A BAYESIAN APPROACH TO DOSE-RESPONSE ASSESSMENT AND DRUG-DRUG INTERACTION ANALYSIS: APPLICATION TO IN VITRO STUDIES

The considerable search for synergistic agents in cancer research is motivated by the therapeutic benefits achieved by combining anti-cancer agents. Synergistic agents make it possible to reduce dosage while maintaining or enhancing a desired effect. Other favorable outcomes of synergistic agents include reduction in toxicity and minimizing or delaying drug resistance. Dose-response assessment and drug-drug interaction analysis play an important part in the drug discovery process, however analysis are often poorly done. This dissertation is an effort to notably improve dose-response assessment and drug-drug interaction analysis. The most commonly used method in published analysis is the Median-Effect Principle/Combination Index method (Chou and Talalay, 1984). The Median-Effect Principle/Combination Index method leads to inefficiency by ignoring important sources of variation inherent in dose-response data and discarding data points that do not fit the Median-Effect Principle. Previous work has shown that the conventional method yields a high rate of false positives (Boik, Boik, Newman, 2008; Hennessey, Rosner, Bast, Chen, 2010) and, in some cases, low power to detect synergy. There is a great need for improving the current methodology. We developed a Bayesian framework for dose-response modeling and drug-drug interaction analysis. First, we developed a hierarchical meta-regression dose-response model that accounts for various sources of variation and uncertainty and allows one to incorporate knowledge from prior studies into the current analysis, thus offering a more efficient and reliable inference. Second, in the case that parametric dose-response models do not fit the data, we developed a practical and flexible nonparametric regression method for meta-analysis of independently repeated dose-response experiments. Third, and lastly, we developed a method, based on Loewe additivity that allows one to quantitatively assess interaction between two agents combined at a fixed dose ratio. The proposed method makes a comprehensive and honest account of uncertainty within drug interaction assessment. Extensive simulation studies show that the novel methodology improves the screening process of effective/synergistic agents and reduces the incidence of type I error. We consider an ovarian cancer cell line study that investigates the combined effect of DNA methylation inhibitors and histone deacetylation inhibitors in human ovarian cancer cell lines. The hypothesis is that the combination of DNA methylation inhibitors and histone deacetylation inhibitors will enhance antiproliferative activity in human ovarian cancer cell lines compared to treatment with each inhibitor alone. By applying the proposed Bayesian methodology, in vitro synergy was declared for DNA methylation inhibitor, 5-AZA-2'-deoxycytidine combined with one histone deacetylation inhibitor, suberoylanilide hydroxamic acid or trichostatin A in the cell lines HEY and SKOV3. This suggests potential new epigenetic therapies in cell growth inhibition of ovarian cancer cells.

Cost and power analysis of linkage disequilibrium methods for locating genes influencing quantitative traits in humans

Linkage disequilibrium methods can be used to find genes influencing quantitative trait variation in humans. Linkage disequilibrium methods can require smaller sample sizes than linkage equilibrium methods, such as the variance component approach to find loci with a specific effect size. The increase in power is at the expense of requiring more markers to be typed to scan the entire genome. This thesis compares different linkage disequilibrium methods to determine which factors influence the power to detect disequilibrium. The costs of disequilibrium and equilibrium tests were compared to determine whether the savings in phenotyping costs when using disequilibrium methods outweigh the additional genotyping costs.^ Nine linkage disequilibrium tests were examined by simulation. Five tests involve selecting isolated unrelated individuals while four involved the selection of parent child trios (TDT). All nine tests were found to be able to identify disequilibrium with the correct significance level in Hardy-Weinberg populations. Increasing linked genetic variance and trait allele frequency were found to increase the power to detect disequilibrium, while increasing the number of generations and distance between marker and trait loci decreased the power to detect disequilibrium. Discordant sampling was used for several of the tests. It was found that the more stringent the sampling, the greater the power to detect disequilibrium in a sample of given size. The power to detect disequilibrium was not affected by the presence of polygenic effects.^ When the trait locus had more than two trait alleles, the power of the tests maximized to less than one. For the simulation methods used here, when there were more than two-trait alleles there was a probability equal to 1-heterozygosity of the marker locus that both trait alleles were in disequilibrium with the same marker allele, resulting in the marker being uninformative for disequilibrium.^ The five tests using isolated unrelated individuals were found to have excess error rates when there was disequilibrium due to population admixture. Increased error rates also resulted from increased unlinked major gene effects, discordant trait allele frequency, and increased disequilibrium. Polygenic effects did not affect the error rates. The TDT, Transmission Disequilibrium Test, based tests were not liable to any increase in error rates.^ For all sample ascertainment costs, for recent mutations ($<$100 generations) linkage disequilibrium tests were less expensive than the variance component test to carry out. Candidate gene scans saved even more money. The use of recently admixed populations also decreased the cost of performing a linkage disequilibrium test. ^

