Receiver Operating Characteristic (ROC) analysis is one of the most widely used methods for summarizing intrinsic properties of a diagnostic system, and is often used in evaluation and comparison of diagnostic technologies, practices or systems. These methods play an important role in public health since they enable researchers to achieve a greater insight into the properties of diagnostic tests and eventually to identify a more appropriate and beneficial procedure for diagnosing or screening for a specific disease or condition. The topic of this dissertation is the nonparametric testing of hypotheses about ROC curves in a paired design setting. Presently only a few nonparametric tests are available for the task of comparing two correlated ROC curves. Thus we focus on this basic problem leaving the extensions to more complex settings for future research. In this work, we study the small-sample properties of the conventional nonparametric method presented by DeLong et al. and develop three novel nonparametric approaches for comparing diagnostic systems using the area under the ROC curve. The permutation approach that we present enables conducting an exact test and allows for an easy-to-use asymptotic approximation. Next, we derive a closed-form bootstrap-variance, construct an asymptotic test, and compare them to the existing competitors. Finally exploiting the idea of discordances we develop a conceptually new conditional approach that offers advantages in certain types of studies.

Gray's extension of Cox's proportional hazards (PH) model for right-censored survival data allows for a departure from the PH assumption via introduction of time-varying regression coefficients (TVC) using penalized splines. Gray's work focused on estimation, inference and residual analyses, but no estimator for the survival function has been proposed. We derive a survival function estimator for one important member of the class of TVC models - a piecewise-constant time-varying coefficients (PC-TVC) model. We also derive an estimate for the confidence limits of the survival function. Accuracy in estimating underlying survival times and survival quantiles is assessed for both Cox's and Gray's PC-TVC model using a simulation study featuring scenarios violating the PH assumption. Finally, an example of the estimated survival functions and the corresponding confidence limits derived from Cox's PH and Gray's PC-TVC model, respectively, is presented for a liver transplant data set. In the second part of the thesis we examine the effect of model misspecification for two classes of regression models for right-censored survival data - additive and multiplicative models for the conditional hazard rate. A particular attention is given to data exhibiting time-varying regression coefficients. The class of multiplicative models is represented by Cox PH model and Gray's TVC model, respectively, and for additive models we use Aalen's linear model. Both Gray's TVC model and Aalen's linear model incorporate time-varying coefficients. A simulation study is performed to cross-analyze survival data which follows either a multiplicative or an additive model for the conditional hazard rate. The effect of misspecifying the true model for the conditional hazard rate is assessed by looking at the power of the individual models to detect an existing effect, bias and mean square error observed for each conditional model-based estimator of survival. We also show that Aalen's model formulae is a first order Taylor series approximation of that of Gray's model which explains the comparably higher flexibility on part of the Aalen's model as compared to the Cox PH when the Gray's TVC model for the data is misspecified.

Parametric regression models are widely used in public health sciences. This dissertation is concerned with statistical inference under such models with some covariates missing at random. Under natural conditions, parameters remain identifiable from the observed (reduced) data. If the always observed covariates are discrete or can be discretized, we propose a semiparametric maximum likelihood method which requires no parametric specification of the selection mechanism or the covariate distribution. Simple conditions are given under which the semiparametric maximum likelihood estimator (MLE) exists. For ease of computation, we also consider a restricted MLE which maximizes the likelihood over covariate distributions supported by the observed values. The two MLEs are asymptotically equivalent and strongly consistent for a class of topologies on the parameter set. Upon normalization, they converge weakly to a zero-mean Gaussian process in a suitable space. The MLE of the regression parameter, in particular, achieves the semiparametric information bound, which can be consistently estimated by perturbing the profile log-likelihood. Furthermore, the profile likelihood ratio statistic is asymptotically chi-squared. An EM algorithm is proposed for computing the restricted MLE and for variance estimation. Simulation results suggest that the proposed method performs resonably well in moderate-sized samples. In contrast, the analogous parametric maximum likelihood method is subject to severe bias under model misspecification, even in large samples. The proposed method can be applied to related statistical problems.

