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. ^

Left ventricular growth from age 8 to 18 and its anthropometric determinants: Longitudinal results from Project Heartbeat!

Left ventricular mass (LVM) is a strong predictor of cardiovascular disease (CVD) in adults. However, normal growth of LVM in healthy children is not well understood, and previous results on independent effects of body size and body fatness on LVM have been inconsistent. The purpose of this study was (1) to establish the normal growth curve of LVM from age 8 to age 18, and evaluate the determinants of change in LVM with age, and (2) to assess the independent effects of body size and body fatness on LVM.^ In Project HeartBeat!, 678 healthy children aged 8, 11 and 14 years at baseline were enrolled and examined at 4-monthly intervals for up to 4 years. A synthetic cohort with continuous observations from age 8 to 18 years was constructed. A total of 4608 LVM measurements was made from M-mode echocardiography. The multilevel linear model was used for analysis.^ Sex-specific trajectories of normal growth of LVM from age 8 to 18 was displayed. On average, LVM was 15 g higher in males than females. Average LVM increased linearly in males from 78 g at age 8 to 145 g at age 18. For females, the trajectory was curvilinear, nearly constant after age 14. No significant racial differences were found. After adjustment for the effects of body size and body fatness, average LVM decreased slightly from age 8 to 18, and sex differences in changes of LVM remained constant.^ The impact of body size on LVM was examined by adding to a basic LVM-sex-age model one of 9 body size indicators. The impact of body fatness was tested by further introducing into each of the 9 LVM models (with one or another of the body size indicators) one of 4 body fatness indicators, yielding 36 models with different body size and body fatness combinations. The results indicated that effects of body size on LVM can be distinguished between fat-free body mass and fat body mass, both being independent, positive predictors. The former is the stronger determinant. When a non-fat-free body size indicator is used as predictor, the estimated residual effect of body fatness on LVM becomes negative. ^

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. ^

Lifetime changes in body mass index and risk of breast cancer in minority women

Introduction: Obesity is an epidemic in the United States, especially among Hispanics and African-Americans. Studies of obesity and breast cancer risk and subtype have been conducted primarily in non-Hispanic whites. Obesity is inversely associated with premenopausal breast cancer, but both obesity and weight gain increase the risk of postmenopausal disease. Obesity has been associated with breast cancer subtype in many studies. Methods: To assess the association between changes in body mass index (BMI) over the lifetime, weight gain, and breast cancer in Mexican-American women, we conducted a case-control study using 149 cases and 330 age-matched controls. In a second study, we identified 212 African-American and 167 Mexican-American women with breast cancer in the ongoing ELLA Bi-National Breast Cancer Study, abstracted medical charts to classify tumors as ER+/PR+, HER2+, or ER-/PR-/HER2-, and assessed the association between lifetime changes in body mass index, weight gain, and breast cancer subtype. In both studies, growth mixture modeling was use to identify trajectories of change in BMI over the lifetime, and these trajectories were used as exposures in a logistic regression model to calculate odds ratios (OR). Results: There was no association between trajectories of change in BMI and breast cancer risk in Mexican-American women. In addition, BMI at ages 15 and 30 and at diagnosis was not associated with breast cancer. However, adult weight gain was inversely associated with breast cancer risk (per 5kg, OR=0.92, 95% CI: 0.85-0.99). The case-only analysis found no association between obesity at ages 15 and 30 and at diagnosis and breast cancer subtype. Further, there was no association between adult weight gain (defined as weight change from age 15 to time of diagnosis) and breast cancer subtype. Conclusions: Obesity was not associated with breast cancer risk in Mexican-American women, while adult weight gain reduced the risk independently of menopausal status. These results are contradictory of those in non-Hispanic white women and suggest that the etiology of breast cancer may differ by race/ethnicity. Further, obesity was not associated with breast cancer subtype in African-American and Mexican-American women, contrary to results in non-Hispanic white women. ^

Predictive oncology: a review of multidisciplinary, multiscale in silico modeling linking phenotype, morphology and growth.

