A LAPLACE TRANSFORM PAIR MODEL TO DETERMINE BREMSSTRAHLUNG SPECTRA FROM ATTENUATION DATA (RADIATION, X-RAY, SPECTRAL MODELING)

Every x-ray attenuation curve inherently contains all the information necessary to extract the complete energy spectrum of a beam. To date, attempts to obtain accurate spectral information from attenuation data have been inadequate.^ This investigation presents a mathematical pair model, grounded in physical reality by the Laplace Transformation, to describe the attenuation of a photon beam and the corresponding bremsstrahlung spectral distribution. In addition the Laplace model has been mathematically extended to include characteristic radiation in a physically meaningful way. A method to determine the fraction of characteristic radiation in any diagnostic x-ray beam was introduced for use with the extended model.^ This work has examined the reconstructive capability of the Laplace pair model for a photon beam range of from 50 kVp to 25 MV, using both theoretical and experimental methods.^ In the diagnostic region, excellent agreement between a wide variety of experimental spectra and those reconstructed with the Laplace model was obtained when the atomic composition of the attenuators was accurately known. The model successfully reproduced a 2 MV spectrum but demonstrated difficulty in accurately reconstructing orthovoltage and 6 MV spectra. The 25 MV spectrum was successfully reconstructed although poor agreement with the spectrum obtained by Levy was found.^ The analysis of errors, performed with diagnostic energy data, demonstrated the relative insensitivity of the model to typical experimental errors and confirmed that the model can be successfully used to theoretically derive accurate spectral information from experimental attenuation data. ^

Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

A model of the roles of essential kinases in the induction and expression of late long-term potentiation.

The induction of late long-term potentiation (L-LTP) involves complex interactions among second-messenger cascades. To gain insights into these interactions, a mathematical model was developed for L-LTP induction in the CA1 region of the hippocampus. The differential equation-based model represents actions of protein kinase A (PKA), MAP kinase (MAPK), and CaM kinase II (CAMKII) in the vicinity of the synapse, and activation of transcription by CaM kinase IV (CAMKIV) and MAPK. L-LTP is represented by increases in a synaptic weight. Simulations suggest that steep, supralinear stimulus-response relationships between stimuli (e.g., elevations in [Ca(2+)]) and kinase activation are essential for translating brief stimuli into long-lasting gene activation and synaptic weight increases. Convergence of multiple kinase activities to induce L-LTP helps to generate a threshold whereby the amount of L-LTP varies steeply with the number of brief (tetanic) electrical stimuli. The model simulates tetanic, -burst, pairing-induced, and chemical L-LTP, as well as L-LTP due to synaptic tagging. The model also simulates inhibition of L-LTP by inhibition of MAPK, CAMKII, PKA, or CAMKIV. The model predicts results of experiments to delineate mechanisms underlying L-LTP induction and expression. For example, the cAMP antagonist RpcAMPs, which inhibits L-LTP induction, is predicted to inhibit ERK activation. The model also appears useful to clarify similarities and differences between hippocampal L-LTP and long-term synaptic strengthening in other systems.

A model of late long-term potentiation simulates aspects of memory maintenance.

Late long-term potentiation (L-LTP) denotes long-lasting strengthening of synapses between neurons. L-LTP appears essential for the formation of long-term memory, with memories at least partly encoded by patterns of strengthened synapses. How memories are preserved for months or years, despite molecular turnover, is not well understood. Ongoing recurrent neuronal activity, during memory recall or during sleep, has been hypothesized to preferentially potentiate strong synapses, preserving memories. This hypothesis has not been evaluated in the context of a mathematical model representing ongoing activity and biochemical pathways important for L-LTP. In this study, ongoing activity was incorporated into two such models - a reduced model that represents some of the essential biochemical processes, and a more detailed published model. The reduced model represents synaptic tagging and gene induction simply and intuitively, and the detailed model adds activation of essential kinases by Ca(2+). Ongoing activity was modeled as continual brief elevations of Ca(2+). In each model, two stable states of synaptic strength/weight resulted. Positive feedback between synaptic weight and the amplitude of ongoing Ca(2+) transients underlies this bistability. A tetanic or theta-burst stimulus switches a model synapse from a low basal weight to a high weight that is stabilized by ongoing activity. Bistability was robust to parameter variations in both models. Simulations illustrated that prolonged periods of decreased activity reset synaptic strengths to low values, suggesting a plausible forgetting mechanism. However, episodic activity with shorter inactive intervals maintained strong synapses. Both models support experimental predictions. Tests of these predictions are expected to further understanding of how neuronal activity is coupled to maintenance of synaptic strength. Further investigations that examine the dynamics of activity and synaptic maintenance can be expected to help in understanding how memories are preserved for up to a lifetime in animals including humans.