Detecting genetic and nutritional lung cancer risk factors related to folate metabolism using Bayesian generalized linear models

Complex diseases, such as cancer, are caused by various genetic and environmental factors, and their interactions. Joint analysis of these factors and their interactions would increase the power to detect risk factors but is statistically. Bayesian generalized linear models using student-t prior distributions on coefficients, is a novel method to simultaneously analyze genetic factors, environmental factors, and interactions. I performed simulation studies using three different disease models and demonstrated that the variable selection performance of Bayesian generalized linear models is comparable to that of Bayesian stochastic search variable selection, an improved method for variable selection when compared to standard methods. I further evaluated the variable selection performance of Bayesian generalized linear models using different numbers of candidate covariates and different sample sizes, and provided a guideline for required sample size to achieve a high power of variable selection using Bayesian generalize linear models, considering different scales of number of candidate covariates. ^ Polymorphisms in folate metabolism genes and nutritional factors have been previously associated with lung cancer risk. In this study, I simultaneously analyzed 115 tag SNPs in folate metabolism genes, 14 nutritional factors, and all possible genetic-nutritional interactions from 1239 lung cancer cases and 1692 controls using Bayesian generalized linear models stratified by never, former, and current smoking status. SNPs in MTRR were significantly associated with lung cancer risk across never, former, and current smokers. In never smokers, three SNPs in TYMS and three gene-nutrient interactions, including an interaction between SHMT1 and vitamin B12, an interaction between MTRR and total fat intake, and an interaction between MTR and alcohol use, were also identified as associated with lung cancer risk. These lung cancer risk factors are worthy of further investigation.^

Assessment of interrater agreement using a binomial-based statistic: K(bin)

This project develops K(bin), a relatively simple, binomial based statistic for assessing interrater agreement in which expected agreement is calculated a priori from the number of raters involved in the study and number of categories on the rating tool. The statistic is logical in interpretation, easily calculated, stable for small sample sizes, and has application over a wide range of possible combinations from the simplest case of two raters using a binomial scale to multiple raters using a multiple level scale.^ Tables of expected agreement values and tables of critical values for K(bin) which include power to detect three levels of the population parameter K for n from 2 to 30 and observed agreement $\ge$.70 calculated at alpha =.05,.025, and.01 are included.^ An example is also included which describes the use of the tables for planning and evaluating an interrater reliability study using the statistic, K(bin). ^

An evaluation of a community-based program for homeless adults with mental disorders and comorbid alcohol drug and mental disorders

