Genes to blood pressure: The effects of variation in genes of the renin-angiotensin system on the hormonal and renal control of blood pressure

Objective. Essential hypertension affects 25% of the US adult population and is a leading contributor to morbidity and mortality. Because BP is a multifactorial phenotype that resists simple genetic analysis, intermediate phenotypes within the complex network of BP regulatory systems may be more accessible to genetic dissection. The Renin-Angiotensin System (RAS) is known to influence intermediate and long-term blood pressure regulation through alterations in vascular tone and renal sodium and fluid resorption. This dissertation examines associations between renin (REN), angiotensinogen (AGT), angiotensin-converting enzyme (ACE) and angiotensin II type 1 receptor (AT1) gene variation and interindividual differences in plasma hormone levels, renal hemodynamics, and BP homeostasis.^ Methods. A total of 150 unrelated men and 150 unrelated women, between 20.0 and 49.9 years of age and free of acute or chronic illness except for a history of hypertension (11 men and 7 women, all off medications), were studied after one week on a controlled sodium diet. RAS plasma hormone levels, renal hemodynamics and BP were determined prior to and during angiotensin II (Ang II) infusion. Individuals were genotyped by PCR for a variable number tandem repeat (VNTR) polymorphism in REN, and for the following restriction fragment length polymorphisms (RFLP): AGT M235T, ACE I/D, and AT1 A1166C. Associations between clinical measurements and allelic variation were examined using multiple linear regression statistical models.^ Results. Women homozygous for the AT1 1166C allele demonstrated higher intracellular levels of sodium (p = 0.044). Men homozygous for the AGT T235 allele demonstrated a blunted decrement in renal plasma flow in response to Ang II infusion (p = 0.0002). There were no significant associations between RAS gene variation and interindividual variation in RAS plasma hormone levels or BP.^ Conclusions. Rather than identifying new BP controlling genes or alleles, the study paradigm employed in this thesis (i.e., measured genes, controlled environments and interventions) may provide mechanistic insight into how candidate genes affect BP homeostasis. ^

The role of cardiovascular comorbidities in ovarian cancer survival

Objective. One facet of cancer care that often goes ignored is comorbidities, or diseases that exist in concert with cancer. Comorbid conditions may affect survival by influencing treatment decisions and prognosis. The purpose of this secondary data analysis was to identify whether a history of cardiovascular comorbidities among ovarian cancer patients influenced survival time at the University of Texas M. D. Anderson Cancer Center. The parent study, Project Peace, has a longitudinal design with an embedded randomized efficacy study which seeks to improve detection of depressive disorders in ovarian, peritoneal, and fallopian tube cancers. ^ Methods. Survival time was calculated for the 249 ovarian cancer patients abstracted by Project Peace staff. Cardiovascular comorbidities were documented as present, based upon information from medical records in addition to self reported comorbidities in a baseline study questionnaire. Kaplan-Meier survival curves were used to compare survival time among patients with a presence or absence of particular cardiovascular comorbidities. Cox Regression proportional models accounted for multivariable factors such as age, staging, family history of cardiovascular comorbidities, and treatment. ^ Results. Among our patient population, there was a statistically significant relationship between shorter survival time and a history of thrombosis, pericardial disease/tamponade, or COPD/pulmonary hypertension. Ovarian cancer patients with a history of thrombosis lived approximately half as long as patients without thrombosis (58.06 months vs. 121.55 months; p=.001). In addition, patients who suffered from pericardial disease/tamponade had poorer survival than those without a history of pericardial disease/tamponade (48 months vs. 80.07 months; p=.002). Ovarian cancer patients with a history of COPD or pulmonary hypertension had a median survival of 60.2 months, while the median survival for patients without these comorbidities was 80.2 months (p=.014). ^ Conclusion. Especially because of its relatively lower survival rate, greater emphasis needs to be placed on the potential influence of cardiovascular comorbid conditions in ovarian cancer.^

Evaluation of the Hosmer -Lemeshow global goodness -of-fit statistic for mixed variable logistic regression models

