Tracking and surveillance of the HIV epidemic depend on accurate estimation of the number of new infections in the population. The rate at which these infections occur, known as the incidence, is also critical for effectively designing, targeting, and evaluating prevention efforts. Incidence can be estimated through cross-sectional surveys by using biomarkers, such as HIV viral load, CD4 cell count, and recently developed serologic assays, which define and mark people in an early disease stage. The total number of individuals found in this stage, that is possessing markers of recent infection, gives a snapshot of how the epidemic is progressing.

We explore how these biomarkers should best be combined to define this early disease stage by examining how the definition influences the bias and variability of the cross-sectional incidence estimator. These calculations depend on estimating the probability that persons will remain in the early disease stage $t$ years after seroconversion. We present two different approaches for estimating this probability curve. Once we have defined viable methods for combining these biomarkers we derive the sample sizes needed to conduct one or more cross-sectional surveys and explore how missing biomarker data should be handled in the context of implementing these surveys.

In this thesis, we consider statistical issues in classification for disease using diagnostic testing. We discuss two aspects of disease classification: the generation of testing algorithms to combine multiple diagnostic tests that address both accuracy and cost considerations and the application of an imperfect diagnostic test to determine cases in a case-control study.

Motivated by the problem of combining multiple biomarkers to identify recent HIV infection (<1 year), we first develop methods for identifying "serial testing algorithms" to reduce the cost of diagnosis. These "serial testing algorithms" are characterized by the ability to make a classification determination before all diagnostic markers are acquired. These algorithms are able to maintain accuracy while controlling costs of the diagnostic testing.

We present two approaches to this problem. A logic regression approach in which serial testing algorithms are developed by means of logical combinations of dichotomous tests. Testing costs are optimized through a permutation algorithm on the logical rule. We also develop a serial risk score classification approach. In this method, we establish multiple ordered stages of classification determined by a risk score model. In each stage, one or more diagnostic tests are added to the risk score model from the previous stage and each observation is either determined to continue on for further testing or classified as positive or negative.

The methods are studied in simulations and compared with logistic regression. We applied the methods to data from HIV cohort studies to identify HIV infected individuals who are recently infected (< 1 year) by testing with assays for multiple biomarkers. The biomarkers that we used as part of the classification rule were the CD4 count, viral load, BED assay and avidity assay. We find that serial testing algorithms can maintain accuracy while achieving a reduction in cost compared to testing all individuals with all assays.

We then investigate the application of a non-gold standard test to a case control study. This work was motivated by case-control studies for risk factors associated with recent (<1 year) HIV infection when the duration of infection cannot be directly observed. In this type of study, recently (< 1 year) and chronically (>1 year) infected people represent two types of cases. When the case type is misclassified, the usual standard estimates for an odds ratio associated with one of the case types can be biased. We discuss methods to adjust the odds ratio from a case control study using the performance characteristics of a classification rule. In particular, we discuss a matrix adjustment method to adjust the observed counts of each case type, and an adjustment method based on a multinomial logistic regression model. These methods have shown to reduce bias in the estimation of the odds ratio.

We conclude with a discussion of the described methods in disease classification that were motivated by problems in HIV research. These problems included the cost of diagnostic tests and the fact that dates of infection cannot often be determined. The methods we developed may also have application to other settings especially when the costs of diagnostic testing is high and there are multiple types of cases that cannot be distinguished with complete accuracy.

Progress in HIV (human immunodeficiency virus) prevention interventions has been made in recent years. These developments have raised questions concerning the impact and optimal combination of biomedical and behavioral interventions. Agent-based models offer a way to compare intervention combinations that could not be readily accomplished with large scale prevention trials because of cost and logistical considerations. An agent-based model is a community of individuals whose behavior and interactions are simulated according to well- defined rules.

We describe two agent-based social network models and methods of calibration to sexual contact parameters relevant to MSM (men who have sex with men) in South Africa: a model with static partnerships and a novel model featuring self-reinforcing partnership edges. We only have sexual contact summary statistics (i.e. coarse network statistics) and these models are calibrated to replicate these statistics. A calibration approach was developed using recent advances in multi-objective optimization and applied to the self-reinforcing model.

