Sequential updating via dynamic hierarchical models: A Bayesian approach to longitudinal data analysis

Most statistical analysis, theory and practice, is concerned with static models; models with a proposed set of parameters whose values are fixed across observational units. Static models implicitly assume that the quantified relationships remain the same across the design space of the data. While this is reasonable under many circumstances this can be a dangerous assumption when dealing with sequentially ordered data. The mere passage of time always brings fresh considerations and the interrelationships among parameters, or subsets of parameters, may need to be continually revised. ^ When data are gathered sequentially dynamic interim monitoring may be useful as new subject-specific parameters are introduced with each new observational unit. Sequential imputation via dynamic hierarchical models is an efficient strategy for handling missing data and analyzing longitudinal studies. Dynamic conditional independence models offers a flexible framework that exploits the Bayesian updating scheme for capturing the evolution of both the population and individual effects over time. While static models often describe aggregate information well they often do not reflect conflicts in the information at the individual level. Dynamic models prove advantageous over static models in capturing both individual and aggregate trends. Computations for such models can be carried out via the Gibbs sampler. An application using a small sample repeated measures normally distributed growth curve data is presented. ^

Integrating sequence information in microarray data analysis by free energy modeling

Microarray technology is a high-throughput method for genotyping and gene expression profiling. Limited sensitivity and specificity are one of the essential problems for this technology. Most of existing methods of microarray data analysis have an apparent limitation for they merely deal with the numerical part of microarray data and have made little use of gene sequence information. Because it's the gene sequences that precisely define the physical objects being measured by a microarray, it is natural to make the gene sequences an essential part of the data analysis. This dissertation focused on the development of free energy models to integrate sequence information in microarray data analysis. The models were used to characterize the mechanism of hybridization on microarrays and enhance sensitivity and specificity of microarray measurements. ^ Cross-hybridization is a major obstacle factor for the sensitivity and specificity of microarray measurements. In this dissertation, we evaluated the scope of cross-hybridization problem on short-oligo microarrays. The results showed that cross hybridization on arrays is mostly caused by oligo fragments with a run of 10 to 16 nucleotides complementary to the probes. Furthermore, a free-energy based model was proposed to quantify the amount of cross-hybridization signal on each probe. This model treats cross-hybridization as an integral effect of the interactions between a probe and various off-target oligo fragments. Using public spike-in datasets, the model showed high accuracy in predicting the cross-hybridization signals on those probes whose intended targets are absent in the sample. ^ Several prospective models were proposed to improve Positional Dependent Nearest-Neighbor (PDNN) model for better quantification of gene expression and cross-hybridization. ^ The problem addressed in this dissertation is fundamental to the microarray technology. We expect that this study will help us to understand the detailed mechanism that determines sensitivity and specificity on the microarrays. Consequently, this research will have a wide impact on how microarrays are designed and how the data are interpreted. ^

Secondary data analysis of a pilot study of use of an instructional video for dietary assessment

Introduction. Food frequency questionnaires (FFQ) are used study the association between dietary intake and disease. An instructional video may potentially offer a low cost, practical method of dietary assessment training for participants thereby reducing recall bias in FFQs. There is little evidence in the literature of the effect of using instructional videos on FFQ-based intake. Objective. This analysis compared the reported energy and macronutrient intake of two groups that were randomized either to watch an instructional video before completing an FFQ or to view the same instructional video after completing the same FFQ. Methods. In the parent study, a diverse group of students, faculty and staff from Houston Community College were randomized to two groups, stratified by ethnicity, and completed an FFQ. The "video before" group watched an instructional video about completing the FFQ prior to answering the FFQ. The "video after" group watched the instructional video after completing the FFQ. The two groups were compared on mean daily energy (Kcal/day), fat (g/day), protein (g/day), carbohydrate (g/day) and fiber (g/day) intakes using descriptive statistics and one-way ANOVA. Demographic, height, and weight information was collected. Dietary intakes were adjusted for total energy intake before the comparative analysis. BMI and age were ruled out as potential confounders. Results. There were no significant differences between the two groups in mean daily dietary intakes of energy, total fat, protein, carbohydrates and fiber. However, a pattern of higher energy intake and lower fiber intake was reported in the group that viewed the instructional video before completing the FFQ compared to those who viewed the video after. Discussion. Analysis of the difference between reported intake of energy and macronutrients showed an overall pattern, albeit not statistically significant, of higher intake in the video before versus the video after group. Application of instructional videos for dietary assessment may require further research to address the validity of reported dietary intakes in those who are randomized to watch an instructional video before reporting diet compared to a control groups that does not view a video.^

