A Bayesian analysis for spatial processes with application to mapping

In geographical epidemiology, maps of disease rates and disease risk provide a spatial perspective for researching disease etiology. For rare diseases or when the population base is small, the rate and risk estimates may be unstable. Empirical Bayesian (EB) methods have been used to spatially smooth the estimates by permitting an area estimate to "borrow strength" from its neighbors. Such EB methods include the use of a Gamma model, of a James-Stein estimator, and of a conditional autoregressive (CAR) process. A fully Bayesian analysis of the CAR process is proposed. One advantage of this fully Bayesian analysis is that it can be implemented simply by using repeated sampling from the posterior densities. Use of a Markov chain Monte Carlo technique such as Gibbs sampler was not necessary. Direct resampling from the posterior densities provides exact small sample inferences instead of the approximate asymptotic analyses of maximum likelihood methods (Clayton & Kaldor, 1987). Further, the proposed CAR model provides for covariates to be included in the model. A simulation demonstrates the effect of sample size on the fully Bayesian analysis of the CAR process. The methods are applied to lip cancer data from Scotland, and the results are compared. ^

BAYESIAN STATISTICAL METHODS IN GENE-ENVIRONMENT AND GENE-GENE INTERACTION STUDIES

Complex diseases such as cancer result from multiple genetic changes and environmental exposures. Due to the rapid development of genotyping and sequencing technologies, we are now able to more accurately assess causal effects of many genetic and environmental factors. Genome-wide association studies have been able to localize many causal genetic variants predisposing to certain diseases. However, these studies only explain a small portion of variations in the heritability of diseases. More advanced statistical models are urgently needed to identify and characterize some additional genetic and environmental factors and their interactions, which will enable us to better understand the causes of complex diseases. In the past decade, thanks to the increasing computational capabilities and novel statistical developments, Bayesian methods have been widely applied in the genetics/genomics researches and demonstrating superiority over some regular approaches in certain research areas. Gene-environment and gene-gene interaction studies are among the areas where Bayesian methods may fully exert its functionalities and advantages. This dissertation focuses on developing new Bayesian statistical methods for data analysis with complex gene-environment and gene-gene interactions, as well as extending some existing methods for gene-environment interactions to other related areas. It includes three sections: (1) Deriving the Bayesian variable selection framework for the hierarchical gene-environment and gene-gene interactions; (2) Developing the Bayesian Natural and Orthogonal Interaction (NOIA) models for gene-environment interactions; and (3) extending the applications of two Bayesian statistical methods which were developed for gene-environment interaction studies, to other related types of studies such as adaptive borrowing historical data. We propose a Bayesian hierarchical mixture model framework that allows us to investigate the genetic and environmental effects, gene by gene interactions (epistasis) and gene by environment interactions in the same model. It is well known that, in many practical situations, there exists a natural hierarchical structure between the main effects and interactions in the linear model. Here we propose a model that incorporates this hierarchical structure into the Bayesian mixture model, such that the irrelevant interaction effects can be removed more efficiently, resulting in more robust, parsimonious and powerful models. We evaluate both of the 'strong hierarchical' and 'weak hierarchical' models, which specify that both or one of the main effects between interacting factors must be present for the interactions to be included in the model. The extensive simulation results show that the proposed strong and weak hierarchical mixture models control the proportion of false positive discoveries and yield a powerful approach to identify the predisposing main effects and interactions in the studies with complex gene-environment and gene-gene interactions. We also compare these two models with the 'independent' model that does not impose this hierarchical constraint and observe their superior performances in most of the considered situations. The proposed models are implemented in the real data analysis of gene and environment interactions in the cases of lung cancer and cutaneous melanoma case-control studies. The Bayesian statistical models enjoy the properties of being allowed to incorporate useful prior information in the modeling process. Moreover, the Bayesian mixture model outperforms the multivariate logistic model in terms of the performances on the parameter estimation and variable selection in most cases. Our proposed models hold the hierarchical constraints, that further improve the Bayesian mixture model by reducing the proportion of false positive findings among the identified interactions and successfully identifying the reported associations. This is practically appealing for the study of investigating the causal factors from a moderate number of candidate genetic and environmental factors along with a relatively large number of interactions. The natural and orthogonal interaction (NOIA) models of genetic effects have previously been developed to provide an analysis framework, by which the estimates of effects for a quantitative trait are statistically orthogonal regardless of the existence of Hardy-Weinberg Equilibrium (HWE) within loci. Ma et al. (2012) recently developed a NOIA model for the gene-environment interaction studies and have shown the advantages of using the model for detecting the true main effects and interactions, compared with the usual functional model. In this project, we propose a novel Bayesian statistical model that combines the Bayesian hierarchical mixture model with the NOIA statistical model and the usual functional model. The proposed Bayesian NOIA model demonstrates more power at detecting the non-null effects with higher marginal posterior probabilities. Also, we review two Bayesian statistical models (Bayesian empirical shrinkage-type estimator and Bayesian model averaging), which were developed for the gene-environment interaction studies. Inspired by these Bayesian models, we develop two novel statistical methods that are able to handle the related problems such as borrowing data from historical studies. The proposed methods are analogous to the methods for the gene-environment interactions on behalf of the success on balancing the statistical efficiency and bias in a unified model. By extensive simulation studies, we compare the operating characteristics of the proposed models with the existing models including the hierarchical meta-analysis model. The results show that the proposed approaches adaptively borrow the historical data in a data-driven way. These novel models may have a broad range of statistical applications in both of genetic/genomic and clinical studies.

