BEST SUBSET SELECTION FOR CATEGORICAL DATA

When choosing among models to describe categorical data, the necessity to consider interactions makes selection more difficult. With just four variables, considering all interactions, there are 166 different hierarchical models and many more non-hierarchical models. Two procedures have been developed for categorical data which will produce the "best" subset or subsets of each model size where size refers to the number of effects in the model. Both procedures are patterned after the Leaps and Bounds approach used by Furnival and Wilson for continuous data and do not generally require fitting all models. For hierarchical models, likelihood ratio statistics (G('2)) are computed using iterative proportional fitting and "best" is determined by comparing, among models with the same number of effects, the Pr((chi)(,k)('2) (GREATERTHEQ) G(,ij)('2)) where k is the degrees of freedom for ith model of size j. To fit non-hierarchical as well as hierarchical models, a weighted least squares procedure has been developed.^ The procedures are applied to published occupational data relating to the occurrence of byssinosis. These results are compared to previously published analyses of the same data. Also, the procedures are applied to published data on symptoms in psychiatric patients and again compared to previously published analyses.^ These procedures will make categorical data analysis more accessible to researchers who are not statisticians. The procedures should also encourage more complex exploratory analyses of epidemiologic data and contribute to the development of new hypotheses for study. ^

STUDIES ON THE PATTERNS OF NUCLEOTIDE AND AMINO ACID SUBSTITUTION (ELECTROPHORESIS, MUTATION RATE, SELECTION, BASE, COMPOSITION)

Theoretical and empirical studies were conducted on the pattern of nucleotide and amino acid substitution in evolution, taking into account the effects of mutation at the nucleotide level and purifying selection at the amino acid level. A theoretical model for predicting the evolutionary change in electrophoretic mobility of a protein was also developed by using information on the pattern of amino acid substitution. The specific problems studied and the main results obtained are as follows: (1) Estimation of the pattern of nucleotide substitution in DNA nuclear genomes. The pattern of point mutations and nucleotide substitutions among the four different nucleotides are inferred from the evolutionary changes of pseudogenes and functional genes, respectively. Both patterns are non-random, the rate of change varying considerably with nucleotide pair, and that in both cases transitions occur somewhat more frequently than transversions. In protein evolution, substitution occurs more often between amino acids with similar physico-chemical properties than between dissimilar amino acids. (2) Estimation of the pattern of nucleotide substitution in RNA genomes. The majority of mutations in retroviruses accumulate at the reverse transcription stage. Selection at the amino acid level is very weak, and almost non-existent between synonymous codons. The pattern of mutation is very different from that in DNA genomes. Nevertheless, the pattern of purifying selection at the amino acid level is similar to that in DNA genomes, although selection intensity is much weaker. (3) Evaluation of the determinants of molecular evolutionary rates in protein-coding genes. Based on rates of nucleotide substitution for mammalian genes, the rate of amino acid substitution of a protein is determined by its amino acid composition. The content of glycine is shown to correlate strongly and negatively with the rate of substitution. Empirical formulae, called indices of mutability, are developed in order to predict the rate of molecular evolution of a protein from data on its amino acid sequence. (4) Studies on the evolutionary patterns of electrophoretic mobility of proteins. A theoretical model was constructed that predicts the electric charge of a protein at any given pH and its isoelectric point from data on its primary and quaternary structures. Using this model, the evolutionary change in electrophoretic mobilities of different proteins and the expected amount of electrophoretically hidden genetic variation were studied. In the absence of selection for the pI value, proteins will on the average evolve toward a mildly basic pI. (Abstract shortened with permission of author.) ^

