned with patient heterogeneity, both of which complicate the determination of a treatment’s usefulness. A third complicating factor is the duration of treatment use. Chapter 3 features proposed methods for assessing the impact of treatment as a function of time, as well as methods for summarizing the impact of treatment across a range of follow-up times. Chapter 4 addresses the issue of meta-analysis, a commonly used tool for combining information for multiple independent studies, primarily for the purpose of answering a clinical question not suitably addressed by any one single study. This approach has proven highly useful and attractive in recent years, but often relies on parametric assumptions that cannot be verified. We propose a non-parametric approach to meta-analysis, valid in a wider range of scenarios, minimizing concerns over compromised validity.

Diabetes is a major risk factor for the development of cataract [3,14,20,22]. In this thesis, we create a model that allows us to understand the incidence of one disease in the context of another; in particular, cataract in the presence of diabetes. The World Health Organization's Vision 2020 blindness-prevention initiative administers surgeries to remove cataracts, the leading cause of blindness worldwide [24]. One of the geographic areas most impacted by cataract-related blindness is Sub-Saharan Africa. In order to plan the number of surgeries to administer, the World Health Organization uses data on cataract prevalence. However, an estimation of the incidence of cataract is more useful than prevalence data for the purpose of resource planning. In 2012, Dray and Williams developed a method for estimating incidence based on prevalence data [5]. Incidence estimates can be further refined by considering associated risk factors such as diabetes. We therefore extend the Dray and Williams model to include diabetes prevalence when calculating cataract incidence estimates. We explore two possible approaches to our model construction, one a detailed extension, and the other, a simplification of that extension. We provide a discussion comparing the two approaches.