One of the most popular uses for tree-based methods is in survival analysis for censored time data where the goal is to identify factors that are predictive of survival. Tree-based methods, due to their ability to identify subgroups in a hierarchical manner, can sometimes provide a useful alternative to Coxs proportional hazards model (1972) for the exploration of survival data. Since the data are partitioned into approximately homogeneous groups, Kaplan-Meier estimators can be used to compare prognosis between the groups presented by nodes in the tree. The demand for tree-based methods comes from clinical studies where the investigators are interested in grouping patients with differing prognoses. Tree-based methods are usually conducted at landmark time points, for example, five-year overall survival, but the effects of some covariates might be attenuated or increased at some other landmark time point. In some applications, it may be of interest to also determine the time point with respect to the outcome interest where the greatest discrimination between subgroups occurs. Consequently, by using a conventional approach, the time point at which the discrimination is the greatest might be missed. To remediate this potential problem, we propose a tree-structure method that will split based on the potential time-varying effects of the covariates. Accordingly, with our method, we find the best point of discrimination of a covariate with respect to not only a particular value of that covariate but also to the time when the endpoint of interest is observed. We analyze survival data from the National Surgical Adjuvant Breast and Bowel Project (NSABP) Protocol B-09 to demonstrate our method. Simulations are used to assess the statistical properties of this proposed methodology. We propose a new method in survival analysis, which is an area of statistics that is commonly used to assess prognoses of patients or participants in large public health studies. Our proposed method has public health significance because it could potentially facilitate a more refined assessment of the effect of biological and clinical markers on the survival times of different patient populations.

The dopamine transporter gene is an untranslated polymorphic region, which consists of a replication of 40-base pairs. The locus of this 3 variable number tandem repeat (VNTR) polymorphism is on 5p15.3 and repeats from 3 to 13 times. In most populations, the most common alleles are 9 and 10. The distribution of the dopamine transporter genotypes also varies among races. These genotypes have been shown to be associated with different conditions of health such as smoking status, obesity and food intake. Nine-carriers have been associated with late initiation of smoking. Homozygous for SCL6A3 10 are related to have higher concentration of dopamine transporter protein and to have lower postsynaptic concentration of dopamine. In this paper, the role of the SCL6A3 genotypes and allele carriers are investigated in a sample of women smokers willing to quit smoking who are concerned with postcessation weight gain. Because of the small number of women carrying alleles other than 9 or 10 allele, the sample size was limited to three genotypes. The main purpose of this work is to test departure from Hardy-Weinberg Equilibrium. The result shows that the proportions of the genotype were p^2, 2pq, and q^2; therefore, this gene is in Hardy-Weinberg Equilibrium. The genotype proportions in Caucasian women were similar to those previously reported in European-Caucasian women, and the proportions in African-American women were similar to previously reported literature values among African-American. These findings could have public health relevance in smoking cessation programs.

Genetic association studies have an important role in public health because they help us understand the biological basis of conditions (e.g. diabetes, obesity) that have important public health implications. They can help us develop and direct both treatments and prevention activities. As both Type II diabetes and obesity tend to run in families, it is reasonable to want to ascertain whether a genetic association or linkage exists between a particular allele or alleles and these conditions. Genetic association studies are, generally, the preferred method for detecting genes that are causal variants of complex diseases like diabetes because they have greater power to detect alleles that are susceptible to disease. However, the Case control genetic association studies are known to be prone to false positive associations in the presence of population stratification. We hypothesize that assortative mating in a given population can lead to a form of population stratification and subsequently false positives. We hypothesize that assortative mating in a given population can lead to a form of population stratification and subsequently false positives. We also investigate the role of gene-gene interactions in the presence of assortative mating in producing spurious results. These hypotheses are tested via studies on 10,000 simulated individuals. Our results show that assortative mating does lead to a greater than expected number of false positives as compared to a situation where there is no assortative mating. Our tests on the role of gene-gene interactions also suggest that they contribute to false positives in the presence of assortative mating.