Limited research has been conducted evaluating programs that are designed to improve the outcomes of homeless adults with mental disorders and comorbid alcohol, drug and mental disorders. This study conducted such an evaluation in a community-based day treatment setting with clients of the Harris County Mental Health and Mental Retardation Authority's Bristow Clinic. The study population included all clients who received treatment at the clinic for a minimum of six months between January 1, 1995 and August 31, 1996. An electronic database was used to identify clients and to track their program involvement. A profile was developed of the study participants and their level of program involvement included an examination of the amount of time spent in clinical, social and other interventions, the type of interventions encountered and the number of interventions encountered. Results were analyzed to determine whether social, demographic and mental history affected levels of program involvement and the effects of the levels of program involvement on housing status and psychiatric functioning status.^ A total of 101 clients met the inclusion criteria. Of the 101 clients, 96 had a mental disorder, and five had comorbidity. Due to the limited numbers of participants with comorbidity, only those with mental disorders were included in the analysis. The study found the Bristow Clinic population to be primarily single, Black, male, between the ages of 31 and 40 years, and with a gross family income of less than $4,000. There were more persons residing on the streets at entry and at six months following treatment than in any other residential setting. The most prevalent psychiatric diagnoses were depressive disorders and schizophrenia. The Global Assessment of Functioning (GAF) scale which was used to determine the degree of psychiatric functioning revealed a modal GAF score of 31--40 at entry and following six months in treatment. The study found that the majority of clients spent less than 17 hours in treatment, had less than 51 encounters and had clinical, social, and other encounters. In regard to social and demographic factors and levels of program involvement, there were statistically significant associations between gender and ethnicity and the types of interventions encountered as well as the number of interventions encountered. There was also a statistically significant difference between the amount of time spent in clinical interventions and gender. Relative to outcomes measured, the study found female gender to be the only background variable that was significantly associated with improved housing status and the female gender and previous MHMRA involvement to be statistically associated with improvement in GAF score. The total time in other (not clinical or social) interventions and the total number of encounters with other interventions were also significantly associated with improvement in housing outcome. The analysis of previous services and levels of program involvement revealed significant associations between time spent in social and clinical interventions and previous hospitalizations and previous MHMRA involvement.^ Major limitations of this study include the small sample size which may have resulted in very little power to detect differences and the lack of generalizability of findings due to site locations used in the study. Despite these limitations, the study makes an important contribution to the literature by documenting the levels of program involvement and the social and demographic factors necessary to produce outcomes of improved housing status and psychiatric functioning status. ^

Community participation in health services

This study critically analyzes and synthesizes community participation (CP) theory across disciplines, defining and beginning to map out the elements of CP according to a preliminary framework of structure, process, intermediate outcomes, and ultimate outcomes. The first study component sought to determine the impact of Sight N' Soul, a CP project utilizing neighborhood health workers (NHWs), on appointment missing in an indigent urban African-American population. It found that persons entering the vision care system through contact with an NEW were about a third less likely to miss an appointment than those persons entering the system through some other avenue. While theory in this area remains too poorly developed to hypothesize causal relationships between structure, process, and outcomes, a summary of the elements of Sight N' Soul's structure and process both developed the preliminary framework and serves as a first step to mapping these relationships. The second component of the study uncovered the elements of structure and process that may contribute to a sustained egalitarian partnership between community people and professionals, a CP program called Project HEAL. Elements of Project HEAL's structure and process included a shared belief in the program; spirituality; contribution, ownership, and reciprocation; a feeling of family; making it together; honesty, trust, and openness about conflict; the inevitability of uncertainty and change; and the guiding interactional principles of respect; love, care, and compassion; and personal responsibility. The third component analyzed the existing literature, identifying and addressing gaps and inconsistencies and highlighting areas needing more highly developed ethical analysis. Focal issues include the political, economic, and historical context of CP; the power of naming; the issue of purpose; the nature of community; the power to muster and allocate resources; and the need to move to a systems view of health and well-being, expanding our understanding of the universe of potential outcomes of CP, including iatrogenic outcomes. Intermediate outcomes might include change in community, program, and individual capacity, as well as improved health care delivery. Ultimate outcomes include increased positive interdependencies and opportunities for contribution; improved mental, physical, and spiritual health; increased social justice; and decreased exploitation. ^

A full pedigree based method for the statistical assessment of genetic anticipation

Genetic anticipation is defined as a decrease in age of onset or increase in severity as the disorder is transmitted through subsequent generations. Anticipation has been noted in the literature for over a century. Recently, anticipation in several diseases including Huntington's Disease, Myotonic Dystrophy and Fragile X Syndrome were shown to be caused by expansion of triplet repeats. Anticipation effects have also been observed in numerous mental disorders (e.g. Schizophrenia, Bipolar Disorder), cancers (Li-Fraumeni Syndrome, Leukemia) and other complex diseases. ^ Several statistical methods have been applied to determine whether anticipation is a true phenomenon in a particular disorder, including standard statistical tests and newly developed affected parent/affected child pair methods. These methods have been shown to be inappropriate for assessing anticipation for a variety of reasons, including familial correlation and low power. Therefore, we have developed family-based likelihood modeling approaches to model the underlying transmission of the disease gene and penetrance function and hence detect anticipation. These methods can be applied in extended families, thus improving the power to detect anticipation compared with existing methods based only upon parents and children. The first method we have proposed is based on the regressive logistic hazard model. This approach models anticipation by a generational covariate. The second method allows alleles to mutate as they are transmitted from parents to offspring and is appropriate for modeling the known triplet repeat diseases in which the disease alleles can become more deleterious as they are transmitted across generations. ^ To evaluate the new methods, we performed extensive simulation studies for data simulated under different conditions to evaluate the effectiveness of the algorithms to detect genetic anticipation. Results from analysis by the first method yielded empirical power greater than 87% based on the 5% type I error critical value identified in each simulation depending on the method of data generation and current age criteria. Analysis by the second method was not possible due to the current formulation of the software. The application of this method to Huntington's Disease and Li-Fraumeni Syndrome data sets revealed evidence for a generation effect in both cases. ^

