Robust effect sizes and their confidence intervals for group difference between trajectories in hierarchical linear growth model

Hierarchical linear growth model (HLGM), as a flexible and powerful analytic method, has played an increased important role in psychology, public health and medical sciences in recent decades. Mostly, researchers who conduct HLGM are interested in the treatment effect on individual trajectories, which can be indicated by the cross-level interaction effects. However, the statistical hypothesis test for the effect of cross-level interaction in HLGM only show us whether there is a significant group difference in the average rate of change, rate of acceleration or higher polynomial effect; it fails to convey information about the magnitude of the difference between the group trajectories at specific time point. Thus, reporting and interpreting effect sizes have been increased emphases in HLGM in recent years, due to the limitations and increased criticisms for statistical hypothesis testing. However, most researchers fail to report these model-implied effect sizes for group trajectories comparison and their corresponding confidence intervals in HLGM analysis, since lack of appropriate and standard functions to estimate effect sizes associated with the model-implied difference between grouping trajectories in HLGM, and also lack of computing packages in the popular statistical software to automatically calculate them. ^ The present project is the first to establish the appropriate computing functions to assess the standard difference between grouping trajectories in HLGM. We proposed the two functions to estimate effect sizes on model-based grouping trajectories difference at specific time, we also suggested the robust effect sizes to reduce the bias of estimated effect sizes. Then, we applied the proposed functions to estimate the population effect sizes (d ) and robust effect sizes (du) on the cross-level interaction in HLGM by using the three simulated datasets, and also we compared the three methods of constructing confidence intervals around d and du recommended the best one for application. At the end, we constructed 95% confidence intervals with the suitable method for the effect sizes what we obtained with the three simulated datasets. ^ The effect sizes between grouping trajectories for the three simulated longitudinal datasets indicated that even though the statistical hypothesis test shows no significant difference between grouping trajectories, effect sizes between these grouping trajectories can still be large at some time points. Therefore, effect sizes between grouping trajectories in HLGM analysis provide us additional and meaningful information to assess group effect on individual trajectories. In addition, we also compared the three methods to construct 95% confident intervals around corresponding effect sizes in this project, which handled with the uncertainty of effect sizes to population parameter. We suggested the noncentral t-distribution based method when the assumptions held, and the bootstrap bias-corrected and accelerated method when the assumptions are not met.^

Effect of maternal weight status on the relationship between prenatal smoking and infant birth weight

The purpose of this study was to assess the effect of maternal pre-pregnancy weight status on the relationship between prenatal smoking and infant birth weight (IBW). Prenatal cigarette smoking and maternal weight exert opposing effects on IBW; smoking decreases birth weight while maternal pre-pregnancy weight is positively correlated with birth weight. As such, mutual effect modification may be sufficiently significant to alter the independent effects of these two birth weight correlates. Finding of such an effect has implications of prenatal smoking cessation education. Perception of risk is an important determinant of smoking cessation, and reduced or low birth weight (LBW) as a smoking-associated risk predominates prenatal smoking counseling and education. In a population such as the US, where obesity is becoming epidemic, particularly among minority and low-income groups, perception of risk may be lowered should increased maternal size attenuate the effect of smoking. Previous studies have not found a significant interaction effect of prenatal smoking and maternal pre-pregnancy weight on IBW; however, use of self-reported smoking status may have biased findings. Reliability of self-reported smoking status reported in the literature is variable, with deception rates ranging from a low of 5% to as high as 16%. This study, using data from a prenatal smoking cessation project, in which smoking status was validated by saliva cotinine, was an opportunity to assess effect modification of smoking and maternal weight using biochemically determined smoking status in lieu of self report. Stratified by saliva cotinine, 151 women from a prenatal smoking cessation cohort, who were 18 years and older and had full-term, singleton births, were included in this study. The effect of smoking in terms of mean birth weight across three levels of maternal pre-pregnancy weight was assessed by general linear modeling procedures, adjusting for other known correlates of IBW. Effect modification was marginally significant, p = .104, but only with control for differential effects among racial/ethnic groups. A smaller than planned sample of nonsmokers, or women who quit smoking during the pregnancy, prohibited rejection of the null hypothesis of no difference in the effect of smoking across levels of pre-pregnancy weight. ^