The level of physical activity is important for maintenance of good health. Research has demonstrated that virtually all individuals can benefit from physical activities which have been shown to reduce the morbidity from many chronic diseases, like cardiovascular disease and diabetes. Therefore, understanding the trend in activity level from adolescence to young adulthood is very important for public health study. The purpose of this thesis is to describe the natural history of participation in leisure time physical activity from adolescence to young adulthood. The study data are from the University of Pittsburgh Physical Activity Study (PittPAS), which recorded physical activities of 1245 high school students over a period of 14 years. Two longitudinal growth models, a latent growth curve (LGC) model and a random coefficient model are applied to characterize the changes in activity hours per week (HRWK) as well as the effects of sex, race, and grade on these changes. Our analysis results show: Male students are more physically active and have the larger decline rate than Female students; White students are more active, and also have the larger decline rate than Black students; Students from the lower grades spend more time in physical activity and also have the larger decline rate than students in the higher grades. Through analyzing the above physical activity, we also investigate the similarities and differences of LGC models and random coefficient models, such as both models share the same objectives. The LGC model is a multivariate approach, while random coefficient model is a univariate one in terms of the dependent variables. Random coefficient model does not require time-structure data and allows the explanatory variable 'time' to take on different values for each subject. Thus, the random coefficient model has the advantage to handle large amount of missing and irregular data acquired in non-uniform time occasions. Since our study data have a large amount of missing observations and are non-uniformly acquired, random coefficient model is more appropriate in characterizing the changes of HRWK.

Objective: To investigate the relationship between the area under the Receiver Operating Characteristic curve (AUC) of the propensity model for exposure and the accuracy of the estimated effect of the exposure on the outcome of interest. Methods: A Monte Carlo simulation study was performed where multiple realizations of three binary variables: outcome, exposure of interest and a covariate were repeatedly generated from the distribution determined by the parameters of the propensity and main models and the prevalence of the exposure. Propensity model was a logistic regression with the exposure of interest as a dependent variable and a single covariate as an independent variable. Main model was a logistic regression with outcome as a dependent variable, exposure of interest and covariate as independent variables. A total of 500 simulations were performed for each considered combination of the model parameters and the prevalence of the exposure. AUC was estimated from the probabilities predicted by the propensity score model. The accuracy of the estimated effect of exposure was primarily assessed with the square root of Mean Square Error (RMSE); the fifth and ninety-fifth percentile of the empirical distribution of the estimator were used to illustrate a range of not unlikely deviations from the true value. Results: The square root of Mean Square Error of the estimated effect of exposure increases as AUC increases from 0.6 to 0.9. Varying values for parameters of the propensity score model or the main effect model does not change the direction of this trend. As the proportion of exposed subjects changes away from 0.5 the RMSE increases, but the effect of AUC on RMSE remains approximately the same. Similarly, as sample size changes from 50 to 100 or 200, the RMSE of effect estimate decreases on average, but the effect of AUC on RMSE remains approximately the same. Also, the rate of change in RMSE increases with increasing AUC; the rate is the lowest when AUC changes from 0.6 to 0.7 and is highest when AUC changes from 0.8 to 0.9. Conclusions: The AUC of the propensity score model for exposure provides a single, relatively easy to compute, and suitable for various kind of data statistic, which can be used as an important indicator of the accuracy of the estimated effect of exposure on the outcome of interest. The public health importance is that it can be considered as an alternative to the previously suggested (Rubin, 2001) simultaneous consideration of the conditions of closeness of means and variances of the propensity scores in the different exposure groups. Our simulations indicate that the estimated effect of exposure is highly unreliable if AUC of the propensity model is larger than 0.8; at the same time AUCs of less than 0.7 are not associated with any substantial increase of inaccuracy of the estimated effect of exposure.