The performance of the Hosmer-Lemeshow global goodness-of-fit statistic for logistic regression models was explored in a wide variety of conditions not previously fully investigated. Computer simulations, each consisting of 500 regression models, were run to assess the statistic in 23 different situations. The items which varied among the situations included the number of observations used in each regression, the number of covariates, the degree of dependence among the covariates, the combinations of continuous and discrete variables, and the generation of the values of the dependent variable for model fit or lack of fit.^ The study found that the $\rm\ C$g* statistic was adequate in tests of significance for most situations. However, when testing data which deviate from a logistic model, the statistic has low power to detect such deviation. Although grouping of the estimated probabilities into quantiles from 8 to 30 was studied, the deciles of risk approach was generally sufficient. Subdividing the estimated probabilities into more than 10 quantiles when there are many covariates in the model is not necessary, despite theoretical reasons which suggest otherwise. Because it does not follow a X$\sp2$ distribution, the statistic is not recommended for use in models containing only categorical variables with a limited number of covariate patterns.^ The statistic performed adequately when there were at least 10 observations per quantile. Large numbers of observations per quantile did not lead to incorrect conclusions that the model did not fit the data when it actually did. However, the statistic failed to detect lack of fit when it existed and should be supplemented with further tests for the influence of individual observations. Careful examination of the parameter estimates is also essential since the statistic did not perform as desired when there was moderate to severe collinearity among covariates.^ Two methods studied for handling tied values of the estimated probabilities made only a slight difference in conclusions about model fit. Neither method split observations with identical probabilities into different quantiles. Approaches which create equal size groups by separating ties should be avoided. ^

Logistic regression models for ordinal response: A study of self-efficacy in colorectal cancer screening

The ordinal logistic regression models are used to analyze the dependant variable with multiple outcomes that can be ranked, but have been underutilized. In this study, we describe four logistic regression models for analyzing the ordinal response variable. ^ In this methodological study, the four regression models are proposed. The first model uses the multinomial logistic model. The second is adjacent-category logit model. The third is the proportional odds model and the fourth model is the continuation-ratio model. We illustrate and compare the fit of these models using data from the survey designed by the University of Texas, School of Public Health research project PCCaSO (Promoting Colon Cancer Screening in people 50 and Over), to study the patient’s confidence in the completion colorectal cancer screening (CRCS). ^ The purpose of this study is two fold: first, to provide a synthesized review of models for analyzing data with ordinal response, and second, to evaluate their usefulness in epidemiological research, with particular emphasis on model formulation, interpretation of model coefficients, and their implications. Four ordinal logistic models that are used in this study include (1) Multinomial logistic model, (2) Adjacent-category logistic model [9], (3) Continuation-ratio logistic model [10], (4) Proportional logistic model [11]. We recommend that the analyst performs (1) goodness-of-fit tests, (2) sensitivity analysis by fitting and comparing different models.^

Selection bias and the cross-validation of regression models for prediction

Strategies are compared for the development of a linear regression model with stochastic (multivariate normal) regressor variables and the subsequent assessment of its predictive ability. Bias and mean squared error of four estimators of predictive performance are evaluated in simulated samples of 32 population correlation matrices. Models including all of the available predictors are compared with those obtained using selected subsets. The subset selection procedures investigated include two stopping rules, C$\sb{\rm p}$ and S$\sb{\rm p}$, each combined with an 'all possible subsets' or 'forward selection' of variables. The estimators of performance utilized include parametric (MSEP$\sb{\rm m}$) and non-parametric (PRESS) assessments in the entire sample, and two data splitting estimates restricted to a random or balanced (Snee's DUPLEX) 'validation' half sample. The simulations were performed as a designed experiment, with population correlation matrices representing a broad range of data structures.^ The techniques examined for subset selection do not generally result in improved predictions relative to the full model. Approaches using 'forward selection' result in slightly smaller prediction errors and less biased estimators of predictive accuracy than 'all possible subsets' approaches but no differences are detected between the performances of C$\sb{\rm p}$ and S$\sb{\rm p}$. In every case, prediction errors of models obtained by subset selection in either of the half splits exceed those obtained using all predictors and the entire sample.^ Only the random split estimator is conditionally (on $\\beta$) unbiased, however MSEP$\sb{\rm m}$ is unbiased on average and PRESS is nearly so in unselected (fixed form) models. When subset selection techniques are used, MSEP$\sb{\rm m}$ and PRESS always underestimate prediction errors, by as much as 27 percent (on average) in small samples. Despite their bias, the mean squared errors (MSE) of these estimators are at least 30 percent less than that of the unbiased random split estimator. The DUPLEX split estimator suffers from large MSE as well as bias, and seems of little value within the context of stochastic regressor variables.^ To maximize predictive accuracy while retaining a reliable estimate of that accuracy, it is recommended that the entire sample be used for model development, and a leave-one-out statistic (e.g. PRESS) be used for assessment. ^