Psychosocial and environmental predictors of calcium intake, physical activity and bone health among adolescent girls

Objectives. The purpose of this study was to identify the psychosocial and environmental predictors and the pathways they use to influence calcium intake, physical activity and bone health among adolescent girls. Methods. A secondary data analysis using a cross-sectional and longitudinal study design was implemented to examine the associations of interest. Data from the Incorporating More Physical Activity and Calcium in Teens (IMPACT) study collected in 2001-2003 were utilized for the analyses. IMPACT was a 1½ year nutrition and physical activity intervention study conducted among 718 middle-school girls in central Texas. Hierarchical regression modeling and Structural Equation Modeling (SEM) were used to determine the psychosocial predictors of calcium intake, physical activity and bone health at baseline. Hierarchical regression was used to determine if psychosocial factors at baseline were significant predictors of calcium intake and physical activity at follow-up. Data was adjusted for included BMI, lactose intolerance, ethnicity, menarchal status, intervention and participation in 7th grade PE/athletics. Results. Results of the baseline regression analysis revealed that calcium self-efficacy and milk availability at home were the strongest predictors of calcium intake. Friend engagement in physical activity, physical activity self-efficacy and participation in sports teams were the strongest predictors of physical activity. Finally, physical activity outcome expectations, social support and participation in sports teams were significant predictors of stiffness index at baseline. Results of the baseline SEM path analysis found that outcome expectations and milk availability at home directly influenced calcium intake. Knowledge and calcium self-efficacy indirectly influenced calcium intake with outcome expectations as the mediator. Physical activity self-efficacy and social support had significant direct and indirect influence on physical activity with participation in sports teams as the mediator. Participation in sports teams had a direct effect on both physical activity and stiffness index. Results of regression analysis for baseline predicting follow-up showed that participation in sports teams, self-efficacy, outcome expectations and social support at baseline were significant predictors of physical activity at follow-up. Conclusion. Results of this study reinforce the relevance of addressing both, psychosocial and environmental factors which are critical when developing interventions to improve bone health among adolescent girls. ^

Obesity during pregnancy on vagal tone, hemoglobin A1c, oxygenation, and perinatal outcomes

Purpose: To examine the effect of obesity and gestational weight gain on heart rate variability (HRV), oxygenation (HbO 2 and SpO2), hemoglobin A1c (HbA1c) and the frequency of pregnancy complications in obese (O) and non-obese (NO) women.^ Design: The study was an observational comparison study with a repeated measures design. ^ Setting: The setting was a low risk prenatal, university clinic located in a large southeastern metropolitan city. ^ Sample: The sample consisted of a volunteer group of 41 pregnant women who were observed at the three time points of 20, 28, and 36 weeks gestation. ^ Analysis: Analysis included general linear modeling with repeated measures to test for group differences with changes over time on vagal response, HbA1c, and oxygenation. Odds ratios were computed to compare the frequency of birth outcomes. ^ Findings: The interaction effect of time between O and NO women on HbO2 was significant. The mean HP, RSA, and HbO2 changed significantly over time within the NO women. The mean HbA 1c increased significantly over time within the O women. Women with excess gestational weight gain had significantly lower heart period than women with weight gain within the IOM recommendations. Obese women were more likely to have Group B streptococcal infections, gestational hypertension, give birth by cesarean or instrument assistance, and have at least one postnatal event. ^ Conclusions: Monitoring HRV, oxygenation, and HbA1c using minimally invasive measures may permit early identification of alterations in autonomic response. Implementation of interventions to promote vagal tone may help to reduce risks for adverse perinatal outcomes related to obesity. Future studies should examine the effect of obesity on the vagal response and perinatal outcomes. ^

A descriptive and exploratory analysis of occupational injuries at a chemical manufacturing facility