An empirical examination of relative profitability in the nursing facility industry between ownership form and regionality in the state of Texas

The purpose of this research is to examine the relative profitability of the firm within the nursing facility industry in Texas. An examination is made of the variables expected to affect profitability and of importance to the design and implementation of regulatory policy. To facilitate this inquiry, specific questions addressed are: (1) Do differences in ownership form affect profitability (defined as operating income before fixed costs)? (2) What impact does regional location have on profitability? (3) Do patient case-mix and access to care by Medicaid patients differ between proprietary and non-profit firms and facilities located in urban versus rural regions, and what association exists between these variables and profitability? (4) Are economies of scale present in the nursing home industry? (5) Do nursing facilities operate in a competitive output market characterized by the inability of a single firm to exhibit influence over market price?^ Prior studies have principally employed a cost function to assess efficiency differences between classifications of nursing facilities. The inherent weakness in this approach is that it only considers technical efficiency. Not both technical and price efficiency which are the two components of overall economic efficiency. One firm is more technically efficient compared to another if it is able to produce a given quantity of output at the least possible costs. Price efficiency means that scarce resources are being directed towards their most valued use. Assuming similar prices in both input and output markets, differences in overall economic efficiency between firm classes are assessed through profitability, hence a profit function.^ Using the framework of the profit function, data from 1990 Medicaid Costs Reports for Texas, and the analytic technique of Ordinary Least Squares Regression, the findings of the study indicated (1) similar profitability between nursing facilities organized as for-profit versus non-profit and located in urban versus rural regions, (2) an inverse association between both payor-mix and patient case-mix with profitability, (3) strong evidence for the presence of scale economies, and (4) existence of a competitive market structure. The paper concludes with implications regarding reimbursement methodology and construction moratorium policies in Texas. ^

Design and evaluation of the parent education component of a comprehensive violence prevention project in middle schools