Functional data analysis approaches for genotype-phenotype association studies from next-generation sequencing

Next-generation DNA sequencing platforms can effectively detect the entire spectrum of genomic variation and is emerging to be a major tool for systematic exploration of the universe of variants and interactions in the entire genome. However, the data produced by next-generation sequencing technologies will suffer from three basic problems: sequence errors, assembly errors, and missing data. Current statistical methods for genetic analysis are well suited for detecting the association of common variants, but are less suitable to rare variants. This raises great challenge for sequence-based genetic studies of complex diseases.^ This research dissertation utilized genome continuum model as a general principle, and stochastic calculus and functional data analysis as tools for developing novel and powerful statistical methods for next generation of association studies of both qualitative and quantitative traits in the context of sequencing data, which finally lead to shifting the paradigm of association analysis from the current locus-by-locus analysis to collectively analyzing genome regions.^ In this project, the functional principal component (FPC) methods coupled with high-dimensional data reduction techniques will be used to develop novel and powerful methods for testing the associations of the entire spectrum of genetic variation within a segment of genome or a gene regardless of whether the variants are common or rare.^ The classical quantitative genetics suffer from high type I error rates and low power for rare variants. To overcome these limitations for resequencing data, this project used functional linear models with scalar response to develop statistics for identifying quantitative trait loci (QTLs) for both common and rare variants. To illustrate their applications, the functional linear models were applied to five quantitative traits in Framingham heart studies. ^ This project proposed a novel concept of gene-gene co-association in which a gene or a genomic region is taken as a unit of association analysis and used stochastic calculus to develop a unified framework for testing the association of multiple genes or genomic regions for both common and rare alleles. The proposed methods were applied to gene-gene co-association analysis of psoriasis in two independent GWAS datasets which led to discovery of networks significantly associated with psoriasis.^

Secondary data analysis of lead screening compliance in high-risk children

Introduction. Despite the ban of lead-containing gasoline and paint, childhood lead poisoning remains a public health issue. Furthermore, a Medicaid-eligible child is 8 times more likely to have an elevated blood lead level (EBLL) than a non-Medicaid child, which is the primary reason for the early detection lead screening mandate for ages 12 and 24 months among the Medicaid population. Based on field observations, there was evidence that suggested a screening compliance issue. Objective. The purpose of this study was to analyze blood lead screening compliance in previously lead poisoned Medicaid children and test for an association between timely lead screening and timely childhood immunizations. The mean months between follow-up tests were also examined for a significant difference between the non-compliant and compliant lead screened children. Methods. Access to the surveillance data of all childhood lead poisoned cases in Bexar County was granted by the San Antonio Metropolitan Health District. A database was constructed and analyzed using descriptive statistics, logistic regression methods and non-parametric tests. Lead screening at 12 months of age was analyzed separately from lead screening at 24 months. The small portion of the population who were also related were included in one analysis and removed from a second analysis to check for significance. Gender, ethnicity, age of home, and having a sibling with an EBLL were ruled out as confounders for the association tests but ethnicity and age of home were adjusted in the nonparametric tests. Results. There was a strong significant association between lead screening compliance at 12 months and childhood immunization compliance, with or without including related children (p<0.00). However, there was no significant association between the two variables at the age of 24 months. Furthermore, there was no significant difference between the median of the mean months of follow-up blood tests among the non-compliant and compliant lead screened population for at the 12 month screening group but there was a significant difference at the 24 month screening group (p<0.01). Discussion. Descriptive statistics showed that 61% and 56% of the previously lead poisoned Medicaid population did not receive their 12 and 24 month mandated lead screening on time, respectively. This suggests that their elevated blood lead level may have been diagnosed earlier in their childhood. Furthermore, a child who is compliant with their lead screening at 12 months of age is 2.36 times more likely to also receive their childhood immunizations on time compared to a child who was not compliant with their 12 month screening. Even though there was no statistical significant association found for the 24 month group, the public health significance of a screening compliance issue is no less important. The Texas Medicaid program needs to enforce lead screening compliance because it is evident that there has been no monitoring system in place. Further recommendations include a need for an increased focus on parental education and the importance of taking their children for wellness exams on time.^