Empirical evidence and theoretical studies suggest that the phenotype, i.e., cellular- and molecular-scale dynamics, including proliferation rate and adhesiveness due to microenvironmental factors and gene expression that govern tumor growth and invasiveness, also determine gross tumor-scale morphology. It has been difficult to quantify the relative effect of these links on disease progression and prognosis using conventional clinical and experimental methods and observables. As a result, successful individualized treatment of highly malignant and invasive cancers, such as glioblastoma, via surgical resection and chemotherapy cannot be offered and outcomes are generally poor. What is needed is a deterministic, quantifiable method to enable understanding of the connections between phenotype and tumor morphology. Here, we critically assess advantages and disadvantages of recent computational modeling efforts (e.g., continuum, discrete, and cellular automata models) that have pursued this understanding. Based on this assessment, we review a multiscale, i.e., from the molecular to the gross tumor scale, mathematical and computational "first-principle" approach based on mass conservation and other physical laws, such as employed in reaction-diffusion systems. Model variables describe known characteristics of tumor behavior, and parameters and functional relationships across scales are informed from in vitro, in vivo and ex vivo biology. We review the feasibility of this methodology that, once coupled to tumor imaging and tumor biopsy or cell culture data, should enable prediction of tumor growth and therapy outcome through quantification of the relation between the underlying dynamics and morphological characteristics. In particular, morphologic stability analysis of this mathematical model reveals that tumor cell patterning at the tumor-host interface is regulated by cell proliferation, adhesion and other phenotypic characteristics: histopathology information of tumor boundary can be inputted to the mathematical model and used as a phenotype-diagnostic tool to predict collective and individual tumor cell invasion of surrounding tissue. This approach further provides a means to deterministically test effects of novel and hypothetical therapy strategies on tumor behavior.