Environmental sustainability and the human element: Decision making in National Cancer Institute-designated cancer centers and Practice Greenhealth subscribing institutions

Background. Various aspects of sustainability have taken root in the hospital environment; however, decisions to pursue sustainable practices within the framework of a master plan are not fully developed in National Cancer Institute (NCI) -designated cancer centers and subscribing institutions to the Practice Greenhealth (PGH) listserv.^ Methods. This cross sectional study was designed to identify the organizational characteristics each study group pursed to implement sustainability practices, describe the barriers they encountered and reasons behind their choices for undertaking certain sustainability practices. A web-based questionnaire was pilot tested, and then sent out to 64 NCI-designated cancer centers and 1638 subscribing institutions to the PGH listserv.^ Results. Complete responses were received from 39 NCI-designated cancer centers and 58 subscribing institutions to the PGH listserv. NCI-designated cancer centers reported greater progress in integrating sustainability criteria into design and construction projects than hospitals of institutions subscribing to the PHG listserv (p-value = <0.05). Statistically significant differences were also identified between these two study groups in undertaking work life options, conducting energy usage assessments, developing energy conservation and optimization plans, implementing solid waste and hazardous waste minimization programs, using energy efficient vehicles and reporting sustainability progress to external stakeholders. NCI-designated cancer centers were further along in implementing these programs (p-value = <0.05). In comparing the self-identified NCI-designated cancer centers to centers that indicated they were both and NCI and PGH, the later had made greater progress in using their collective buying power to pursue sustainable purchasing practices within the medical community (p-value = <0.05). In both study groups, recycling programs were well developed.^ Conclusions. Employee involvement was viewed as the most important reason for both study groups to pursue recycling initiatives and incorporated environmental criteria into purchasing decisions. A written sustainability commitment did not readily translate into a high percentage that had developed a sustainability master plan. Coordination of sustainability programs through a designated sustainability professional was not being undertaken by a large number of institutions within each study group. This may be due to the current economic downturn or management's attention to the emerging health care legislation being debated in congress. ^ Lifecycle assessments, an element of a carbon footprint, are seen as emerging areas of opportunity for health care institutions that can be used to evaluate the total lifecycle costs of products and services.^

The association between CD4+ lymphocyte count and measures of body composition in HIV-infected men