A retrospective study of 1353 occupational injuries occurring at a chemical manufacturing facility in Houston, Texas from January, 1982 through May, 1988 was performed to investigate the etiology of the occupational injury process. Injury incidence rates were calculated for various sub-populations of workers to determine differences in the risk of injury for various groups. Linear modeling techniques were used to determine the association between certain collected independent variables and severity of an injury event. Finally, two sub-groups of the worker population, shiftworkers and injury recidivists, were examined. An injury recidivist as defined is any worker experiencing one or more injury per year. Overall, female shiftworkers evidenced the highest average injury incidence rate compared to all other worker groups analyzed. Although the female shiftworkers were younger and less experienced, the etiology of their increased risk of injury remains unclear, although the rigors of performing shiftwork itself or ergonomic factors are suspect. In general, females were injured more frequently than males, but they did not incur more severe injuries. For all workers, many injuries were caused by erroneous or foregone training, and risk taking behaviors. Injuries of these types are avoidable. The distribution of injuries by severity level was bimodal; either injuries were of minor or major severity with only a small number of cases falling in between. Of the variables collected, only the type of injury incurred and the worker's titlecode were statistically significantly associated with injury severity. Shiftworkers did not sustain more severe injuries than other worker groups. Injury to shiftworkers varied as a 24-hour pattern; the greatest number occurred between 1200-1230 hours, (p = 0.002) by Cosinor analysis. Recidivists made up 3.3% of the population (23 males and 10 females), yet suffered 17.8% of the injuries. Although past research suggests that injury recidivism is a random statistical event, analysis of the data by logistic regression implicates gender, area worked, age and job titlecode as being statistically significantly related to injury recidivism at this facility. ^

Associations between teacher support and students' fruit and vegetable consumption in low-income elementary schools in central Texas

Background. Similar to parent support in the home environment, teacher support at school may positively influence children's fruit and vegetable (FV) consumption. This study assessed the relationship between teacher support for FV consumption and the FV intake of 4th and 5th grade students in low-income elementary schools in central Texas. Methods. A secondary analysis was performed on baseline data collected from 496 parent-child dyads during the Marathon Kids study carried out by the Michael & Susan Dell Center for Healthy Living at the University of Texas School of Public Health. A hierarchical linear regression analysis adjusting for key demographic variables, parent support, and home FV availability was conducted. In addition, separate linear regression models stratified by quartiles of home FV availability were conducted to assess the relationship between teacher support and FV intake by level of home FV availability. Results. Teacher support was not significantly related to students' FV intake (p = .44). However, the interaction of teacher support and home FV availability was positively associated with students' FV consumption (p < .05). For students in the lowest quartile of home FV availability, teacher support accounted for approximately 6% of the FV intake variance (p = .02). For higher levels of FV availability, teacher support and FV intake were not related. Conclusions. For lower income elementary school-aged children with low FV availability at home, greater teacher support may lead to modest increases in FV consumption.^