TIME SERIES ANALYSIS AS INPUT FOR PREDICTIVE MODELING: PREDICTING CARDIAC ARREST IN A PEDIATRIC INTENSIVE CARE UNIT

The first manuscript, entitled "Time-Series Analysis as Input for Clinical Predictive Modeling: Modeling Cardiac Arrest in a Pediatric ICU" lays out the theoretical background for the project. There are several core concepts presented in this paper. First, traditional multivariate models (where each variable is represented by only one value) provide single point-in-time snapshots of patient status: they are incapable of characterizing deterioration. Since deterioration is consistently identified as a precursor to cardiac arrests, we maintain that the traditional multivariate paradigm is insufficient for predicting arrests. We identify time series analysis as a method capable of characterizing deterioration in an objective, mathematical fashion, and describe how to build a general foundation for predictive modeling using time series analysis results as latent variables. Building a solid foundation for any given modeling task involves addressing a number of issues during the design phase. These include selecting the proper candidate features on which to base the model, and selecting the most appropriate tool to measure them. We also identified several unique design issues that are introduced when time series data elements are added to the set of candidate features. One such issue is in defining the duration and resolution of time series elements required to sufficiently characterize the time series phenomena being considered as candidate features for the predictive model. Once the duration and resolution are established, there must also be explicit mathematical or statistical operations that produce the time series analysis result to be used as a latent candidate feature. In synthesizing the comprehensive framework for building a predictive model based on time series data elements, we identified at least four classes of data that can be used in the model design. The first two classes are shared with traditional multivariate models: multivariate data and clinical latent features. Multivariate data is represented by the standard one value per variable paradigm and is widely employed in a host of clinical models and tools. These are often represented by a number present in a given cell of a table. Clinical latent features derived, rather than directly measured, data elements that more accurately represent a particular clinical phenomenon than any of the directly measured data elements in isolation. The second two classes are unique to the time series data elements. The first of these is the raw data elements. These are represented by multiple values per variable, and constitute the measured observations that are typically available to end users when they review time series data. These are often represented as dots on a graph. The final class of data results from performing time series analysis. This class of data represents the fundamental concept on which our hypothesis is based. The specific statistical or mathematical operations are up to the modeler to determine, but we generally recommend that a variety of analyses be performed in order to maximize the likelihood that a representation of the time series data elements is produced that is able to distinguish between two or more classes of outcomes. The second manuscript, entitled "Building Clinical Prediction Models Using Time Series Data: Modeling Cardiac Arrest in a Pediatric ICU" provides a detailed description, start to finish, of the methods required to prepare the data, build, and validate a predictive model that uses the time series data elements determined in the first paper. One of the fundamental tenets of the second paper is that manual implementations of time series based models are unfeasible due to the relatively large number of data elements and the complexity of preprocessing that must occur before data can be presented to the model. Each of the seventeen steps is analyzed from the perspective of how it may be automated, when necessary. We identify the general objectives and available strategies of each of the steps, and we present our rationale for choosing a specific strategy for each step in the case of predicting cardiac arrest in a pediatric intensive care unit. Another issue brought to light by the second paper is that the individual steps required to use time series data for predictive modeling are more numerous and more complex than those used for modeling with traditional multivariate data. Even after complexities attributable to the design phase (addressed in our first paper) have been accounted for, the management and manipulation of the time series elements (the preprocessing steps in particular) are issues that are not present in a traditional multivariate modeling paradigm. In our methods, we present the issues that arise from the time series data elements: defining a reference time; imputing and reducing time series data in order to conform to a predefined structure that was specified during the design phase; and normalizing variable families rather than individual variable instances. The final manuscript, entitled: "Using Time-Series Analysis to Predict Cardiac Arrest in a Pediatric Intensive Care Unit" presents the results that were obtained by applying the theoretical construct and its associated methods (detailed in the first two papers) to the case of cardiac arrest prediction in a pediatric intensive care unit. Our results showed that utilizing the trend analysis from the time series data elements reduced the number of classification errors by 73%. The area under the Receiver Operating Characteristic curve increased from a baseline of 87% to 98% by including the trend analysis. In addition to the performance measures, we were also able to demonstrate that adding raw time series data elements without their associated trend analyses improved classification accuracy as compared to the baseline multivariate model, but diminished classification accuracy as compared to when just the trend analysis features were added (ie, without adding the raw time series data elements). We believe this phenomenon was largely attributable to overfitting, which is known to increase as the ratio of candidate features to class examples rises. Furthermore, although we employed several feature reduction strategies to counteract the overfitting problem, they failed to improve the performance beyond that which was achieved by exclusion of the raw time series elements. Finally, our data demonstrated that pulse oximetry and systolic blood pressure readings tend to start diminishing about 10-20 minutes before an arrest, whereas heart rates tend to diminish rapidly less than 5 minutes before an arrest.

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 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. ^

Mixed effects model in negative exponential curve

Despite many researches on development in education and psychology, not often is the methodology tested with real data. A major barrier to test the growth model is that the design of study includes repeated observations and the nature of the growth is nonlinear. The repeat measurements on a nonlinear model require sophisticated statistical methods. In this study, we present mixed effects model in a negative exponential curve to describe the development of children's reading skills. This model can describe the nature of the growth on children's reading skills and account for intra-individual and inter-individual variation. We also apply simple techniques including cross-validation, regression, and graphical methods to determine the most appropriate curve for data, to find efficient initial values of parameters, and to select potential covariates. We illustrate with an example that motivated this research: a longitudinal study of academic skills from grade 1 to grade 12 in Connecticut public schools. ^