Development of a Bayesian Joint Logistic Model to Better Study the Association between Haplotypes and Disease

In 2011, there will be an estimated 1,596,670 new cancer cases and 571,950 cancer-related deaths in the US. With the ever-increasing applications of cancer genetics in epidemiology, there is great potential to identify genetic risk factors that would help identify individuals with increased genetic susceptibility to cancer, which could be used to develop interventions or targeted therapies that could hopefully reduce cancer risk and mortality. In this dissertation, I propose to develop a new statistical method to evaluate the role of haplotypes in cancer susceptibility and development. This model will be flexible enough to handle not only haplotypes of any size, but also a variety of covariates. I will then apply this method to three cancer-related data sets (Hodgkin Disease, Glioma, and Lung Cancer). I hypothesize that there is substantial improvement in the estimation of association between haplotypes and disease, with the use of a Bayesian mathematical method to infer haplotypes that uses prior information from known genetics sources. Analysis based on haplotypes using information from publically available genetic sources generally show increased odds ratios and smaller p-values in both the Hodgkin, Glioma, and Lung data sets. For instance, the Bayesian Joint Logistic Model (BJLM) inferred haplotype TC had a substantially higher estimated effect size (OR=12.16, 95% CI = 2.47-90.1 vs. 9.24, 95% CI = 1.81-47.2) and more significant p-value (0.00044 vs. 0.008) for Hodgkin Disease compared to a traditional logistic regression approach. Also, the effect sizes of haplotypes modeled with recessive genetic effects were higher (and had more significant p-values) when analyzed with the BJLM. Full genetic models with haplotype information developed with the BJLM resulted in significantly higher discriminatory power and a significantly higher Net Reclassification Index compared to those developed with haplo.stats for lung cancer. Future analysis for this work could be to incorporate the 1000 Genomes project, which offers a larger selection of SNPs can be incorporated into the information from known genetic sources as well. Other future analysis include testing non-binary outcomes, like the levels of biomarkers that are present in lung cancer (NNK), and extending this analysis to full GWAS studies.

A longitudinal comparison of cardiovascular disease risk factors among children and adolescents in the U.S. and Japan: Project HeartBeat!

Blood cholesterol and blood pressure development in childhood and adolescence have important impact on the future adult level of cholesterol and blood pressure, and on increased risk of cardiovascular diseases. The U.S. has higher mortality rates of coronary heart diseases than Japan. A longitudinal comparison in children of risk factor development in the two countries provides more understanding about the causes of cardiovascular disease and its prevention. Such comparisons have not been reported in the past. ^ In Project HeartBeat!, 506 non-Hispanic white, 136 black and 369 Japanese children participated in the study in the U.S. and Japan from 1991 to 1995. A synthetic cohort of ages 8 to 18 years was composed by three cohorts with starting ages at 8, 11, and 14. A multilevel regression model was used for data analysis. ^ The study revealed that the Japanese children had significantly higher slopes of mean total cholesterol (TC) and high density lipoprotein (HDL) cholesterol levels than the U.S. children after adjusting for age and sex. The mean TC level of Japanese children was not significantly different from white and black children. The mean HDL level of Japanese children was significantly higher than white and black children after adjusting for age and sex. The ratio of HDL/TC in Japanese children was significantly higher than in U.S. whites, but not significantly different from the black children. The Japanese group had significantly lower mean diastolic blood pressure phase IV (DBP4) and phase V (DBP5) than the two U.S. groups. The Japanese group also showed significantly higher slopes in systolic blood pressure, DBP5 and DBP4 during the study period than both U.S. groups. The differences were independent from height and body mass index. ^ The study provided the first longitudinal comparison of blood cholesterol and blood pressure between the U.S. and Japanese children and adolescents. It revealed the dynamic process of these factors in the three ethnic groups. ^

CATCH across Texas: Building a model for the diffusion of effective school-based health promotion programs