A categorical data analysis approach to estimation of demographic characteristics for Texas county populations

The need for timely population data for health planning and Indicators of need has Increased the demand for population estimates. The data required to produce estimates is difficult to obtain and the process is time consuming. Estimation methods that require less effort and fewer data are needed. The structure preserving estimator (SPREE) is a promising technique not previously used to estimate county population characteristics. This study first uses traditional regression estimation techniques to produce estimates of county population totals. Then the structure preserving estimator, using the results produced in the first phase as constraints, is evaluated.^ Regression methods are among the most frequently used demographic methods for estimating populations. These methods use symptomatic indicators to predict population change. This research evaluates three regression methods to determine which will produce the best estimates based on the 1970 to 1980 indicators of population change. Strategies for stratifying data to improve the ability of the methods to predict change were tested. Difference-correlation using PMSA strata produced the equation which fit the data the best. Regression diagnostics were used to evaluate the residuals.^ The second phase of this study is to evaluate use of the structure preserving estimator in making estimates of population characteristics. The SPREE estimation approach uses existing data (the association structure) to establish the relationship between the variable of interest and the associated variable(s) at the county level. Marginals at the state level (the allocation structure) supply the current relationship between the variables. The full allocation structure model uses current estimates of county population totals to limit the magnitude of county estimates. The limited full allocation structure model has no constraints on county size. The 1970 county census age - gender population provides the association structure, the allocation structure is the 1980 state age - gender distribution.^ The full allocation model produces good estimates of the 1980 county age - gender populations. An unanticipated finding of this research is that the limited full allocation model produces estimates of county population totals that are superior to those produced by the regression methods. The full allocation model is used to produce estimates of 1986 county population characteristics. ^

Longitudinal dyadic data analysis of stroke survivors and their spousal caregivers

Approximately 795,000 new and recurrent strokes occur each year. Because of the resulting functional impairment, stroke survivors are often discharged into the care of a family caregiver, most often their spouse. This dissertation explored the effect that mutuality, a measure of the perceived positive aspects of the caregiving relationship, had on the stress and depression of 159 stroke survivors and their spousal caregivers over the first 12 months post discharge from inpatient rehabilitation. Specifically, cross-lagged regression was utilized to investigate the dyadic, longitudinal relationship between caregiver and stroke survivor mutuality and caregiver and stroke survivor stress over time. Longitudinal meditational analysis was employed to examine the mediating effect of mutuality on the dyads’ perception of family function and caregiver and stroke survivor depression over time.^ Caregivers’ mutuality was found to be associated with their own stress over time but not the stress of the stroke survivor. Caregivers who had higher mutuality scores over the 12 months of the study had lower perceived stress. Additionally, a partner effect of stress for the stroke survivor but not the caregiver was found, indicating that stroke survivors’ stress over time was associated with caregivers’ stress but caregivers’ stress over time was not significantly associated with the stress of the stroke survivor.^ This dissertation did not find mutuality to mediate the relationship between caregivers’ and stroke survivors’ perception of family function at baseline and their own or their partners’ depression at 12 months as hypothesized. However, caregivers who perceived healthier family functioning at baseline and stroke survivors who had higher perceived mutuality at 12 months had lower depression at one year post discharge from inpatient rehabilitation. Additionally, caregiver mutuality at 6 months, but not at baseline or 12 months, was found to be inversely related to caregiver depression at 12 months.^ These findings highlight the interpersonal nature of stress in the context of caregiving, especially among spousal relationships. Thus, health professionals should encourage caregivers and stroke survivors to focus on the positive aspects of the caregiving relationship in order to mitigate stress and depression. ^

