Mediation analyses are common in the field of psychology or social science research. Mediators are variables that explain the mechanism of action forming the observed relationships between independent and dependent variables. The advantage of testing models is that it helps the researcher to construct the conceptual framework regarding the intercorrelation of variables of interest because pure relationships between independent and dependent variables are usually unlikely. This thesis was conducted to clarify whether the use of IT in MDS software would possibly influence the relationship between nurse staffing levels and quality of care in nursing homes. Literatures on the concepts of mediation and moderation effects were reviewed and analyses using STATA Sobel-Goodman tests were performed. Variables from three resources were used, including the use of IT in MDS software, three nurse staffing levels (RN, LPN, NA), and nursing home compare quality measures. Results of the Sobel-Goodman test indicated the indirect path for the use of IT was statistically significant in all cases of nurse staffing levels, and the tests of moderation effects showed the use of IT was a statistically significant moderator. Studies in this area can be further enhanced by taking into account more associated variables and by using extensive statistical mediation analysis. The public health importance for the present study is that it provides researchers with more information not only about the scientific evidences for exploring possible mediating variable effect from previous literatures but also about the statistical procedures for examining the statistical significance of an mediating effect.

Study of multiple drug usage is common in chemotherapy. Many research studies examine the effect multiple usage of these anticancer drugs. The study of these drugs together could help clarify the biological effects of agents that affect microtubules. This could guide future cancer treatment for patients especially these with breast cancer, an important public health issue. The main purpose of this paper is to apply and compare methods for examining the combined effects of anticancer drugs. We focus on Paclitaxel and Discodermolide. While in the process of modeling the single drug effect, we noticed that these anticancer drugs may be unable to kill all the cells even at high concentration, or that, some subpopulation is far less sensitive: there may be a mixed population of two types of cells with very different sensitivities. According to this description, one population of cell is very sensitive to the drug and the other one is nearly resistant to the drug. This model is difficult to fit. One approach is to fit the low-concentration and high-concentration portion of the dose-response curve separately, and then combine them. We constructed a simple method to predict the combined drug effects while adjusting for the assumption of mixed cell populations. We will summarize the commonly used methods for evaluating drug combination. Two models are commonly used as reference models to test the drug additive effect, which are dose-additive models and effect-additive models. For effect-additive models, we focus on the mutually exclusive and mutually non-exclusive additive effect models, and another additive effect model based on a population log kill mixture model.

Severe obesity (BMI >= 40 kg/m2) increases risk for many diseases (e.g., hypertension, diabetes). Bariatric surgery is the treatment with the greatest long-term success for severe obesity, sustaining weight loss and improving health. The number of bariatric surgeries has increased tremendously in recent years, although the percentage of adults eligible for surgery that receive the surgery is very small. Using the National Hospital Discharge Survey (1999-2004), patient, surgical, and hospital characteristics were analyzed over this six year time period. Using the National Health and Nutrition Examination Survey (NHANES), severely obese adults were compared to bariatric surgical patients with respect to age, sex, and health insurance for the years 2003 and 2004. Chi-square tests were used to test for differences in characteristics, and tests for trend were performed to test for temporal trends. Poisson regression was used to model length of hospital stay. From 1999 to 2004, most bariatric surgical patients were 30-49 years old, female, and were expected to pay with private insurance only. The most common comorbidities among bariatric surgical patients were hypertension (45.5%), sleep apnea (25.8%), and diabetes (21.8%). The majority of bariatric surgeries performed were high gastric bypasses. The number of bariatric surgeries increased more than 15-fold from 2000 to 2003. Length of hospital stay decreased from 1999 to 2004. Those who had gastroplasty were more likely to have a shorter hospital stay compared to other procedures. Only about 2.3% of severely obese individuals in the United States received bariatric surgery in 2003-2004. Males, younger and older adults, and those with public insurance were under-represented among bariatric surgical patients in 2003 and 2004. Because obesity is a major public health concern, discrepancies in characteristics of adults who are eligible for bariatric surgery compared to those receiving the surgery need to be addressed. Clinical practices should make sure everyone eligible is aware and well-informed of bariatric surgery. Healthcare policies should eventually allow every candidate the choice of having bariatric surgery, to improve health and reduce healthcare costs.