The impact of health promotion programs is related to both program effectiveness and the extent to which the program is implemented among the target population. The purpose of this dissertation was to describe the development and evaluation of a school-based program diffusion intervention designed to increase the rate of dissemination and adoption of the Child and Adolescent Trial for Cardiovascular Health, or CATCH program (recently renamed the Coordinated Approach to Child Health). ^ The first study described the process by which schools across the state of Texas spontaneously began to adopt the CATCH program after it was tested and proven effective in a multi-site randomized efficacy trial. A survey of teachers and administrator representatives of all schools on record that purchased the CATCH program, but were not involved in the efficacy trial, was used to find out who brought CATCH into the schools, how they garnered support for its adoption, why they decided to adopt the program, and what was involved in deciding to adopt. ^ The second study described how the Intervention Mapping framework guided the planning, development and implementation of a program for the diffusion of CATCH. An iterative process was used to integrate theory, literature, the experience of project staff and data from the target population into a meaningful set of program determinants and performance objectives. Proximal program objectives were specified and translated into both media and interpersonal communication strategies for program diffusion. ^ The third study assessed the effectiveness of the diffusion program in a case-comparison design. Three of the twenty Education Service Center regions in Texas were chosen, selected based on similar demographic criteria, and were followed for adoption of the CATCH curriculum. One of these regions received the full media and interpersonal channel intervention; a second received a reduced media-only intervention, and a third received no intervention. Results suggested the use of the interpersonal channels with media follow-up is an effective means to facilitate program dissemination and adoption. The media-alone condition was not effective in facilitating program adoption. ^

Study of length of stay in the cardiovascular intensive care unit

Coronary artery bypass graft (CABG) surgery is among the most common operations performed in the United States and accounts for more resources expended in cardiovascular medicine than any other single procedure. CABG surgery patients initially recover in the Cardiovascular Intensive Care Unit (CVICU). The post-procedure CVICU length of stay (LOS) goal is two days or less. A longer ICU LOS is associated with a prolonged hospital LOS, poor health outcomes, greater use of limited resources, and increased medical costs. ^ Research has shown that experienced clinicians can predict LOS no better than chance. Current CABG surgery LOS risk models differ greatly in generalizability and ease of use in the clinical setting. A predictive model that identified modifiable pre- and intra-operative risk factors for CVICU LOS greater than two days could have major public health implications as modification of these identified factors could decrease CVICU LOS and potentially minimize morbidity and mortality, optimize use of limited health care resources, and decrease medical costs. ^ The primary aim of this study was to identify modifiable pre-and intra-operative predictors of CVICU LOS greater than two days for CABG surgery patients with cardiopulmonary bypass (CPB). A secondary aim was to build a probability equation for CVICU LOS greater than two days. Data were extracted from 416 medical records of CABG surgery patients with CPB, 50 to 80 years of age, recovered in the CVICU of a large teaching, referral hospital in southeastern Texas, during the calendar year 2004 and the first quarter of 2005. Exclusion criteria included Diagnosis Related Group (DRG) 106, CABG surgery without CPB, CABG surgery with other procedures, and operative deaths. The data were analyzed using multivariate logistic regression for an alpha=0.05, power=0.80, and correlation=0.26. ^ This study found age, history of peripheral arterial disease, and total operative time equal to and greater than four hours to be independent predictors of CVICU LOS greater than two days. The probability of CVICU LOS greater than two days can be calculated by the following equation: -2.872941 +.0323081 (age in years) + .8177223 (history of peripheral arterial disease) + .70379 (operative time). ^

Body mass index trajectories and predictors among 3rd to 12th graders using growth curve mixture modeling the Child and Adolescent Trial for Cardiovascular Health (CATCH) study