Low parental monitoring is related to youth risk behaviors such as delinquency and aggression. The purpose of this dissertation was to describe the development and evaluation of a parent education intervention to increase parental monitoring in Hispanic parents of middle school children.^ The first study described the process of intervention mapping as used to develop Padres Trabajando por la Paz, a newsletter intervention for parents. Using theory, empirical literature, and information from the target population, performance objectives and determinants for monitoring were defined. Learning objectives were specified and a staged social-cognitive approach was used to develop methods and strategies delivered through newsletters.^ The second study examined the outcomes of a randomized trial of the newsletter intervention. Outcome measures consisted of a general measure of monitoring, parent and child reports of monitoring behaviors targeted by the intervention, and psychosocial determinants of monitoring (self-efficacy, norms, outcome expectancies, knowledge, and beliefs). Seventy-seven parents completed the randomized trial, half of which received four newsletters over an eight-week period. Results revealed a significant interaction effect for baseline and treatment for parent's reports of norms for monitoring (p =.009). Parents in the experimental condition who scored low at baseline reported increased norms for monitoring at follow-up. A significant interaction effect for child reports of parental monitoring behaviors (p =.04) reflected an small increase across baseline levels in the experimental condition and decreases for the control condition at higher baseline scores. Both groups of parents reported increased levels of monitoring at follow-up. No other outcome measures varied significantly by condition.^ The third study examined the relationship between the psychosocial determinants of parental monitoring and parental monitoring behaviors in the study population. Weak evidence for a relationship between outcome expectancies and parental monitoring behaviors suggests further research in the area utilizing stronger empirical models such as longitudinal design and structural equation modeling.^ The low-cost, minimal newsletter intervention showed promise for changing norms among Hispanic parents for parental monitoring. In light of the importance of parental monitoring as a protective factor for youth health risk behaviors, more research needs to be done to develop and evaluate interventions to increase parental monitoring. ^

Structural equation modeling of the medical outcome study: Short Form 36 (SF-36)

The factorial validity of the SF-36 was evaluated using confirmatory factor analysis (CFA) methods, structural equation modeling (SEM), and multigroup structural equation modeling (MSEM). First, the measurement and structural model of the hypothesized SF-36 was explicated. Second, the model was tested for the validity of a second-order factorial structure, upon evidence of model misfit, determined the best-fitting model, and tested the validity of the best-fitting model on a second random sample from the same population. Third, the best-fitting model was tested for invariance of the factorial structure across race, age, and educational subgroups using MSEM.^ The findings support the second-order factorial structure of the SF-36 as proposed by Ware and Sherbourne (1992). However, the results suggest that: (a) Mental Health and Physical Health covary; (b) general mental health cross-loads onto Physical Health; (c) general health perception loads onto Mental Health instead of Physical Health; (d) many of the error terms are correlated; and (e) the physical function scale is not reliable across these two samples. This hierarchical factor pattern was replicated across both samples of health care workers, suggesting that the post hoc model fitting was not data specific. Subgroup analysis suggests that the physical function scale is not reliable across the "age" or "education" subgroups and that the general mental health scale path from Mental Health is not reliable across the "white/nonwhite" or "education" subgroups.^ The importance of this study is in the use of SEM and MSEM in evaluating sample data from the use of the SF-36. These methods are uniquely suited to the analysis of latent variable structures and are widely used in other fields. The use of latent variable models for self reported outcome measures has become widespread, and should now be applied to medical outcomes research. Invariance testing is superior to mean scores or summary scores when evaluating differences between groups. From a practical, as well as, psychometric perspective, it seems imperative that construct validity research related to the SF-36 establish whether this same hierarchical structure and invariance holds for other populations.^ This project is presented as three articles to be submitted for publication. ^

HIV-related malignancies: A community-based study using a linkage of cancer registry and HIV registry data