With the availability of tons of expression profiles, the need for meta-analyses to integrate different types of microarray data are obvious. For detection of differentially expressed genes, most of the current efforts are focused on comparing and evaluating gene lists obtained from each individual dataset. Several statistical meta-analysis methods, including Fisher's method and the random effects model, have been proposed but the statistcal framework is not often rigorously formulated for evaluation and comparison. In this dissertation, we attempt to formulate meta-analysis in genomic studies and develop systematic integration methods for two-class studies and multi-class studies. First, we tackle two often-asked biological questions: "Which genes are significant in one or more data sets?" and "Which genes are significant in all data sets?". We illustrate two statistical hypothesis settings and propose an optimally weighted statistic and compare to classical Fisher's equally weighted statistic and Tippett's minimum p-value statistic. Gener- ally there exists no uniformly most powerful test and we show that all of the three methods are admissible under simplified Gaussian assumptions. Furthermore, the optimally weighted statistic maintains advantages of the two classical methods and consistently performs well when the two methods perform poorly in respective extreme alternative hypotheses. The optimal weights provide natural categorization of the detected genes to facilitate further bio- logical investigation. We demonstrate the comparison and advantages of optimally weighted statistic by power analysis, simulations and two real data analyses of combining multi-tissue energy metabolism mouse data sets and prostate cancer data sets. Second, we propose two methods for identifying biomarkers of concordant patterns across studies, when there are more than two classes in each study. So far, published meta-analysis methods for this purpose mostly consider two-class comparison. Methods for combining multi-class studies and pattern concordance are rarely explored. We first consider a natural extension of combining p-values from the traditional ANOVA model. Since p-values from ANOVA do not reflect pattern information, we propose a multi-class correlation measure (MCC) under equal-weight bivariate mixture model to specifically seek for biomarkers of concordant patterns across a pair of studies. For both approaches, we focus to identify biomarkers differentially expressed in all studies (ANOVA-maxP, min-MCC). Both ANOVA- maxP and min-MCC are evaluated by simulation studies and by applications to a multi-tissue mouse metabolism data set and a multi-platform mouse trauma data set. Finally, we develop a "genomeMeta" R package. genomeMeta produces visualization and summarization of biomarkers identified by methods that we describe and propose in this dissertation. This work could improve public health by providing more effective methodologies for biomarker detection in the integration of multiple genomic studies.

Low ankle-arm index (AAI), a marker of peripheral arterial disease, predicts incident disability in older adults. Elevated pulse wave velocity (PWV), a measure of arterial stiffness, increases risk of cardiovascular events and mortality. However, the relationship between PWV and mobility has not been well characterized in older adults. To evaluate the potential local and systemic influences of vascular disease on physical function, we compared the associations of AAI and PWV with usual gait speed over eight years in the Health, Aging and Body Composition (Health ABC) Study. The study population consisted of 2,066 participants (mean age ± SD 73.6 ± 2.8 years, 48.1% men, 37.8% black) with valid PWV, AAI and gait speed data at baseline after exclusion of those with either revascularization or angioplasty of the leg arteries. Random coefficient models were used to evaluate the relationships of both subclinical vascular disease measures with gait speed decline over time. After adjustment for risk factors and comorbidities, each SD higher PWV was associated with a 0.008 m/s slower gait speed over the study period (SE 0.004, p = 0.03). Compared to high-normal AAI (greater than 1.3 - 1.4), low AAI and noncompressible arteries were each associated with slower gait speed over the study period: Beta (SE) = -0.10 (0.03), p less than 0.001 for AAI < 0.7, and Beta (SE) = -0.16 (0.04), p less than 0.001 for noncompressible arteries. The public health relevance of these findings is the potential contribution of subclinical vascular disease, particularly low AAI and noncompressible arteries, to poor physical function in aging.