This dissertation examined body mass index (BMI) growth trajectories and the effects of gender, ethnicity, dietary intake, and physical activity (PA) on BMI growth trajectories among 3rd to 12th graders (9-18 years of age). Growth curve model analysis was performed using data from The Child and Adolescent Trial for Cardiovascular Health (CATCH) study. The study population included 2909 students who were followed up from grades 3-12. The main outcome was BMI at grades 3, 4, 5, 8, and 12. ^ The results revealed that BMI growth differed across two distinct developmental periods of childhood and adolescence. Rate of BMI growth was faster in middle childhood (9-11 years old or 3rd - 5th grades) than in adolescence (11-18 years old or 5th - 12th grades). Students with higher BMI at 3rd grade (baseline) had faster rates of BMI growth. Three groups of students with distinct BMI growth trajectories were identified: high, average, and low. ^ Black and Hispanic children were more likely to be in the groups with higher baseline BMI and faster rates of BMI growth over time. The effects of gender or ethnicity on BMI growth differed across the three groups. The effects of ethnicity on BMI growth were weakened as the children aged. The effects of gender on BMI growth were attenuated in the groups with a large proportion of black and Hispanic children, i.e., “high” or “average” BMI trajectory group. After controlling for gender, ethnicity, and age at baseline, in the “high BMI trajectory”, rate of yearly BMI growth in middle childhood increased 0.102 for every 500 Kcals increase (p=0.049). No significant effects of percentage of energy from total fat and saturated fat on BMI growth were found. Baseline BMI increased 0.041 for every 30 minutes increased in moderate-to-vigorous PA (MVPA) in the “low BMI trajectory”, while Baseline BMI decreased 0.345 for every 30 minutes increased in vigorous PA (VPA) in the “high BMI trajectory”. ^ Childhood overweight and obesity interventions should start at the earliest possible ages, prior to 3rd grade and continue through grade school. Interventions should focus on all children, but specifically black and Hispanic children, who are more likely to be highest at-risk. Promoting VPA earlier in childhood is important for preventing overweight and obesity among children and adolescents. Interventions should target total energy intake, rather than only percentage of energy from total fat or saturated fat. ^

The combined effect of pravastatin and aspirin on clinical cardiovascular events

The 3-hydroxy-3methylglutaryl coenzyme A (HMG-CoA) reductase inhibitors, or statins, can achieve significant reductions in plasma low-density lipoprotein (LDL)-cholesterol levels. Experimental and clinical evidence now shows that some statins interfere with formation of atherosclerotic lesions independent of their hypolipidemic properties. Vulnerable plaque rupture can result in thrombus formation and artery occlusion; this plaque deterioration is responsible for most acute coronary syndromes, including myocardial infarction (MI), unstable angina, and coronary death, as well as coronary heart diseaseequivalent non-hemorrhagic stroke. Inhibition of HMG-CoA reductase has potential pleiotropic effects other than lipid-lowering, as statins block mevalonic acid production, a precursor to cholesterol and numerous other metabolites. Statins' beneficial effects on clinical events may also thus involve nonlipid-related mechanisms that modify endothelial function, inflammatory responses, plaque stability, and thrombus formation. Aspirin, routinely prescribed to post-MI patients as adjunct therapy, may potentiate statins beneficial effects, as aspirin does not compete metabolically with statins but acts similarly on atherosclerotic lesions. Common functions of both medications include inhibition of platelet activity and aggregation, reduction in atherosclerotic plaque macrophage cell count, and prevention of atherosclerotic vessel endothelial dysfunction. The Cholesterol and Recurrent Events (CARE) trial provides an ideal population in which to examine the combined effects of pravastatin and aspirin. Lipid levels, intermediate outcomes, are examined by pravastatin and aspirin status, and differences between the two pravastatin groups are found. A modified Cox proportional-hazards model with aspirin as a time-dependent covariate was used to determine the effect of aspirin and pravastatin on the clinical cardiovascular composite endpoint of coronary heart disease death, recurrent MI or stroke. Among those assigned to pravastatin, use of aspirin reduced the composite primary endpoint by 35%; this result was similar by gender, race, and diabetic status. Older patients demonstrated a nonsignificant 21% reduction in the primary outcome, whereas the younger had a significant reduction of 43% in the composite primary outcome. Secondary outcomes examined include coronary artery bypass graft (38% reduction), nonsurgical bypass, peripheral vascular disease, and unstable angina. Pravastatin and aspirin in a post-MI population was found to be a beneficial combination that seems to work through lipid and nonlipid, anti-inflammatory mechanisms. ^

A novel method for evaluating an interaction effect of correlated continuous covariates in a linear model