Purpose. This project was designed to describe the association between wasting and CD4 cell counts in HIV-infected men in order to better understand the role of wasting in progression of HIV infection.^ Methods. Baseline and prevalence data were collected from a cross-sectional survey of 278 HIV-infected men seen at the Houston Veterans Affairs Medical Center Special Medicine Clinic, from June 1, 1991 to January 1, 1994. A follow-up study was conducted among those at risk, to investigate the incidence of wasting and the association between wasting and low CD4 cell counts. Wasting was described by four methods. Z-scores for age-, sex-, and height-adjusted weight; sex-, and age-adjusted mid-arm muscle circumference (MAMC); and fat-free mass; and the ratio of extra-cellular mass (ECM) to body-cell mass (BCM) $>$ 1.20. FFM, ECM, and BCM were estimated from bioelectrical impedance analysis. MAMC was calculated from triceps skinfold and mid-arm circumference. The relationship between wasting and covariates was examined with logistic regression in the cross-sectional study, and with Poisson regression in the follow-up study. The association between death and wasting was examined with Cox's regression.^ Results. The prevalence of wasting ranged from 5% (weight and ECM:BCM) to almost 14% (MAMC and FFM) among the 278 men examined. The odds of wasting, associated with baseline CD4 cell count $<$200, was significant for each method but weight, and ranged from 4.6 to 12.7. Use of antiviral therapy was significantly protective of MAMC, FFM and ECM:BCM (OR $\approx$ 0.2), whereas the need for antibacterial therapy was a risk (OR 3.1, 95% CI 1.1-8.7). The average incidence of wasting ranged from 4 to 16 per 100 person-years among the approximately 145 men followed for 160 person-years. Low CD4 cell count seemed to increase the risk of wasting, but statistical significance was not reached. The effect of the small sample size on the power to detect a significant association should be considered. Wasting, by MAMC and FFM, was significantly associated with death, after adjusting for baseline serum albumin concentration and CD4 cell count.^ Conclusions. Wasting by MAMC and FFM were strongly associated with baseline CD4 cell counts in both the prevalence and incidence study and strong predictors of death. Of the two methods, MAMC is convenient, has available reference population data, may be the most appropriate for assessing the nutritional status of HIV-infected men. ^

Logistic regression with Markov chains as covariates

The tobacco-specific nitrosamine 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanone (NNK) is an obvious carcinogen for lung cancer. Since CBMN (Cytokinesis-blocked micronucleus) has been found to be extremely sensitive to NNK-induced genetic damage, it is a potential important factor to predict the lung cancer risk. However, the association between lung cancer and NNK-induced genetic damage measured by CBMN assay has not been rigorously examined. ^ This research develops a methodology to model the chromosomal changes under NNK-induced genetic damage in a logistic regression framework in order to predict the occurrence of lung cancer. Since these chromosomal changes were usually not observed very long due to laboratory cost and time, a resampling technique was applied to generate the Markov chain of the normal and the damaged cell for each individual. A joint likelihood between the resampled Markov chains and the logistic regression model including transition probabilities of this chain as covariates was established. The Maximum likelihood estimation was applied to carry on the statistical test for comparison. The ability of this approach to increase discriminating power to predict lung cancer was compared to a baseline "non-genetic" model. ^ Our method offered an option to understand the association between the dynamic cell information and lung cancer. Our study indicated the extent of DNA damage/non-damage using the CBMN assay provides critical information that impacts public health studies of lung cancer risk. This novel statistical method could simultaneously estimate the process of DNA damage/non-damage and its relationship with lung cancer for each individual.^

Bayesian Adaptive Designs for Early Phase Clinical Trials

My dissertation focuses mainly on Bayesian adaptive designs for phase I and phase II clinical trials. It includes three specific topics: (1) proposing a novel two-dimensional dose-finding algorithm for biological agents, (2) developing Bayesian adaptive screening designs to provide more efficient and ethical clinical trials, and (3) incorporating missing late-onset responses to make an early stopping decision. Treating patients with novel biological agents is becoming a leading trend in oncology. Unlike cytotoxic agents, for which toxicity and efficacy monotonically increase with dose, biological agents may exhibit non-monotonic patterns in their dose-response relationships. Using a trial with two biological agents as an example, we propose a phase I/II trial design to identify the biologically optimal dose combination (BODC), which is defined as the dose combination of the two agents with the highest efficacy and tolerable toxicity. A change-point model is used to reflect the fact that the dose-toxicity surface of the combinational agents may plateau at higher dose levels, and a flexible logistic model is proposed to accommodate the possible non-monotonic pattern for the dose-efficacy relationship. During the trial, we continuously update the posterior estimates of toxicity and efficacy and assign patients to the most appropriate dose combination. We propose a novel dose-finding algorithm to encourage sufficient exploration of untried dose combinations in the two-dimensional space. Extensive simulation studies show that the proposed design has desirable operating characteristics in identifying the BODC under various patterns of dose-toxicity and dose-efficacy relationships. Trials of combination therapies for the treatment of cancer are playing an increasingly important role in the battle against this disease. To more efficiently handle the large number of combination therapies that must be tested, we propose a novel Bayesian phase II adaptive screening design to simultaneously select among possible treatment combinations involving multiple agents. Our design is based on formulating the selection procedure as a Bayesian hypothesis testing problem in which the superiority of each treatment combination is equated to a single hypothesis. During the trial conduct, we use the current values of the posterior probabilities of all hypotheses to adaptively allocate patients to treatment combinations. Simulation studies show that the proposed design substantially outperforms the conventional multi-arm balanced factorial trial design. The proposed design yields a significantly higher probability for selecting the best treatment while at the same time allocating substantially more patients to efficacious treatments. The proposed design is most appropriate for the trials combining multiple agents and screening out the efficacious combination to be further investigated. The proposed Bayesian adaptive phase II screening design substantially outperformed the conventional complete factorial design. Our design allocates more patients to better treatments while at the same time providing higher power to identify the best treatment at the end of the trial. Phase II trial studies usually are single-arm trials which are conducted to test the efficacy of experimental agents and decide whether agents are promising to be sent to phase III trials. Interim monitoring is employed to stop the trial early for futility to avoid assigning unacceptable number of patients to inferior treatments. We propose a Bayesian single-arm phase II design with continuous monitoring for estimating the response rate of the experimental drug. To address the issue of late-onset responses, we use a piece-wise exponential model to estimate the hazard function of time to response data and handle the missing responses using the multiple imputation approach. We evaluate the operating characteristics of the proposed method through extensive simulation studies. We show that the proposed method reduces the total length of the trial duration and yields desirable operating characteristics for different physician-specified lower bounds of response rate with different true response rates.