Microarray technology has been used to predict patient prognosis and response to treatment, which is starting to have an impact on disease intervention and control, and is a significant measure for public health. However, the process has been hindered by a lack of adequate clinical validation. Since both microarray analyses and clinical trials are time and effort intensive, it is crucial to use accumulated inter-study data to validate information from individual studies. For over a decade, microarray data have been accumulated from different technologies. However, using data from one platform to build a model that robustly predicts the clinical characteristics of a new data from another platform remains a challenge. Current cross-platform gene prediction methods use only genes common to both training and test datasets. There are two main drawbacks to that approach: model reconstruction and loss of information. As a result, the prediction accuracy of those methods is unstable. In this dissertation, a module-based prediction strategy was developed to overcome the aforementioned drawbacks. By the current method, groups of genes sharing similar expression patterns rather than individual genes were used as the basic elements of the model predictor. Such an approach borrows information from genes¡¯ similarity when genes are absent in test data. By overcoming the problems of missing genes and noise across platforms, this method yielded robust predictions independent of information from the test data. The performance of this method was evaluated using publicly available microarray data. K-means clustering was used to group genes sharing similar expression profiles into gene modules and small modules were merged into their nearest neighbors. A univariate or multivariate feature selection procedures was applied and a representative gene from each selected module was identified. A prediction model was then constructed by the representative genes from selected gene modules. As a result, the prediction model is portable to any test study as long as partial genes in each module exist in the test study. The newly developed method showed advantages over the traditional methods in terms of prediction robustness to gene noise and gene mismatch issues in inter-study prediction.

This dissertation applies two statistical analysis techniques for neuroimaging data. The first aim of this dissertation is to apply randomized singular value decomposition for the approximation of the top singular vectors of the singular value decomposition of a large matrix. Randomized singular value decomposition is an algorithm that approximates the top singular vectors of a matrix given a subset of its rows or columns. Several statistical applications, such as partial least squares, require the computation of the singular value decomposition of a matrix. Statistical packages have built in functions that can compute the singular value decomposition of a matrix. In many applications, however, computing the SVD of a matrix is not possible because computer memory requirements associated with matrix allocation is high, limiting its use in high-dimensional settings. Neuroimaging studies can generate measurements for hundreds of thousands of voxels from an image. Therefore, performing partial least squares analysis on these datasets is not possible using statistical packages. Simulation studies showed that the randomized singular value decomposition method provides a good approximation of the top singular vectors and therefore a good approximation of the partial least squares summary scores. This method is significant for public health since it allows researchers to perform statistical analysis at a voxel level with only a sample of a large dataset. The second aim is to apply a thin plate spline method for spatial normalization of structural magnetic resonance images. Spatial normalization is the process of standardizing images of different subjects into the same anatomical space. The idea behind this procedure is to match each data volume from a subject to a template, so that specific anatomic structures will occupy the same voxels. Spatial normalization is a critical step in the analysis of brain imaging data since it produces the raw data for subsequent statistical analyses.

Age-related maculopathy (ARM) is a common cause of irreparable vision loss in industrialized countries. The disease is characterized by progressive loss of central vision making everyday tasks challenging. The etiology is complex and has both an environmental and a strong genetic components. The public health relevance of the work is to improve the understanding genetic causes in the disease etiology and ultimately to lead to better disease management and prevention. From my ARM work, I present four papers covering range of statistical approaches. The first paper presents fine-mapping efforts, using both linkage and association methods, under previously identified linkage peaks on chromosomes 1q31 and 10q26. We replicate the discovery of the complement factor H (CFH) gene on 1q31 and identify a novel locus, harboring three closely linked genes (PLEKHA1, LOC387715, and HTRA1), on 10q26. Both discoveries have been widely replicated. In the next paper I present meta-analysis of 11 CFH and 5 LOC387715 data sets. We also replicate these findings in two independent case-control cohorts, including one cohort, where ARM status was not a factor in the ascertainment. In the third paper we replicate discoveries of new complement related loci (C2 and CFB) on chromosome 19p13 as well as developing classification models based on SNPs from CFH, LOC387715, and C2. The last paper focuses on applying statistical techniques from the diagnostic medicine literature to ARM. We comment on the importance of understanding the difference and similarities between different goals of genetic studies: improving etiological understanding or finding variants that discriminate well between cases and controls. This work is particularly relevant today when there has been explosion in the availability of direct-to-consumer DNA tests. In addition to carrying out linkage and association analysis, I also have extended the statistical theory behind score-based linkage analyses for X chromosomal markers. This work has public health relevance because many complex common diseases have sex-specific differences, such as prevalence and age of onset. Modeling those appropriately with powerful and robust methods will bring an improved understanding of their genetic basis.