Interaction effect is an important scientific interest for many areas of research. Common approach for investigating the interaction effect of two continuous covariates on a response variable is through a cross-product term in multiple linear regression. In epidemiological studies, the two-way analysis of variance (ANOVA) type of method has also been utilized to examine the interaction effect by replacing the continuous covariates with their discretized levels. However, the implications of model assumptions of either approach have not been examined and the statistical validation has only focused on the general method, not specifically for the interaction effect.^ In this dissertation, we investigated the validity of both approaches based on the mathematical assumptions for non-skewed data. We showed that linear regression may not be an appropriate model when the interaction effect exists because it implies a highly skewed distribution for the response variable. We also showed that the normality and constant variance assumptions required by ANOVA are not satisfied in the model where the continuous covariates are replaced with their discretized levels. Therefore, naïve application of ANOVA method may lead to an incorrect conclusion. ^ Given the problems identified above, we proposed a novel method modifying from the traditional ANOVA approach to rigorously evaluate the interaction effect. The analytical expression of the interaction effect was derived based on the conditional distribution of the response variable given the discretized continuous covariates. A testing procedure that combines the p-values from each level of the discretized covariates was developed to test the overall significance of the interaction effect. According to the simulation study, the proposed method is more powerful then the least squares regression and the ANOVA method in detecting the interaction effect when data comes from a trivariate normal distribution. The proposed method was applied to a dataset from the National Institute of Neurological Disorders and Stroke (NINDS) tissue plasminogen activator (t-PA) stroke trial, and baseline age-by-weight interaction effect was found significant in predicting the change from baseline in NIHSS at Month-3 among patients received t-PA therapy.^

POLYCHOTOMOUS LOGISTIC REGRESSION ANALYSIS (HYPERTENSION, CORONARY HEART DISEASE)

The history of the logistic function since its introduction in 1838 is reviewed, and the logistic model for a polychotomous response variable is presented with a discussion of the assumptions involved in its derivation and use. Following this, the maximum likelihood estimators for the model parameters are derived along with a Newton-Raphson iterative procedure for evaluation. A rigorous mathematical derivation of the limiting distribution of the maximum likelihood estimators is then presented using a characteristic function approach. An appendix with theorems on the asymptotic normality of sample sums when the observations are not identically distributed, with proofs, supports the presentation on asymptotic properties of the maximum likelihood estimators. Finally, two applications of the model are presented using data from the Hypertension Detection and Follow-up Program, a prospective, population-based, randomized trial of treatment for hypertension. The first application compares the risk of five-year mortality from cardiovascular causes with that from noncardiovascular causes; the second application compares risk factors for fatal or nonfatal coronary heart disease with those for fatal or nonfatal stroke. ^

Spatial analysis of cardiovascular disease mortality and air pollution in Harris County, Texas

The association between fine particulate matter air pollution (PM2.5) and cardiovascular disease (CVD) mortality was spatially analyzed for Harris County, Texas, at the census tract level. The objective was to assess how increased PM2.5 exposure related to CVD mortality in this area while controlling for race, income, education, and age. An estimated exposure raster was created for Harris County using Kriging to estimate the PM2.5 exposure at the census tract level. The PM2.5 exposure and the CVD mortality rates were analyzed in an Ordinary Least Squares (OLS) regression model and the residuals were subsequently assessed for spatial autocorrelation. Race, median household income, and age were all found to be significant (p<0.05) predictors in the model. This study found that for every one μg/m3 increase in PM2.5 exposure, holding age and education variables constant, an increase of 16.57 CVD deaths per 100,000 would be predicted for increased minimum exposure values and an increase of 14.47 CVD deaths per 100,000 would be predicted for increased maximum exposure values. This finding supports previous studies associating PM2.5 exposure with CVD mortality. This study further identified the areas of greatest PM2.5 exposure in Harris County as being the geographical locations of populations with the highest risk of CVD (i.e., predominantly older, low-income populations with a predominance of African Americans). The magnitude of the effect of PM2.5 exposure on CVD mortality rates in the study region indicates a need for further community-level studies in Harris County, and suggests that reducing excess PM2.5 exposure would reduce CVD mortality.^

Identification of genes associated with quantitative traits involved in cardiovascular disease and lipoprotein metabolism

Cardiovascular disease (CVD) is a threat to public health. It has been reported to be the leading cause of death in United States. The invention of next generation sequencing (NGS) technology has revolutionized the biomedical research. To investigate NGS data of CVD related quantitative traits would contribute to address the unknown etiology and disease mechanism of CVD. NHLBI's Exome Sequencing Project (ESP) contains CVD related phenotypes and their associated NGS exomes sequence data. Initially, a subset of next generation sequencing data consisting of 13 CVD-related quantitative traits was investigated. Only 6 traits, systolic blood pressure (SBP), diastolic blood pressure (DBP), height, platelet counts, waist circumference, and weight, were analyzed by functional linear model (FLM) and 7 currently existing methods. FLM outperformed all currently existing methods by identifying the highest number of significant genes and had identified 96, 139, 756, 1162, 1106, and 298 genes associated with SBP, DBP, Height, Platelet, Waist, and Weight respectively. ^