Factors influencing participation in individuals with disability: A secondary data analysis

Individuals with disabilities face numerous barriers to participation due to biological and physical characteristics of the disability as well as social and environmental factors. Participation can be impacted on all levels from societal, to activities of daily living, exercise, education, and interpersonal relationships. This study evaluated the impact of pain, mood, depression, quality of life and fatigue on participation for individuals with mobility impairments. This cross sectional study derives from self-report data collected from a wheelchair using sample. Bivariate correlational and multivariate analysis were employed to examine the relationship between pain, quality of life, positive and negative mood, fatigue, and depression with participation while controlling for relevant socio-demographic variables (sex, age, time with disability, race, and education). Results from the 122 respondents with mobility impairments demonstrated that after controlling for socio-demographic characteristics in the full model, 20% of the variance in participation scores were accounted for by pain, quality of life, positive and negative mood, and depression. Notably, quality of life emerged as being the single variable that was significantly related to participation in the full model. Contrary to other studies, pain did not appear to significantly impact participation outcomes for wheelchair users in this sample. Participation is an emerging area of interest among rehabilitation and disability researchers, and results of this study provide compelling evidence that several psychosocial factors are related to participation. This area of inquiry warrants further study, as many of the psychosocial variables identified in this study (mood, depression, quality of life) may be amenable to intervention, which may also positively influence participation.^

The relationship between obesity, autoimmune disease, and C-reactive protein: A secondary data analysis of the National Health and Nutrition Examination Survey (NHANES) 2009--2010

Autoimmune diseases are a group of inflammatory conditions in which the body's immune system attacks its own cells. There are over 80 diseases classified as autoimmune disorders, affecting up to 23.5 million Americans. Obesity affects 32.3% of the US adult population, and could also be considered an inflammatory condition, as indicated by the presence of chronic low-grade inflammation. C-reactive protein (CRP) is a marker of inflammation, and is associated with both adiposity and autoimmune inflammation. This study sought to determine the cross-sectional association between obesity and autoimmune diseases in a large, nationally representative population derived from NHANES 2009–10 data, and the role CRP might play in this relationship. Overall, the results determined that individuals with autoimmune disease were 2.11 times more likely to report being overweight than individuals without autoimmune disease and that CRP had a mediating affect on the obesity-autoimmune relationship. ^

DEVELOPMENT OF NOVEL METHODS TO MINIMIZE THE IMPACT OF SEQUENCING ERRORS IN THE NEXT-GENERATION SEQUENCING DATA ANALYSIS

Next-generation sequencing (NGS) technology has become a prominent tool in biological and biomedical research. However, NGS data analysis, such as de novo assembly, mapping and variants detection is far from maturity, and the high sequencing error-rate is one of the major problems. . To minimize the impact of sequencing errors, we developed a highly robust and efficient method, MTM, to correct the errors in NGS reads. We demonstrated the effectiveness of MTM on both single-cell data with highly non-uniform coverage and normal data with uniformly high coverage, reflecting that MTM’s performance does not rely on the coverage of the sequencing reads. MTM was also compared with Hammer and Quake, the best methods for correcting non-uniform and uniform data respectively. For non-uniform data, MTM outperformed both Hammer and Quake. For uniform data, MTM showed better performance than Quake and comparable results to Hammer. By making better error correction with MTM, the quality of downstream analysis, such as mapping and SNP detection, was improved. SNP calling is a major application of NGS technologies. However, the existence of sequencing errors complicates this process, especially for the low coverage (