The epidemiology of left ventricular outflow tract obstruction defects in Texas, 2002-2008: An update and assessment of effect heterogeneity

Left ventricular outflow tract (LVOT) defects are an important group of congenital heart defects (CHDs) because of their associated mortality and long-term complications. LVOT defects include aortic valve stenosis (AVS), coarctation of aorta (CoA), and hypoplastic left heart syndrome (HLHS). Despite their clinical significance, their etiology is not completely understood. Even though the individual component phenotypes (AVS, CoA, and HLHS) may have different etiologies, they are often "lumped" together in epidemiological studies. Though "lumping" of component phenotypes may improve the power to detect associations, it may also lead to ambiguous findings if these defects are etiologically distinct. This is due to potential for effect heterogeneity across component phenotypes. ^ This study had two aims: (1) to identify the association between various risk factors and both the component (i.e., split) and composite (i.e., lumped) LVOT phenotypes, and (2) to assess the effect heterogeneity of risk factors across component phenotypes of LVOT defects. ^ This study was a secondary data analysis. Primary data were obtained from the Texas Birth Defect Registry (TBDR). TBDR uses an active surveillance method to ascertain birth defects in Texas. All cases of non complex LVOT defects which met our inclusion criteria during the period of 2002–2008 were included in the study. The comparison groups included all unaffected live births for the same period (2002–2008). Data from vital statistics were used to evaluate associations. Statistical associations between selected risk factors and LVOT defects was determined by calculating crude and adjusted prevalence ratio using Poisson regression analysis. Effect heterogeneity was evaluated using polytomous logistic regression. ^ There were a total of 2,353 cases of LVOT defects among 2,730,035 live births during the study period. There were a total of 1,311 definite cases of non-complex LVOT defects for analysis after excluding "complex" cardiac cases and cases associated with syndromes (n=168). Among infant characteristics, males were at a significantly higher risk of developing LVOT defects compared to females. Among maternal characteristics, significant associations were seen with maternal age > 40 years (compared to maternal age 20–24 years) and maternal residence in Texas-Mexico border (compared to non-border residence). Among birth characteristics, significant associations were seen with preterm birth and small for gestation age LVOT defects. ^ When evaluating effect heterogeneity, the following variables had significantly different effects among the component LVOT defect phenotypes: infant sex, plurality, maternal age, maternal race/ethnicity, and Texas-Mexico border residence. ^ This study found significant associations between various demographic factors and LVOT defects. While many findings from this study were consistent with results from previous studies, we also identified new factors associated with LVOT defects. Additionally, this study was the first to assess effect heterogeneity across LVOT defect component phenotypes. These findings contribute to a growing body of literature on characteristics associated with LVOT defects. ^