A coalescent analysis for modeling the mutation process in colorectal cancer

Colorectal cancer is the forth most common diagnosed cancer in the United States. Every year about a hundred forty-seven thousand people will be diagnosed with colorectal cancer and fifty-six thousand people lose their lives due to this disease. Most of the hereditary nonpolyposis colorectal cancer (HNPCC) and 12% of the sporadic colorectal cancer show microsatellite instability. Colorectal cancer is a multistep progressive disease. It starts from a mutation in a normal colorectal cell and grows into a clone of cells that further accumulates mutations and finally develops into a malignant tumor. In terms of molecular evolution, the process of colorectal tumor progression represents the acquisition of sequential mutations. ^ Clinical studies use biomarkers such as microsatellite or single nucleotide polymorphisms (SNPs) to study mutation frequencies in colorectal cancer. Microsatellite data obtained from single genome equivalent PCR or small pool PCR can be used to infer tumor progression. Since tumor progression is similar to population evolution, we used an approach known as coalescent, which is well established in population genetics, to analyze this type of data. Coalescent theory has been known to infer the sample's evolutionary path through the analysis of microsatellite data. ^ The simulation results indicate that the constant population size pattern and the rapid tumor growth pattern have different genetic polymorphic patterns. The simulation results were compared with experimental data collected from HNPCC patients. The preliminary result shows the mutation rate in 6 HNPCC patients range from 0.001 to 0.01. The patients' polymorphic patterns are similar to the constant population size pattern which implies the tumor progression is through multilineage persistence instead of clonal sequential evolution. The results should be further verified using a larger dataset. ^

Growth and development of body fat distribution from skinfold measurements: Longitudinal principal components

Longitudinal principal components analyses on a combination of four subcutaneous skinfolds (biceps, triceps, subscapular and suprailiac) were performed using data from the London Longitudinal Growth Study. The main objectives were to discover at what age during growth sex differences in body fat distribution occur and to see if there is continuity in body fatness and body fat distribution from childhood into the adult status (18 years). The analyses were done for four age sectors (3mon-3yrs, 3yrs-8yrs, 8yrs-18yrs and 3yrs-18yrs). Longitudinal principal component one (LPC1) for each age interval in both sexes represents the population mean fat curve. Component two (LPC2) is a velocity of fatness component. Component three (LPC3) in the 3mon-3yrs age sector represents infant fat wave in both sexes. In the next two age sectors component three in males represents peaks and shifts in fat growth (change in velocity), while in females it represents body fat distribution. Component four (LPC4) in the same two age sectors is a reversal in the sexes of the patterns seen for component three, i.e., in males it is body fat distribution and in females velocity shifts. Components five and above represent more complicated patterns of change (multiple increases and decreases across the age interval). In both sexes there is strong tracking in fatness from middle childhood to adolescence. In males only there is also a low to moderate tracking of infant fat with middle to late childhood fat. These data are strongly supported in the literature. Several factors are known to predict adult fatness among the most important being previous levels of fatness (at earlier ages) and the age at rebound. In addition we found that the velocity of fat change in middle childhood was highly predictive of later fatness (r $\approx -$0.7), even more so than age at rebound (r $\approx -$0.5). In contrast to fatness (LPC1), body fat distribution (LPC3-LPC4) did not track well even though significant components of body fat distribution occur at each age. Tracking of body fat distribution was higher in females than males. Sex differences in body fat distribution are non existent. Some sex differences are evident with the peripheral-to-central ratios after age 14 years. ^

Mixture modeling for joint analysis of survival, discrete, and continuous data

Mixture modeling is commonly used to model categorical latent variables that represent subpopulations in which population membership is unknown but can be inferred from the data. In relatively recent years, the potential of finite mixture models has been applied in time-to-event data. However, the commonly used survival mixture model assumes that the effects of the covariates involved in failure times differ across latent classes, but the covariate distribution is homogeneous. The aim of this dissertation is to develop a method to examine time-to-event data in the presence of unobserved heterogeneity under a framework of mixture modeling. A joint model is developed to incorporate the latent survival trajectory along with the observed information for the joint analysis of a time-to-event variable, its discrete and continuous covariates, and a latent class variable. It is assumed that the effects of covariates on survival times and the distribution of covariates vary across different latent classes. The unobservable survival trajectories are identified through estimating the probability that a subject belongs to a particular class based on observed information. We applied this method to a Hodgkin lymphoma study with long-term follow-up and observed four distinct latent classes in terms of long-term survival and distributions of prognostic factors. Our results from simulation studies and from the Hodgkin lymphoma study demonstrated the superiority of our joint model compared with the conventional survival model. This flexible inference method provides more accurate estimation and accommodates unobservable heterogeneity among individuals while taking involved interactions between covariates into consideration.^