Detecting the signature of natural selection with microsatellites

Natural selection is one of the major factors in the evolution of all organisms. Detecting the signature of natural selection has been a central theme in evolutionary genetics. With the availability of microsatellite data, it is of interest to study how natural selection can be detected with microsatellites. ^ The overall aim of this research is to detect signatures of natural selection with data on genetic variation at microsatellite loci. The null hypothesis to be tested is the neutral mutation theory of molecular evolution, which states that different alleles at a locus have equivalent effects on fitness. Currently used tests of this hypothesis based on data on genetic polymorphism in natural populations presume that mutations at the loci follow the infinite allele/site models (IAM, ISM), in the sense that at each site at most only one mutation event is recorded, and each mutation leads to an allele not seen before in the population. Microsatellite loci, which are abundant in the genome, do not obey these mutation models, since the new alleles at such loci can be created either by contraction or expansion of tandem repeat sizes of core motifs. Since the current genome map is mainly composed of microsatellite loci and this class of loci is still most commonly studied in the context of human genome diversity, this research explores how the current test procedures for testing the neutral mutation hypothesis should be modified to take into account a generalized model of forward-backward stepwise mutations. In addition, recent literature also suggested that past demographic history of populations, presence of population substructure, and varying rates of mutations across loci all have confounding effects for detecting signatures of natural selection. ^ The effects of the stepwise mutation model and other confounding factors on detecting signature of natural selection are the main results of the research. ^

Single nucleotide polymorphism (SNP) selection for genotype-phenotype association studies

With hundreds of single nucleotide polymorphisms (SNPs) in a candidate gene and millions of SNPs across the genome, selecting an informative subset of SNPs to maximize the ability to detect genotype-phenotype association is of great interest and importance. In addition, with a large number of SNPs, analytic methods are needed that allow investigators to control the false positive rate resulting from large numbers of SNP genotype-phenotype analyses. This dissertation uses simulated data to explore methods for selecting SNPs for genotype-phenotype association studies. I examined the pattern of linkage disequilibrium (LD) across a candidate gene region and used this pattern to aid in localizing a disease-influencing mutation. The results indicate that the r2 measure of linkage disequilibrium is preferred over the common D′ measure for use in genotype-phenotype association studies. Using step-wise linear regression, the best predictor of the quantitative trait was not usually the single functional mutation. Rather it was a SNP that was in high linkage disequilibrium with the functional mutation. Next, I compared three strategies for selecting SNPs for application to phenotype association studies: based on measures of linkage disequilibrium, based on a measure of haplotype diversity, and random selection. The results demonstrate that SNPs selected based on maximum haplotype diversity are more informative and yield higher power than randomly selected SNPs or SNPs selected based on low pair-wise LD. The data also indicate that for genes with small contribution to the phenotype, it is more prudent for investigators to increase their sample size than to continuously increase the number of SNPs in order to improve statistical power. When typing large numbers of SNPs, researchers are faced with the challenge of utilizing an appropriate statistical method that controls the type I error rate while maintaining adequate power. We show that an empirical genotype based multi-locus global test that uses permutation testing to investigate the null distribution of the maximum test statistic maintains a desired overall type I error rate while not overly sacrificing statistical power. The results also show that when the penetrance model is simple the multi-locus global test does as well or better than the haplotype analysis. However, for more complex models, haplotype analyses offer advantages. The results of this dissertation will be of utility to human geneticists designing large-scale multi-locus genotype-phenotype association studies. ^

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. ^

Evaluation of therapist and client language in Motivational Interviewing (MI) sessions: A secondary analysis of data from the Southern Methodist Alcohol Research Trial (SMART) study