This dissertation is motivated by data generated from a genetic association study of congenital heart defects in Down syndrome (DS). Congenital heart defects are among the most common abnormalities seen at birth. The genetic basis for most congenital heart defects is unknown. One severe form of congenital heart defect, atrioventricular septal defect (AVSD), is highly associated with DS. This makes the DS population a useful tool for discovering of genes that are associated with this specific form of congenital heart defect. Discovering genes that influence risk of AVSD will lead to a better understanding of heart development and of the etiology of these defects. This in turn can lead eventually to improved public health through better screening, prevention, and treatment strategies. Family trios were collected for the Down syndrome heart study. This dissertation discusses statistical issues raised in genetic association studies using family trio data, including the genotype calling problem (i.e. how to generate genotype data from the raw data produced by high-throughput SNP arrays) and analysis strategies. Although the motivating dataset involves trisomic individuals, we developed statistical methods both for disomic and trisomic data. For the genotype-calling problem, we generated two genotype calling methods specifically for disomic family trio data. The first method is an ad-hoc modification of the K-means clustering algorithm that incorporates family information. The second is a likelihood-based method that combines the mixture model approach with a pedigree likelihood. These two methods out-performed existing methods, which ignore the family information, both in simulation studies and a real data analysis. We also extended these two methods to trisomic trio data. With regard to analysis strategies, we discussed alternative analysis methods for trio designs, particularly for the combination of case trios and control trios that we have in the Down syndrome data. We derived likelihood models that help explain the differences among some published methods. We also proposed an extension of a combined likelihood-based method proposed by Epstein and others for analysis of case trios plus independent controls to our design of case and control trios.

The Belmont Report (1979) presents ethical principles governing clinical research: respect for persons, beneficence, and justice. This dissertation attempts to improve beneficence, in particular, in early stage clinical trials, in three directions. First, we develop a "dose-choice control panel" (DCCP) computer program. Inputs are complete population information and patient utilities. DCCP produces optimal dose assignment decisions, and helps users to explore how the population parameters and utilities affect the dose recommendation. Second, we present a new adaptive Bayesian method for dose-finding in phase I clinical trials based on both response and toxicity. Although clinical responses are rare in cancer trials, biological responses may be common and may help decide how aggressive a phase I escalation should be. The model assumes that response and toxicity events happen depending on respective dose thresholds for the individual, assuming that the thresholds jointly follow a bivariate log-normal distribution or a mixture. The design utilizes prior information about the population threshold distribution as well as accumulated data. The next dose is assigned to maximize expected utility integrated over the current posterior distribution. The design is evaluated in a setting inspired by the Gleevec story, with population parameters equaling estimates from early Gleevec trials. This exercise provides evidence for the value of the use of the proposed design for future clinical trials. Third, we propose an adaptive Bayesian design based on a hierarchical pharmacokinetics/pharmacodynamic (PK/PD) model, incorporating prior knowledge and/or patient-specific measurements related to PK/PD processes. Because genetic variations or drug co-administration can lead to huge inter-individual differences in drug efficacy and toxicity, it is desirable to individualize chemotherapy dosage. Those factors influencing drug metabolism and clearance are expected to affect all PD processes downstream, leading to efficacy and toxicity outcomes, while other genetic variations or drug co-administration may affect only one PD process. Application of the design to the Gleevec and Irinotecan settings is encouraging with regard to patient protection and accuracy of estimates. This work could improve public health by providing more accurate answers quicker, and by encouraging accrual through explicit consideration of what is best for each individual patient.