One difficulty in regression analysis for longitudinal data is that the outcomes are often missing in a non-ignorable way (Little & Rubin, 1987). Likelihood based approaches to deal with non-ignorable missing outcomes can be divided into selection models and pattern mixture models based on the way the joint distribution of the outcome and the missing-data indicators is partitioned. One new approach from each of these two classes of models is proposed. In the first approach, a normal copula-based selection model is constructed to combine the distribution of the outcome of interest and that of the missing-data indicators given the covariates. Parameters in the model are estimated by a pseudo maximum likelihood method (Gong & Samaniego, 1981). In the second approach, a pseudo maximum likelihood method introduced by Gourieroux et al. (1984) is used to estimate the identifiable parameters in a pattern mixture model. This procedure provides consistent estimators when the mean structure is correctly specified for each pattern, with further information on the variance structure giving an efficient estimator. A Hausman type test (Hausman, 1978) of model misspecification is also developed for model simplification to improve efficiency. Separate simulations are carried out to assess the performance of the two approaches, followed by applications to real data sets from an epidemiological cohort study investigating dementia, including Alzheimer's disease.

The primary objective of the study is to assemble population pharmacokinetic models from the cancer pharmacokinetics literature for different types of anti-cancer drugs and to formulate them in ways suitable for input into cancer simulation programs. To fulfill the objectives, a step-based approach is adopted: 1)To catalogue the types of pharmacokinetic models through general review articles and books 2)To develop a search strategy for defining a body of research literature related to cancer pharmacokinetics in clinical trials for a limited set of drugs (Taxol, Platinum compounds. Fluoropyrimidine and Topoisomerase inhibitors) 3)To collect pharmacokinetic articles according to defined search criteria 4)To gather information from the collected PK articles 5)To synthesize the information separately for each drug, using a questionnaire instrument and present them in template form for each class of antineoplastic agent. 6)To formulate population pharmacokinetic models for each anti-cancer drug, from the constituent submodels for components of the overall model. This work will promote public health, specifically in support of the development of anti-cancer drug regimens for cancer patients, by providing standardized information about pharmacokinetics for input into simulations.

Although reliably recognized as a psychiatric syndrome, traumatic grief has not been identified as a primary axis I diagnosis in the Diagnostic and Statistical Manual of Mental Disorders fourth edition (DSM-IV). Due to the newness of recognition of this diagnosis, a universally accepted set of diagnostic criteria does not exist. The objective of this thesis was to evaluate the psychometric properties of a newly developed twenty-nine item structured clinical interview for the diagnosis of traumatic grief (SCI-TG) by: assessing its internal consistency; evaluating its inter-rater reliability; describing its factor structure; and determining its construct validity. The SCI-TG was administered to 166 patients enrolled in an ongoing traumatic grief therapy randomized clinical trial (TGTRCT) MH060783. The SCI-TG showed good internal consistency as assessed by the Cronbachs coefficient alpha (0.74), and good inter-rater reliability (0.81). Exploratory principal components factor analysis yielded the selection of three factors corresponding to symptoms of: guilt, failure to adapt, and separation distress, respectively. Demonstrating convergent validity, the total score of the SCI-TG was significantly correlated with the Inventory of Complicated Grief (ICG), the Hamilton Depression Rating Scale (HDRS), the Structured Interview Guidelines for the Hamilton Rating Scale for Anxiety (SIGH-A), the Impact of Events Scale (IES), and the Adult Separation Anxiety Disorder (ASAD). The estimated factor scores on factor 1, guilt, were not significantly correlated with any of these instruments, and the estimated factor scores on the separation distress factor was not significantly correlated with the ASAD, signifying the uniqueness of traumatic grief symptoms. The results of the factor analyses could be used to create subscales of the new 17-item SCI-TG. The distribution of the SCI-TG scores based on the reduced scale resulting from the factor analyses was proposed to be used in determining the scoring of this instrument. Studies of the treatment of bereavement with antidepressants have proven ineffective in treating grief symptoms. The public health relevance of this thesis is in defining these symptoms and developing an instrument to adequately identify such symptoms.

One of the most important research areas in human genetics is the effort to map genes associated with complex diseases such as cancer, heart disease, and diabetes. The public health relevance of these kinds of work is that gene mapping will bring an understanding of genetic risk and protective factors, and a description of the interaction between environment and genetic variation. In the last ten years there has been a dramatic increase in the number of studies seeking to map genes for quantitative traits. This has caused an explosion of new work on statistical methods for human quantitative trait locus (QTL) mapping. However, little of that work has dealt with selected samples, which are more common than population samples for human studies. This dissertation focuses on sibling pairs and considers the most common types of selected sampling. I surveyed most QTL mapping methods in the literature to evaluate which are appropriate for selected samples, and also developed new statistics for selected samples. Using simulation and analytical approaches, I identified the most powerful statistics for each type of sampling considered. I then compared various sampling designs using the best statistic for each and gave guidelines for choosing appropriate and powerful designs under different scenarios.