In the United States, “binge” drinking among college students is an emerging public health concern due to the significant physical and psychological effects on young adults. The focus is on identifying interventions that can help decrease high-risk drinking behavior among this group of drinkers. One such intervention is Motivational interviewing (MI), a client-centered therapy that aims at resolving client ambivalence by developing discrepancy and engaging the client in change talk. Of late, there is a growing interest in determining the active ingredients that influence the alliance between the therapist and the client. This study is a secondary analysis of the data obtained from the Southern Methodist Alcohol Research Trial (SMART) project, a dismantling trial of MI and feedback among heavy drinking college students. The present project examines the relationship between therapist and client language in MI sessions on a sample of “binge” drinking college students. Of the 126 SMART tapes, 30 tapes (‘MI with feedback’ group = 15, ‘MI only’ group = 15) were randomly selected for this study. MISC 2.1, a mutually exclusive and exhaustive coding system, was used to code the audio/videotaped MI sessions. Therapist and client language were analyzed for communication characteristics. Overall, therapists adopted a MI consistent style and clients were found to engage in change talk. Counselor acceptance, empathy, spirit, and complex reflections were all significantly related to client change talk (p-values ranged from 0.001 to 0.047). Additionally, therapist ‘advice without permission’ and MI Inconsistent therapist behaviors were strongly correlated with client sustain talk (p-values ranged from 0.006 to 0.048). Simple linear regression models showed a significant correlation between MI consistent (MICO) therapist language (independent variable) and change talk (dependent variable) and MI inconsistent (MIIN) therapist language (independent variable) and sustain talk (dependent variable). The study has several limitations such as small sample size, self-selection bias, poor inter-rater reliability for the global scales and the lack of a temporal measure of therapist and client language. Future studies might consider a larger sample size to obtain more statistical power. In addition the correlation between therapist language, client language and drinking outcome needs to be explored.^

A qualitative analysis of leadership styles and the selection of quality improvement in primary care practice

In the Practice Change Model, physicians act as key stakeholders, people who have both an investment in the practice and the capacity to influence how the practice performs. This leadership role is critical to the development and change of the practice. Leadership roles and effectiveness are an important factor in quality improvement in primary care practices.^ The study conducted involved a comparative case study analysis to identify leadership roles and the relationship between leadership roles and the number and type of quality improvement strategies adopted during a Practice Change Model-based intervention study. The research utilized secondary data from four primary care practices with various leadership styles. The practices are located in the San Antonio region and serve a large Hispanic population. The data was collected by two ABC Project Facilitators from each practice during a 12-month period including Key Informant Interviews (all staff members), MAP (Multi-method Assessment Process), and Practice Facilitation field notes. This data was used to evaluate leadership styles, management within the practice, and intervention tools that were implemented. The chief steps will be (1) to analyze if the leader-member relations contribute to the type of quality improvement strategy or strategies selected (2) to investigate if leader-position power contributes to the number of strategies selected and the type of strategy selected (3) and to explore whether the task structure varies across the four primary care practices.^ The research found that involving more members of the clinic staff in decision-making, building bridges between organizational staff and clinical staff, and task structure are all associated with the direct influence on the number and type of quality improvement strategies implemented in primary care practice.^ Although this research only investigated leadership styles of four different practices, it will offer future guidance on how to establish the priorities and implementation of quality improvement strategies that will have the greatest impact on patient care improvement. ^

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. ^

Selection of body fat distribution indices in adults and associations with plasma lipid metabolism variables

Body fat distribution is a cardiovascular health risk factor in adults. Body fat distribution can be measured through various methods including anthropometry. It is not clear which anthropometric index is suitable for epidemiologic studies of fat distribution and cardiovascular disease. The purpose of the present study was to select a measure of body fat distribution from among a series of indices (those traditionally used in the literature and others constructed from the analysis) that is most highly correlated with lipid-related variables and is independent of overall fatness. Subjects were Mexican-American men and women (N = 1004) from a study of gallbladder disease in Starr County, Texas. Multivariate associations were sought between lipid profile measures (lipids, lipoproteins, and apolipoproteins) and two sets of anthropometric variables (4 circumferences and 6 skinfolds). This was done to assess the association between lipid-related measures and the two sets of anthropometric variables and guide the construction of indices.^ Two indices emerged from the analysis that seemed to be highly correlated with lipid profile measures independent of obesity. These indices are: 2*arm circumference-thigh skinfold in pre- and post-menopausal women and arm/thigh circumference ratio in men. Next, using the sum of all skinfolds to represent obesity and the selected body fat distribution indices, the following hypotheses were tested: (1) state of obesity and centrally/upper distributed body fat are equally predictive of lipids, lipoproteins and apolipoproteins, and (2) the correlation among the lipid-related measures is not altered by obesity and body fat distribution.^ With respect to the first hypothesis, the present study found that most lipids, lipoproteins and apolipoproteins were significantly associated with both overall fatness and anatomical location of body fat in both sex and menopausal groups. However, within men and post-menopausal women, certain lipid profile measures (triglyceride and HDLT among post-menopausal women and apos C-II, CIII, and E among men) had substantially higher correlation with body fat distribution as compared with overall fatness.^ With respect to the second hypothesis, both obesity and body fat distribution were found to alter the association among plasma lipid variables in men and women. There was a suggestion from the data that the pattern of correlations among men and post-menopausal women are more comparable. Among men correlations involving apo A-I, HDLT, and HDL$\sb2$ seemed greatly influenced by obesity, and A-II by fat distribution; among post-menopausal women correlations involving apos A-I and A-II were highly affected by the location of body fat.^ Thus, these data point out that not only can obesity and fat distribution affect levels of single measures, they also can markedly influence the pattern of relationship among measures. The fact that such changes are seen for both obesity and fat distribution is significant, since the indices employed were chosen because they were independent of one another. ^