Background. Increased incidence of cancer is documented in immunosuppressed transplant patients. Likewise, as survival increases for persons infected with the Human Immunodeficiency Virus (HIV), we expect their incidence of cancer to increase. The objective of this study was to examine the current gender specific spectrum of cancer in an HIV infected cohort (especially malignancies not currently associated with Acquired Immunodeficiency Syndrome (AIDS)) in relation to the general population.^ Methods. Cancer incidence data was collected for residents of Harris County, Texas who were diagnosed with a malignancy between 1975 and 1994. This data was linked to HIV/AIDS registry data to identify malignancies in an HIV infected cohort of 14,986 persons. A standardized incidence ratio (SIR) analysis was used to compare incidence of cancer in this cohort to that in the general population. Risk factors such as mode of HIV infection, age, race and gender, were evaluated for contribution to the development of cancer within the HIV cohort, using Cox regression techniques.^ Findings. Of those in the HIV infected cohort, 2289 persons (15%) were identified as having one or more malignancies. The linkage identified 29.5% of these malignancies (males 28.7% females 60.9%). HIV infected men and women had incidences of cancer that were 16.7 (16.1, 17.3) and 2.9 (2.3, 3.7) times that expected for the general population of Harris County, Texas, adjusting for age. Significant SIR's were observed for the AIDS-defining malignancies of Kaposi's sarcoma, non-Hodgkin's lymphoma, primary lymphoma of the brain and cancer of the cervix. Additionally, significant SIR's for non-melanotic skin cancer in males, 6.9 (4.8, 9.5) and colon cancer in females, 4.0 (1.1, 10.2) were detected. Among the HIV infected cohort, race/ethnicity of White (relative risk 2.4 with 95% confidence intervals 2.0, 2.8) or Spanish Surname, 2.2 (1.9, 2.7) and an infection route of male to male sex, with, 3.0 (1.9, 4.9) or without, 3.4 (2.1, 5.5) intravenous drug use, increased the risk of having a diagnosis of an incident cancer.^ Interpretation. There appears to be an increased risk of developing cancer if infected with the HIV. In addition to the malignancies routinely associated with HIV infection, there appears to be an increased risk of being diagnosed with non-melanotic skin cancer in males and colon cancer in females. ^

Bayesian generalized linear models for meta-analysis of diagnostic tests

With the recognition of the importance of evidence-based medicine, there is an emerging need for methods to systematically synthesize available data. Specifically, methods to provide accurate estimates of test characteristics for diagnostic tests are needed to help physicians make better clinical decisions. To provide more flexible approaches for meta-analysis of diagnostic tests, we developed three Bayesian generalized linear models. Two of these models, a bivariate normal and a binomial model, analyzed pairs of sensitivity and specificity values while incorporating the correlation between these two outcome variables. Noninformative independent uniform priors were used for the variance of sensitivity, specificity and correlation. We also applied an inverse Wishart prior to check the sensitivity of the results. The third model was a multinomial model where the test results were modeled as multinomial random variables. All three models can include specific imaging techniques as covariates in order to compare performance. Vague normal priors were assigned to the coefficients of the covariates. The computations were carried out using the 'Bayesian inference using Gibbs sampling' implementation of Markov chain Monte Carlo techniques. We investigated the properties of the three proposed models through extensive simulation studies. We also applied these models to a previously published meta-analysis dataset on cervical cancer as well as to an unpublished melanoma dataset. In general, our findings show that the point estimates of sensitivity and specificity were consistent among Bayesian and frequentist bivariate normal and binomial models. However, in the simulation studies, the estimates of the correlation coefficient from Bayesian bivariate models are not as good as those obtained from frequentist estimation regardless of which prior distribution was used for the covariance matrix. The Bayesian multinomial model consistently underestimated the sensitivity and specificity regardless of the sample size and correlation coefficient. In conclusion, the Bayesian bivariate binomial model provides the most flexible framework for future applications because of its following strengths: (1) it facilitates direct comparison between different tests; (2) it captures the variability in both sensitivity and specificity simultaneously as well as the intercorrelation between the two; and (3) it can be directly applied to sparse data without ad hoc correction. ^