MODELING SPORADIC TUMOR FORMATION DRIVEN BY TELOMERE DYSFUNCTION IN THE GASTROINTESTINAL TRACT

Colorectal cancer is a complex disease that is thought to arise when cells accumulate mutations that allow for uncontrolled growth. There are several recognized mechanisms for generating such mutations in sporadic colon cancer; one of which is chromosomal instability (CIN). One hypothesized driver of CIN in cancer is the improper repair of dysfunctional telomeres. Telomeres comprise the linear ends of chromosomes and play a dual role in cancer. Its length is maintained by the ribonucleoprotein, telomerase, which is not a normally expressed in somatic cells and as cells divide, telomeres continuously shorten. Critically shortened telomeres are considered dysfunctional as they are recognized as sites of DNA damage and cells respond by entering into replicative senescence or apoptosis, a process that is p53-dependent and the mechanism for telomere-induced tumor suppression. Loss of this checkpoint and improper repair of dysfunctional telomeres can initiate a cycle of fusion, bridge and breakage that can lead to chromosomal changes and genomic instability, a process that can lead to transformation of normal cells to cancer cells. Mouse models of telomere dysfunction are currently based on knocking out the telomerase protein or RNA component; however, the naturally long telomeres of mice require multiple generational crosses of telomerase null mice to achieve critically short telomeres. Shelterin is a complex of six core proteins that bind to telomeres specifically. Pot1a is a highly conserved member of this complex that specifically binds to the telomeric single-stranded 3’ G-rich overhang. Previous work in our lab has shown that Pot1a is essential for chromosomal end protection as deletion of Pot1a in murine embryonic fibroblasts (MEFs) leads to open telomere ends that initiate a DNA damage response mediated by ATR, resulting in p53-dependent cellular senescence. Loss of Pot1a in the background of p53 deficiency results in increased aberrant homologous recombination at telomeres and elevated genomic instability, which allows Pot1a-/-, p53-/- MEFs to form tumors when injected into SCID mice. These phenotypes are similar to those seen in cells with critically shortened telomeres. In this work, we created a mouse model of telomere ysfunction in the gastrointestinal tract through the conditional deletion of Pot1a that recapitulates the microscopic features seen in severe telomere attrition. Combined intestinal loss of Pot1a and p53 lead to formation of invasive adenocarcinomas in the small and large intestines. The tumors formed with long latency, low multiplicity and had complex genomes due to chromosomal instability, features similar to those seen in sporadic human colorectal cancers. Taken together, we have developed a novel mouse model of intestinal tumorigenesis based on genomic instability driven by telomere dysfunction.

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. ^

A comparison of Markov and generalized linear models of hospital mortality

This paper reports a comparison of three modeling strategies for the analysis of hospital mortality in a sample of general medicine inpatients in a Department of Veterans Affairs medical center. Logistic regression, a Markov chain model, and longitudinal logistic regression were evaluated on predictive performance as measured by the c-index and on accuracy of expected numbers of deaths compared to observed. The logistic regression used patient information collected at admission; the Markov model was comprised of two absorbing states for discharge and death and three transient states reflecting increasing severity of illness as measured by laboratory data collected during the hospital stay; longitudinal regression employed Generalized Estimating Equations (GEE) to model covariance structure for the repeated binary outcome. Results showed that the logistic regression predicted hospital mortality as well as the alternative methods but was limited in scope of application. The Markov chain provides insights into how day to day changes of illness severity lead to discharge or death. The longitudinal logistic regression showed that increasing illness trajectory is associated with hospital mortality. The conclusion is reached that for standard applications in modeling hospital mortality, logistic regression is adequate, but for new challenges facing health services research today, alternative methods are equally predictive, practical, and can provide new insights. ^

Bayesian joint modeling of longitudinal and survival data

The joint modeling of longitudinal and survival data is a new approach to many applications such as HIV, cancer vaccine trials and quality of life studies. There are recent developments of the methodologies with respect to each of the components of the joint model as well as statistical processes that link them together. Among these, second order polynomial random effect models and linear mixed effects models are the most commonly used for the longitudinal trajectory function. In this study, we first relax the parametric constraints for polynomial random effect models by using Dirichlet process priors, then three longitudinal markers rather than only one marker are considered in one joint model. Second, we use a linear mixed effect model for the longitudinal process in a joint model analyzing the three markers. In this research these methods were applied to the Primary Biliary Cirrhosis sequential data, which were collected from a clinical trial of primary biliary cirrhosis (PBC) of the liver. This trial was conducted between 1974 and 1984 at the Mayo Clinic. The effects of three longitudinal markers (1) Total Serum Bilirubin, (2) Serum Albumin and (3) Serum Glutamic-Oxaloacetic transaminase (SGOT) on patients' survival were investigated. Proportion of treatment effect will also be studied using the proposed joint modeling approaches. ^ Based on the results, we conclude that the proposed modeling approaches yield better fit to the data and give less biased parameter estimates for these trajectory functions than previous methods. Model fit is also improved after considering three longitudinal markers instead of one marker only. The results from analysis of proportion of treatment effects from these joint models indicate same conclusion as that from the final model of Fleming and Harrington (1991), which is Bilirubin and Albumin together has stronger impact in predicting patients' survival and as a surrogate endpoints for treatment. ^

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.