A SIMULATION STUDY OF THE SIZE AND POWER OF SOME TWO-SAMPLE TESTS FOR UNEQUALLY CENSORED SURVIVAL DATA (RANK TESTS, LOGRANK, PROPORTIONAL HAZARDS, WILCOXON TESTS, EXPONENTIAL DISTRIBUTION)

Sizes and power of selected two-sample tests of the equality of survival distributions are compared by simulation for small samples from unequally, randomly-censored exponential distributions. The tests investigated include parametric tests (F, Score, Likelihood, Asymptotic), logrank tests (Mantel, Peto-Peto), and Wilcoxon-Type tests (Gehan, Prentice). Equal sized samples, n = 18, 16, 32 with 1000 (size) and 500 (power) simulation trials, are compared for 16 combinations of the censoring proportions 0%, 20%, 40%, and 60%. For n = 8 and 16, the Asymptotic, Peto-Peto, and Wilcoxon tests perform at nominal 5% size expectations, but the F, Score and Mantel tests exceeded 5% size confidence limits for 1/3 of the censoring combinations. For n = 32, all tests showed proper size, with the Peto-Peto test most conservative in the presence of unequal censoring. Powers of all tests are compared for exponential hazard ratios of 1.4 and 2.0. There is little difference in power characteristics of the tests within the classes of tests considered. The Mantel test showed 90% to 95% power efficiency relative to parametric tests. Wilcoxon-type tests have the lowest relative power but are robust to differential censoring patterns. A modified Peto-Peto test shows power comparable to the Mantel test. For n = 32, a specific Weibull-exponential comparison of crossing survival curves suggests that the relative powers of logrank and Wilcoxon-type tests are dependent on the scale parameter of the Weibull distribution. Wilcoxon-type tests appear more powerful than logrank tests in the case of late-crossing and less powerful for early-crossing survival curves. Guidelines for the appropriate selection of two-sample tests are given. ^

Analyzing left-truncated right-censored data with uncertain onset time with parametric models

Prevalent sampling is an efficient and focused approach to the study of the natural history of disease. Right-censored time-to-event data observed from prospective prevalent cohort studies are often subject to left-truncated sampling. Left-truncated samples are not randomly selected from the population of interest and have a selection bias. Extensive studies have focused on estimating the unbiased distribution given left-truncated samples. However, in many applications, the exact date of disease onset was not observed. For example, in an HIV infection study, the exact HIV infection time is not observable. However, it is known that the HIV infection date occurred between two observable dates. Meeting these challenges motivated our study. We propose parametric models to estimate the unbiased distribution of left-truncated, right-censored time-to-event data with uncertain onset times. We first consider data from a length-biased sampling, a specific case in left-truncated samplings. Then we extend the proposed method to general left-truncated sampling. With a parametric model, we construct the full likelihood, given a biased sample with unobservable onset of disease. The parameters are estimated through the maximization of the constructed likelihood by adjusting the selection bias and unobservable exact onset. Simulations are conducted to evaluate the finite sample performance of the proposed methods. We apply the proposed method to an HIV infection study, estimating the unbiased survival function and covariance coefficients. ^