In many maintenance treatment trials, patients are first enrolled into an open treatment before they are randomized into treatment groups. During this period, patients are followed over time with their responses measured longitudinally. This design is very common in today's public health studies of the prevention of many diseases. Using mixed model theory, one can characterize these data using a wide array of across subject models. A state-space representation of the mixed model and use of the Kalman filter allow more fexibility in choosing the within error correlation structure even in the presence of missing and unequally spaced observations. Furthermore, using the state-space approach, one can avoid inverting large matrices resulting in eficient computations. Estimated trajectories from these models can be used as predictors in a survival analysis in judging the efacacy of the maintenance treatments. The statistical problem lies in accounting for the estimation error in these predictors. We considered a bivariate growth curve where the longitudinal responses were unequally spaced and assumed that the within subject errors followed a continuous first order autoregressive (CAR (1)) structure. A simulation study was conducted to validate the model. We developed a method where estimated random effects for each subject from a bivariate growth curve were used as predictors in the Cox proportional hazards model, using the full likelihood based on the conditional expectation of covariates to adjust for the estimation errors in the predictor variables. Simulation studies indicated that error corrected estimators for model parameters are mostly less biased when compared with the nave regression without accounting for estimation errors. These results hold true in Cox models with one or two predictors. An illustrative example is provided with data from a maintenance treatment trial for major depression in an elderly population. A Visual Fortran 90 and a SAS IML program are developed.

The Generalized Additive model (GAM) has been used as a standard tool for epidemiologic analysis exploring the effect of air pollution on population health during the last decade as it allows nonparametric relationships between the independent predictors and response. One major concern to the use of the GAM is the presence of concurvity in the data. The standard statistical software, such as S-plus, can seriously overestimate the GAM model parameters and underestimate their variances in the presence of concurvity. We explore an alternate class of models, generalized linear models with natural cubic splines (GLM+NS), that may not be affected as much by concurvity. We make systematic comparisons between GLM+NS and GAMs with smoothing splines (GAM+S) in the presence of varying degrees of concurvity using simulated data. Our results suggest that GLM+NS perform better than GAM+S when medium-to-high concurvity exists in the data. Since GLM+NS result in loss in flexibility, we also investigate an alternative approach to fit a GAM. This approach, which is based on partial residuals, gives regression coefficients and variance estimates with less bias in the presence of concurvity, compared to the estimates obtained by the standard approach. It can accommodate asymmetric smoothers and is more robust with respect to the choice of smoothing parameters. Illustrative examples are provided. The public health significance of this study is that the proposed approach improves the estimate of adverse health effect of air pollution, which is important for public and governmental agencies to revise health-based regulatory standards for ambient air pollution.

The study examined differences in positive aspects of caregiving (PAC) among 232 Hispanic caregivers and 691 Non-Hispanic Caucasian (NHC) caregivers of individuals with Alzheimer's disease, using baseline data of National Institutes of Health Resources for Enhancing Alzheimer's Care Health (REACH) study. Multiple linear regression models, mediation analysis and Sobel's test were performed to assess the mediating effects of five possible mediators (education, socioeconomic status, behavior bother, social support and religiosity). Hispanics caregivers reported higher scores on PAC than their NHC counterparts. Hispanic caregivers' higher religiosity partially mediated the relationship between ethnicity and PAC. Additional variables that contributed to their higher PAC scores were caregivers' lower education level and lower socioeconomic status. A similar approach was used to compare values of PAC between 77 Mexican and 88 Cuban female caregivers. Mexican female caregivers reported statistically significant higher PAC when compared with Cuban female caregivers. The full mediation of socioeconomic status (SES) and partial mediation of education were seen to exist in the relationship between PAC and ethnicity. The question of how or why the PAC differences exist between ethnic groups was partially answered by employing the mediation analysis. The public health importance of this thesis is to provide the information on the ethnic differences in PAC, which is useful for social and psychological interventions.