Assessing time-by-covariate interactions in Cox proportional hazards regression models using cubic spline functions

This dissertation develops and explores the methodology for the use of cubic spline functions in assessing time-by-covariate interactions in Cox proportional hazards regression models. These interactions indicate violations of the proportional hazards assumption of the Cox model. Use of cubic spline functions allows for the investigation of the shape of a possible covariate time-dependence without having to specify a particular functional form. Cubic spline functions yield both a graphical method and a formal test for the proportional hazards assumption as well as a test of the nonlinearity of the time-by-covariate interaction. Five existing methods for assessing violations of the proportional hazards assumption are reviewed and applied along with cubic splines to three well known two-sample datasets. An additional dataset with three covariates is used to explore the use of cubic spline functions in a more general setting. ^

Predicting childhood sexual or physical abuse: a logistic regression geo-mapping approach to prevention.

This study investigates the degree to which gender, ethnicity, relationship to perpetrator, and geomapped socio-economic factors significantly predict the incidence of childhood sexual abuse, physical abuse and non- abuse. These variables are then linked to geographic identifiers using geographic information system (GIS) technology to develop a geo-mapping framework for child sexual and physical abuse prevention.

Extended kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks.

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

BAYESIAN PHASE I DOSE FINDING IN CANCER TRIALS

This dissertation explores phase I dose-finding designs in cancer trials from three perspectives: the alternative Bayesian dose-escalation rules, a design based on a time-to-dose-limiting toxicity (DLT) model, and a design based on a discrete-time multi-state (DTMS) model. We list alternative Bayesian dose-escalation rules and perform a simulation study for the intra-rule and inter-rule comparisons based on two statistical models to identify the most appropriate rule under certain scenarios. We provide evidence that all the Bayesian rules outperform the traditional ``3+3'' design in the allocation of patients and selection of the maximum tolerated dose. The design based on a time-to-DLT model uses patients' DLT information over multiple treatment cycles in estimating the probability of DLT at the end of treatment cycle 1. Dose-escalation decisions are made whenever a cycle-1 DLT occurs, or two months after the previous check point. Compared to the design based on a logistic regression model, the new design shows more safety benefits for trials in which more late-onset toxicities are expected. As a trade-off, the new design requires more patients on average. The design based on a discrete-time multi-state (DTMS) model has three important attributes: (1) Toxicities are categorized over a distribution of severity levels, (2) Early toxicity may inform dose escalation, and (3) No suspension is required between accrual cohorts. The proposed model accounts for the difference in the importance of the toxicity severity levels and for transitions between toxicity levels. We compare the operating characteristics of the proposed design with those from a similar design based on a fully-evaluated model that directly models the maximum observed toxicity level within the patients' entire assessment window. We describe settings in which, under comparable power, the proposed design shortens the trial. The proposed design offers more benefit compared to the alternative design as patient accrual becomes slower.