Longitudinal categorical data analysis: A continuous -time Markov chain approach

In this dissertation, we propose a continuous-time Markov chain model to examine the longitudinal data that have three categories in the outcome variable. The advantage of this model is that it permits a different number of measurements for each subject and the duration between two consecutive time points of measurements can be irregular. Using the maximum likelihood principle, we can estimate the transition probability between two time points. By using the information provided by the independent variables, this model can also estimate the transition probability for each subject. The Monte Carlo simulation method will be used to investigate the goodness of model fitting compared with that obtained from other models. A public health example will be used to demonstrate the application of this method. ^

New methods for quantification and analysis of quantitative real-time polymerase chain reaction data

Quantitative real-time polymerase chain reaction (qPCR) is a sensitive gene quantitation method that has been widely used in the biological and biomedical fields. The currently used methods for PCR data analysis, including the threshold cycle (CT) method, linear and non-linear model fitting methods, all require subtracting background fluorescence. However, the removal of background fluorescence is usually inaccurate, and therefore can distort results. Here, we propose a new method, the taking-difference linear regression method, to overcome this limitation. Briefly, for each two consecutive PCR cycles, we subtracted the fluorescence in the former cycle from that in the later cycle, transforming the n cycle raw data into n-1 cycle data. Then linear regression was applied to the natural logarithm of the transformed data. Finally, amplification efficiencies and the initial DNA molecular numbers were calculated for each PCR run. To evaluate this new method, we compared it in terms of accuracy and precision with the original linear regression method with three background corrections, being the mean of cycles 1-3, the mean of cycles 3-7, and the minimum. Three criteria, including threshold identification, max R2, and max slope, were employed to search for target data points. Considering that PCR data are time series data, we also applied linear mixed models. Collectively, when the threshold identification criterion was applied and when the linear mixed model was adopted, the taking-difference linear regression method was superior as it gave an accurate estimation of initial DNA amount and a reasonable estimation of PCR amplification efficiencies. When the criteria of max R2 and max slope were used, the original linear regression method gave an accurate estimation of initial DNA amount. Overall, the taking-difference linear regression method avoids the error in subtracting an unknown background and thus it is theoretically more accurate and reliable. This method is easy to perform and the taking-difference strategy can be extended to all current methods for qPCR data analysis.^

SURVIVAL PREDICTION FOR BRAIN TUMOR PATIENTS USING GENE EXPRESSION DATA

Brain tumor is one of the most aggressive types of cancer in humans, with an estimated median survival time of 12 months and only 4% of the patients surviving more than 5 years after disease diagnosis. Until recently, brain tumor prognosis has been based only on clinical information such as tumor grade and patient age, but there are reports indicating that molecular profiling of gliomas can reveal subgroups of patients with distinct survival rates. We hypothesize that coupling molecular profiling of brain tumors with clinical information might improve predictions of patient survival time and, consequently, better guide future treatment decisions. In order to evaluate this hypothesis, the general goal of this research is to build models for survival prediction of glioma patients using DNA molecular profiles (U133 Affymetrix gene expression microarrays) along with clinical information. First, a predictive Random Forest model is built for binary outcomes (i.e. short vs. long-term survival) and a small subset of genes whose expression values can be used to predict survival time is selected. Following, a new statistical methodology is developed for predicting time-to-death outcomes using Bayesian ensemble trees. Due to a large heterogeneity observed within prognostic classes obtained by the Random Forest model, prediction can be improved by relating time-to-death with gene expression profile directly. We propose a Bayesian ensemble model for survival prediction which is appropriate for high-dimensional data such as gene expression data. Our approach is based on the ensemble "sum-of-trees" model which is flexible to incorporate additive and interaction effects between genes. We specify a fully Bayesian hierarchical approach and illustrate our methodology for the CPH, Weibull, and AFT survival models. We overcome the lack of conjugacy using a latent variable formulation to model the covariate effects which decreases computation time for model fitting. Also, our proposed models provides a model-free way to select important predictive prognostic markers based on controlling false discovery rates. We compare the performance of our methods with baseline reference survival methods and apply our methodology to an unpublished data set of brain tumor survival times and gene expression data, selecting genes potentially related to the development of the disease under study. A closing discussion compares results obtained by Random Forest and Bayesian ensemble methods under the biological/clinical perspectives and highlights the statistical advantages and disadvantages of the new methodology in the context of DNA microarray data analysis.