Endometrial cancer is the third most common cause of gynecologic cancer death and shows the largest overall survival difference (34%) between the races. The National Cancer Institute (NCI) Black/White Cancer Survival Study was a population-based study of racial differences in cancer survival. Endometrial cancer cases consisted of 149 black women, ages 20-79 years, residing in three selected metropolitan areas, who were diagnosed with endometrial cancer between 1985 and 1987. Cases were frequency matched in a ratio of approximately 1:2 to a sample of 341 white women with endometrial cancer. Information was derived from abstracts of hospital and physicians records, centralized pathology review, and interviews. Potential explanatory factors for black-white survival differences have been previously investigated using Cox regression. However, there was a high proportion of missing values since 24 percent of patients were never interviewed. Some values were also missing for three other variables derived from medical records. Missing values may introduced bias in previous findings based only on the information available. The primary objective of this thesis is to evaluate the effect of missing data on the estimated black/white mortality ratios adjusted for various explanatory factors. A second objective is to obtain more precise confidence intervals for the estimated mortality ratios. Nearest neighbor hot deck imputation has been used to generate fifty complete datasets. Adjusting for age and geographic location, the black/white mortality ratio for the imputed datasets was 3.3. When adjusted for all covariates, the mortality ratio was only 1.2. Overall, 87% of the excess mortality could be attributed to racial differences in disease stage, tumor characteristics, treatment, sociodemographic characteristics, hormonal and reproductive factors, the number of comorbidities and health behavior. The results based on multiple imputation indicate that missing data did not introduce major bias in the earlier analyses. However, multiple imputation provided narrower confidence intervals than those obtained previously. Multiple imputation was worthwhile since it gave more precise estimates for the relative mortality ratios. These findings have public health importance: they have implications for development of health policies and planning interventions to reduce the excess risk of death among black women with endometrial cancer.

Obstructive Sleep Apnea Hypopnea (OSAH) is a prevalent disorder that occurs in about 5% of the middle-aged adult population. Comprised of repetitive episodes of complete and/or partial upper airway obstruction during sleep, OSAH results in cyclic oxyhemoglobin desaturation-resaturation (e.g. intermittent hypoxia) and arousal from sleep (sleep fragmentation). Consequences of OSAH include increased risk of cardiovascular morbidity and mortality and elevated sympathetic activity (SA) during daytime wakefulness as well as sleep. This has potential clinical relevance because heightened SA is thought to be one mechanism explaining the association between OSAH and cardiovascular disease. Although OSAH is associated with increased sympathetic contribution to cardiac sympatho-vagal balance (SVB), the pathway mediating this effect (intermittent hypoxia, sleep fragmentation (SF) or both) is unclear. Because obstructive upper airway events in OSAH patients precipitate both physiologic phenomena in a generally concomitant manner, it has been difficult to sort the individual contributions of each in clinical populations. The aim of this study was to investigate the relationship between SVB and experimentally induced SF including examination of the possible interaction with being overweight in a healthy non-OSAH population. Twenty-nine subjects entered into a 4 night / 3 day sleep study to evaluate the effect of experimentally induced SF. Subjects provided a spectrum of body mass index (BMI) ranging from normal to overweight. Subjects experienced two nights of undisturbed sleep followed by two nights of fragmented sleep. Awake SVB reflected by heart rate variability was measured during wakefulness before and after a night of undisturbed sleep and a night of fragmented sleep. Sleep duration and architecture were assessed under both sleep conditions. SVB was decreased by transient changes from awake to sleep. SVB was affected by SF on an undisturbed night, but not a disturbed night. BMI had no effect. The public health significance of this study was that both OSAH and increased SVB have increased risk of cardiovascular disease; through improved understanding of the relationship between particular components of OSAH (SF or oxygenation-reoxygenation cycle) and increased SVB could lead to improved treatment of OSAH and the reduction of cardiovascular disease in the population.