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. ^

An empirical evaluation of the Random Forests classifier models for variable selection in a large-scale lung cancer case-control study

Random Forests™ is reported to be one of the most accurate classification algorithms in complex data analysis. It shows excellent performance even when most predictors are noisy and the number of variables is much larger than the number of observations. In this thesis Random Forests was applied to a large-scale lung cancer case-control study. A novel way of automatically selecting prognostic factors was proposed. Also, synthetic positive control was used to validate Random Forests method. Throughout this study we showed that Random Forests can deal with large number of weak input variables without overfitting. It can account for non-additive interactions between these input variables. Random Forests can also be used for variable selection without being adversely affected by collinearities. ^ Random Forests can deal with the large-scale data sets without rigorous data preprocessing. It has robust variable importance ranking measure. Proposed is a novel variable selection method in context of Random Forests that uses the data noise level as the cut-off value to determine the subset of the important predictors. This new approach enhanced the ability of the Random Forests algorithm to automatically identify important predictors for complex data. The cut-off value can also be adjusted based on the results of the synthetic positive control experiments. ^ When the data set had high variables to observations ratio, Random Forests complemented the established logistic regression. This study suggested that Random Forests is recommended for such high dimensionality data. One can use Random Forests to select the important variables and then use logistic regression or Random Forests itself to estimate the effect size of the predictors and to classify new observations. ^ We also found that the mean decrease of accuracy is a more reliable variable ranking measurement than mean decrease of Gini. ^

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. ^

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.^

Effects of informative censoring on the hazard function: Application to the proportional hazards regression model

The standard analyses of survival data involve the assumption that survival and censoring are independent. When censoring and survival are related, the phenomenon is known as informative censoring. This paper examines the effects of an informative censoring assumption on the hazard function and the estimated hazard ratio provided by the Cox model.^ The limiting factor in all analyses of informative censoring is the problem of non-identifiability. Non-identifiability implies that it is impossible to distinguish a situation in which censoring and death are independent from one in which there is dependence. However, it is possible that informative censoring occurs. Examination of the literature indicates how others have approached the problem and covers the relevant theoretical background.^ Three models are examined in detail. The first model uses conditionally independent marginal hazards to obtain the unconditional survival function and hazards. The second model is based on the Gumbel Type A method for combining independent marginal distributions into bivariate distributions using a dependency parameter. Finally, a formulation based on a compartmental model is presented and its results described. For the latter two approaches, the resulting hazard is used in the Cox model in a simulation study.^ The unconditional survival distribution formed from the first model involves dependency, but the crude hazard resulting from this unconditional distribution is identical to the marginal hazard, and inferences based on the hazard are valid. The hazard ratios formed from two distributions following the Gumbel Type A model are biased by a factor dependent on the amount of censoring in the two populations and the strength of the dependency of death and censoring in the two populations. The Cox model estimates this biased hazard ratio. In general, the hazard resulting from the compartmental model is not constant, even if the individual marginal hazards are constant, unless censoring is non-informative. The hazard ratio tends to a specific limit.^ Methods of evaluating situations in which informative censoring is present are described, and the relative utility of the three models examined is discussed. ^

A Bayesian approach to estimating the regression coefficients of a multinomial logit model

A Bayesian approach to estimation of the regression coefficients of a multinominal logit model with ordinal scale response categories is presented. A Monte Carlo method is used to construct the posterior distribution of the link function. The link function is treated as an arbitrary scalar function. Then the Gauss-Markov theorem is used to determine a function of the link which produces a random vector of coefficients. The posterior distribution of the random vector of coefficients is used to estimate the regression coefficients. The method described is referred to as a Bayesian generalized least square (BGLS) analysis. Two cases involving multinominal logit models are described. Case I involves a cumulative logit model and Case II involves a proportional-odds model. All inferences about the coefficients for both cases are described in terms of the posterior distribution of the regression coefficients. The results from the BGLS method are compared to maximum likelihood estimates of the regression coefficients. The BGLS method avoids the nonlinear problems encountered when estimating the regression coefficients of a generalized linear model. The method is not complex or computationally intensive. The BGLS method offers several advantages over Bayesian approaches. ^