Estimating parameters in Markov models for longitudinal studies with missing data or surrogate outcomes

The discrete-time Markov chain is commonly used in describing changes of health states for chronic diseases in a longitudinal study. Statistical inferences on comparing treatment effects or on finding determinants of disease progression usually require estimation of transition probabilities. In many situations when the outcome data have some missing observations or the variable of interest (called a latent variable) can not be measured directly, the estimation of transition probabilities becomes more complicated. In the latter case, a surrogate variable that is easier to access and can gauge the characteristics of the latent one is usually used for data analysis. ^ This dissertation research proposes methods to analyze longitudinal data (1) that have categorical outcome with missing observations or (2) that use complete or incomplete surrogate observations to analyze the categorical latent outcome. For (1), different missing mechanisms were considered for empirical studies using methods that include EM algorithm, Monte Carlo EM and a procedure that is not a data augmentation method. For (2), the hidden Markov model with the forward-backward procedure was applied for parameter estimation. This method was also extended to cover the computation of standard errors. The proposed methods were demonstrated by the Schizophrenia example. The relevance of public health, the strength and limitations, and possible future research were also discussed. ^

Racial disparities in CD4 counts at initial HIV-1 diagnosis: Analysis of the Adult Spectrum of HIV disease dataset and public health implications

Introduction. The HIV/AIDS disease burden disproportionately affects minority populations, specifically African Americans. While sexual risk behaviors play a role in the observed HIV burden, other factors including gender, age, socioeconomics, and barriers to healthcare access may also be contributory. The goal of this study was to determine how far down the HIV/AIDS disease process people of different ethnicities first present for healthcare. The study specifically analyzed the differences in CD4 cell counts at the initial HIV-1 diagnosis with respect to ethnicity. The study also analyzed racial differences in HIV/AIDS risk factors. ^ Methods. This is a retrospective study using data from the Adult Spectrum of HIV Disease (ASD), collected by the City of Houston Department of Health. The ASD database contains information on newly reported HIV cases in the Harris County District Hospitals between 1989 and 2000. Each patient had an initial and a follow-up report. The extracted variables of interest from the ASD data set were CD4 counts at the initial HIV diagnosis, race, gender, age at HIV diagnosis and behavioral risk factors. One-way ANOVA was used to examine differences in baseline CD4 counts at HIV diagnosis between racial/ethnic groups. Chi square was used to analyze racial differences in risk factors. ^ Results. The analyzed study sample was 4767. The study population was 47% Black, 37% White and 16% Hispanic [p<0.05]. The mean and median CD4 counts at diagnosis were 254 and 193 cells per ml, respectively. At the initial HIV diagnosis Blacks had the highest average CD4 counts (285), followed by Whites (233) and Hispanics (212) [p<0.001 ]. These statistical differences, however, were only observed with CD4 counts above 350 [p<0.001], even when adjusted for age at diagnosis and gender [p<0.05]. Looking at risk factors, Blacks were mostly affected by intravenous drug use (IVDU) and heterosexuality, whereas Whites and Hispanics were more affected by male homosexuality [ p<0.05]. ^ Conclusion. (1) There were statistical differences in CD4 counts with respect to ethnicity, but these differences only existed for CD4 counts above 350. These differences however do not appear to have clinical significance. Antithetically, Blacks had the highest CD4 counts followed by Whites and Hispanics. (2) 50% of this study group clinically had AIDS at their initial HIV diagnosis (median=193), irrespective of ethnicity. It was not clear from data analysis if these observations were due to failure of early HIV surveillance, HIV testing policies or healthcare access. More studies need to be done to address this question. (3) Homosexuality and bisexuality were the biggest risk factors for Whites and Hispanics, whereas for Blacks were mostly affected by heterosexuality and IVDU, implying a need for different public health intervention strategies for these racial groups. ^