We use these models to evaluate the varying impact of HIV prevention combinations by simulating community-randomized trials across realistic values of several parameters: ART (anti-retroviral therapy) uptake, PREP (pre-exposure prophylaxis) uptake, HIV testing uptake, and CAI (condomless anal intercourse) reduction. For the static partnership agent-based model, we create a statistical model to describe quantitatively the effects of these parameters and variation. For the self-reinforcing model we model sensitivity across several key parameters. We develop sample size and power formula for community randomized trials that incorporate estimates of variation and effect sizes determined from the agent-based model. We find that traditional sample size approaches that rely on binomial (or Poisson) models are inadequate and can lead to underpowered studies. In our studies of variation and effect sizes, we identified important sensitivities to the network contact structure. We conclude that agent-based models offer a useful tool in the design of HIV prevention trials.

Multistate models are widely used in health research to analyze life history processes in which each individual is assumed to occupy one of a finite number of states at any given point in time. Models allowing for back transitions are necessary when considering recurrent events or disease states from which recovery is possible along with subsequent return to illness. The objective of this dissertation is to consider current challenges in the statistical analyses of multistate models arising in public health. Applications to the fields of HIV/AIDS and dementia are considered.

To assess the effect of concurrent or overlapping partnership patterns on the trajectory of the HIV epidemic in a population, it is necessary to estimate both the extent and the magnitude of concurrency. Data are typically available in the form of retrospective sexual history reports. We introduce a joint multistate and point process model in which states are defined as the number of ongoing partnerships an individual is engaged in at a given time. Sexual partnerships starting and ending on the same date are referred to as one-offs and modeled as discrete events. The proposed method treats each individual's continuation in and transition through various numbers of ongoing partnerships as a separate stochastic process and allows the occurrence of one-offs to impact subsequent rates of partnership formation and dissolution. Among a sample of men having sex with men and seeking HIV testing at a Los Angeles clinic, the estimated point prevalence of concurrency was higher among men later diagnosed HIV positive. One-offs were associated with increased rates of subsequent partnership dissolution.

In constructing a disease progression multistate model, panel data consisting of the states occupied by an individual at a series of discrete time points are often used to to estimate transition intensities of the underlying continuous-time process. When transition intensities depend on the time elapsed in the current state and back transitions between states are possible, this intermittent observation process leads to intractability of the likelihood function. We present an iterative stochastic expectation-maximization (SEM) algorithm that relies on a simulation-based approximation to the likelihood function and implement this algorithm using rejection sampling. In a simulation study, we demonstrate the feasibility and performance of the proposed procedure. We then demonstrate application of the algorithm to a study of dementia, the Nun Study, consisting of intermittently-observed elderly subjects in one of four possible states corresponding to intact cognition, impaired cognition, dementia, and death. We show that the proposed SEM algorithm substantially reduces bias in model parameter estimates compared to an alternative naive approach. We then extend the utility of this disease progression model to settings in which healthy individuals have a non-negligible probability of being misclassified into a disease state. The proposed model accomplishes unbiased estimation of the semi-Markov model parameters associated with transition rates and probabilities while simultaneously estimating the true underlying misclassification rate without requiring information from a gold standard. In applying this SEM algorithm addressing misclassification to the Nun Study, findings suggest that the rate of misclassification may be relatively high among this sample and that true back transitions from impaired to intact cognition are somewhat rare.

By describing and addressing statistical challenges in multistate modeling, we demonstrate the utility of and reduce existing barriers to the implementation of such models across a wide range of applications in the field of public health and in situations where imperfect data are available.

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We consider studies for evaluating the short-term effect of a treatment of interest on a time-to-event outcome. The studies we consider are partially controlled in the following sense: (1) Subjects’ exposure to the treatment of interest can vary over time, but this exposure is not directly controlled by the study; (2) subjects’ follow-up time is not directly controlled by the study; and (3) the study directly controls another factor that can affect subjects’ exposure to the treatment of interest as well as subjects’ follow-up time. When factors (1) and (2) are both present in the study, evaluating the treatment of interest using standard methods, including instrumental variables, does not generally estimate treatment effects. We develop the methodology for estimating the effect of treatment in this setting of partially controlled studies under explicit assumptions using the framework for principal stratiŽ cation for causal inference. We illustrate our methods by a study to evaluate the efŽ cacy of the Baltimore Needle Exchange Program to reduce the risk of human immunodeŽ ciency virus (HIV) transmission, using data on distance of the program’s sites from the subjects.

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