An empirical model to estimate the demand for primary care in urban settings

Objective. To measure the demand for primary care and its associated factors by building and estimating a demand model of primary care in urban settings.^ Data source. Secondary data from 2005 California Health Interview Survey (CHIS 2005), a population-based random-digit dial telephone survey, conducted by the UCLA Center for Health Policy Research in collaboration with the California Department of Health Services, and the Public Health Institute between July 2005 and April 2006.^ Study design. A literature review was done to specify the demand model by identifying relevant predictors and indicators. CHIS 2005 data was utilized for demand estimation.^ Analytical methods. The probit regression was used to estimate the use/non-use equation and the negative binomial regression was applied to the utilization equation with the non-negative integer dependent variable.^ Results. The model included two equations in which the use/non-use equation explained the probability of making a doctor visit in the past twelve months, and the utilization equation estimated the demand for primary conditional on at least one visit. Among independent variables, wage rate and income did not affect the primary care demand whereas age had a negative effect on demand. People with college and graduate educational level were associated with 1.03 (p < 0.05) and 1.58 (p < 0.01) more visits, respectively, compared to those with no formal education. Insurance was significantly and positively related to the demand for primary care (p < 0.01). Need for care variables exhibited positive effects on demand (p < 0.01). Existence of chronic disease was associated with 0.63 more visits, disability status was associated with 1.05 more visits, and people with poor health status had 4.24 more visits than those with excellent health status. ^ Conclusions. The average probability of visiting doctors in the past twelve months was 85% and the average number of visits was 3.45. The study emphasized the importance of need variables in explaining healthcare utilization, as well as the impact of insurance, employment and education on demand. The two-equation model of decision-making, and the probit and negative binomial regression methods, was a useful approach to demand estimation for primary care in urban settings.^

Comparison of Bayesian and frequentist approaches in clinical outcomes between hospitals

Many public health agencies and researchers are interested in comparing hospital outcomes, for example, morbidity, mortality, and hospitalization across areas and hospitals. However, since there is variation of rates in clinical trials among hospitals because of several biases, we are interested in controlling for the bias and assessing real differences in clinical practices. In this study, we compared the variations between hospitals in rates of severe Intraventricular Haemorrhage (IVH) infant using Frequentist statistical approach vs. Bayesian hierarchical model through simulation study. The template data set for simulation study was included the number of severe IVH infants of 24 intensive care units in Australian and New Zealand Neonatal Network from 1995 to 1997 in severe IVH rate in preterm babies. We evaluated the rates of severe IVH for 24 hospitals with two hierarchical models in Bayesian approach comparing their performances with the shrunken rates in Frequentist method. Gamma-Poisson (BGP) and Beta-Binomial (BBB) were introduced into Bayesian model and the shrunken estimator of Gamma-Poisson (FGP) hierarchical model using maximum likelihood method were calculated as Frequentist approach. To simulate data, the total number of infants in each hospital was kept and we analyzed the simulated data for both Bayesian and Frequentist models with two true parameters for severe IVH rate. One was the observed rate and the other was the expected severe IVH rate by adjusting for five predictors variables for the template data. The bias in the rate of severe IVH infant estimated by both models showed that Bayesian models gave less variable estimates than Frequentist model. We also discussed and compared the results from three models to examine the variation in rate of severe IVH by 20th centile rates and avoidable number of severe IVH cases. ^

Capitalizing on success against childhood HIV/AIDS in Botswana: Towards a comprehensive healthcare policy for pediatric oncology in Botswana

Pediatric HIV/AIDS in sub-Saharan Africa has been a major public health crisis with an estimated 3.5 million children infected. Baylor International Pediatric AIDS Initiative (BIPAI) has created a network of centers providing care and treatment for these children in several countries. In Botswana, where the first BIPAI center in Africa was opened, childhood mortality from HIV/AIDS is now less than 1%. Botswana is a middle-income country that previously held the highest HIV prevalence rate in the world. Efforts against HIV/AIDS have resulted in the building of a strong medical infrastructure with clear success against pediatric HIV/AIDS. The WHO predicts the next global health crisis will be cancer. Given the increased incidence of cancer in the setting of HIV/AIDS, Botswana has already implemented strategies to combat HIV-related malignancies in adults, but efforts in pediatrics have been lagging. This policy paper describes the importance of building on success against pediatric HIV/AIDS and extending this success to pediatric cancer in general. Specifically, it outlines a comprehensive pediatric cancer policy for the education and training of health professionals, the development of a pediatric cancer program, a pediatric cancer registry, public awareness efforts, and an appropriate, country specific pediatric cancer research agenda.^