Network-based analysis of genome-wide scans of natural selection

The genomic era brought by recent advances in the next-generation sequencing technology makes the genome-wide scans of natural selection a reality. Currently, almost all the statistical tests and analytical methods for identifying genes under selection was performed on the individual gene basis. Although these methods have the power of identifying gene subject to strong selection, they have limited power in discovering genes targeted by moderate or weak selection forces, which are crucial for understanding the molecular mechanisms of complex phenotypes and diseases. Recent availability and rapid completeness of many gene network and protein-protein interaction databases accompanying the genomic era open the avenues of exploring the possibility of enhancing the power of discovering genes under natural selection. The aim of the thesis is to explore and develop normal mixture model based methods for leveraging gene network information to enhance the power of natural selection target gene discovery. The results show that the developed statistical method, which combines the posterior log odds of the standard normal mixture model and the Guilt-By-Association score of the gene network in a naïve Bayes framework, has the power to discover moderate/weak selection gene which bridges the genes under strong selection and it helps our understanding the biology under complex diseases and related natural selection phenotypes.^

Evaluation of the Hosmer -Lemeshow global goodness -of-fit statistic for mixed variable logistic regression models

The performance of the Hosmer-Lemeshow global goodness-of-fit statistic for logistic regression models was explored in a wide variety of conditions not previously fully investigated. Computer simulations, each consisting of 500 regression models, were run to assess the statistic in 23 different situations. The items which varied among the situations included the number of observations used in each regression, the number of covariates, the degree of dependence among the covariates, the combinations of continuous and discrete variables, and the generation of the values of the dependent variable for model fit or lack of fit.^ The study found that the $\rm\ C$g* statistic was adequate in tests of significance for most situations. However, when testing data which deviate from a logistic model, the statistic has low power to detect such deviation. Although grouping of the estimated probabilities into quantiles from 8 to 30 was studied, the deciles of risk approach was generally sufficient. Subdividing the estimated probabilities into more than 10 quantiles when there are many covariates in the model is not necessary, despite theoretical reasons which suggest otherwise. Because it does not follow a X$\sp2$ distribution, the statistic is not recommended for use in models containing only categorical variables with a limited number of covariate patterns.^ The statistic performed adequately when there were at least 10 observations per quantile. Large numbers of observations per quantile did not lead to incorrect conclusions that the model did not fit the data when it actually did. However, the statistic failed to detect lack of fit when it existed and should be supplemented with further tests for the influence of individual observations. Careful examination of the parameter estimates is also essential since the statistic did not perform as desired when there was moderate to severe collinearity among covariates.^ Two methods studied for handling tied values of the estimated probabilities made only a slight difference in conclusions about model fit. Neither method split observations with identical probabilities into different quantiles. Approaches which create equal size groups by separating ties should be avoided. ^

A simulation study of the effects of small center enrollment in multi -center clinical trials

Multi-center clinical trials are very common in the development of new drugs and devices. One concern in such trials, is the effect of individual investigational sites enrolling small numbers of patients on the overall result. Can the presence of small centers cause an ineffective treatment to appear effective when treatment-by-center interaction is not statistically significant?^ In this research, simulations are used to study the effect that centers enrolling few patients may have on the analysis of clinical trial data. A multi-center clinical trial with 20 sites is simulated to investigate the effect of a new treatment in comparison to a placebo treatment. Twelve of these 20 investigational sites are considered small, each enrolling less than four patients per treatment group. Three clinical trials are simulated with sample sizes of 100, 170 and 300. The simulated data is generated with various characteristics, one in which treatment should be considered effective and another where treatment is not effective. Qualitative interactions are also produced within the small sites to further investigate the effect of small centers under various conditions.^ Standard analysis of variance methods and the "sometimes-pool" testing procedure are applied to the simulated data. One model investigates treatment and center effect and treatment-by-center interaction. Another model investigates treatment effect alone. These analyses are used to determine the power to detect treatment-by-center interactions, and the probability of type I error.^ We find it is difficult to detect treatment-by-center interactions when only a few investigational sites enrolling a limited number of patients participate in the interaction. However, we find no increased risk of type I error in these situations. In a pooled analysis, when the treatment is not effective, the probability of finding a significant treatment effect in the absence of significant treatment-by-center interaction is well within standard limits of type I error. ^