Variance components linkage analysis is a powerful method to detect quantitative trait loci (QTLs) for complex diseases. It has the advantages of easy applicability to large extended pedigrees and provides a good flexible framework to accommodate more complicated models like gene-gene, gene-environmental interactions.</br></br> This dissertation consists of two major parts. In the first part, I propose two approaches for deriving relative-to-relative covariances that are indispensable for expanding the applications of standard variance components linkage approach to more complicated genetic models such as those involving genomic imprinting. In the first approach, I extend 'Li and Sacks' ITO method to model ordered genotypes and derive some generalized linear functions of the extended transition matrices. I demonstrate the wide applicability of this extension by applying it to calculate the covariance in unilineal and bilineal relatives under genomic imprinting.</br></br> In the second approach, I derive a general formula for calculating the genetic covariance using ordered genotypes for any type of relative pair, which does not have the limitation of extended ITO method to biallelic loci and to unilineal and bilineal relatives. I also propose a recursive algorithm to calculate necessary coefficients in the formula, which opens up the possibility of calculating even inbred relative-to-relative covariance. In the second part of my dissertation, I discuss linkage evidence for susceptibility loci for adiposity-related phenotypes in the Samoan population, an extensive summary of our multicenter study "Genome-scan for Obesity Susceptibility Loci in Samoans". Obesity, BMI greater than or equal to 30 kg/m^2, in the U.S. has become a major and serious public health problem, affecting 33% of adults in 2002. Obesity increases risks for serious diet-related diseases, such as cardiovascular disease, type-2 diabetes, and certain forms of cancers. Obesity is a typical multi-factorial disease with overwhelming evidence of genetic effects, yet their roles in obesity are largely unknown. Our current research findings will help further understand the whole picture of the genetics of obesity, which may have great influence on early prevention and later interventions of human obesity, making it a fundamentally important contribution to public health.

Longitudinal studies, which are characterized by repeated measures taken on individual subjects, play a major role in the field of public health. One area of research that has been particularly impacted by longitudinal studies is bipolar disorder. Patients afflicted with this illness often suffer from occupational as well as social disruptions in their normal functioning, not to mention the burden this disease creates on both families of bipolar patients as well as the nations economy. One factor believed to be involved in the pathogenesis of bipolar disorder is circadian abnormalities, such as disturbances in sleep and appetite patterns. One such source of circadian rhythm disruption is brought about by the semi-annual occurrence of daylight savings time (DST). While research has shown that DST may have detrimental, though temporary, effects on circadian functioning in normal populations, little has been done to investigate the effects of DST in patients with bipolar disorder. Due to the high cost and disturbance in daily functioning that bipolar patients frequently experience, it is of public health importance to further investigate this disorder so that more effective ways to manage it may be discovered. A population-averaged approach was taken using GEE modeling on the Global Assessment of Functioning (GAF) outcome, and multinomial logistic regression modeling on the Clinical Global Impressions (CGI). This thesis reviews the literature on methods for analyzing longitudinal data in bipolar research, including both GEE and multinomial regression modeling; also reviewed are two commonly used mental illness rating scales: the GAF and the CGI. A subset of data from a bipolar disorder treatment and maintenance trial (7,315 repeated observations on 1175 patients) was used to conduct the present investigation. The results indicate that while DST changes are significantly associated with changes in clinical symptom severity, the magnitude of these differences is relatively small.

The Three Rivers area of Pittsburgh, Pennsylvania has more combined sewer overflow (CSO) release points than any other city in the United States. CSOs and sanitary sewer overflows (SSOs) release untreated waste directly into receiving water during wet weather events such as rain or snow. A wide range of estrogenic agents is contained in municipal wastewater, including pharmaceutical estrogens, plastic additives, pesticides and detergent breakdown products such as nonyl-phenol. The goal of this analysis was to examine estrogenicity of channel catfish fillet tissue in areas significantly impaired by CSO/SSOs compared to store-bought catfish and catfish from up-river areas on the Allegheny River that are less impacted. Estrogenicity was based on the ability of catfish fillet tissue to proliferate MCF7 human breast cancer cells. Cell proliferation was quantified using a serial dilution assay. Replicate values for each fish at each dilution were analyzed using a random intercept model. Area effects were quantified in terms of absolute and relative differences, controlling for background. In this study, cell proliferation is higher for catfish sampled from the most contaminated CSO/SSO sites than for catfish sampled from areas on the Allegheny with fewer CSOs/SSOs. The risk information concerning cumulative estrogenicity in channel catfish, in this study may provide a linkage between the ecological compounds contained in wastewaters and human health. Estradiol equivalents could be constructed from the estrogenicity index developed in this paper. These findings are significant to public health because they could help to estimate the risk of estrogenic exposure posed to those who consume channel catfish from the Three Rivers Area of Pittsburgh. The findings could also help describe the impact of estrogenic exposure in wildlife.