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. ^

Application of stellar photometry to the analysis of microarray images

Improvements in the analysis of microarray images are critical for accurately quantifying gene expression levels. The acquisition of accurate spot intensities directly influences the results and interpretation of statistical analyses. This dissertation discusses the implementation of a novel approach to the analysis of cDNA microarray images. We use a stellar photometric model, the Moffat function, to quantify microarray spots from nylon microarray images. The inherent flexibility of the Moffat shape model makes it ideal for quantifying microarray spots. We apply our novel approach to a Wilms' tumor microarray study and compare our results with a fixed-circle segmentation approach for spot quantification. Our results suggest that different spot feature extraction methods can have an impact on the ability of statistical methods to identify differentially expressed genes. We also used the Moffat function to simulate a series of microarray images under various experimental conditions. These simulations were used to validate the performance of various statistical methods for identifying differentially expressed genes. Our simulation results indicate that tests taking into account the dependency between mean spot intensity and variance estimation, such as the smoothened t-test, can better identify differentially expressed genes, especially when the number of replicates and mean fold change are low. The analysis of the simulations also showed that overall, a rank sum test (Mann-Whitney) performed well at identifying differentially expressed genes. Previous work has suggested the strengths of nonparametric approaches for identifying differentially expressed genes. We also show that multivariate approaches, such as hierarchical and k-means cluster analysis along with principal components analysis, are only effective at classifying samples when replicate numbers and mean fold change are high. Finally, we show how our stellar shape model approach can be extended to the analysis of 2D-gel images by adapting the Moffat function to take into account the elliptical nature of spots in such images. Our results indicate that stellar shape models offer a previously unexplored approach for the quantification of 2D-gel spots. ^

Evaluation of the causal pathways through which subjective norms influence mammography intention and stage of change in a national sample of women veterans

Few studies have investigated causal pathways linking psychosocial factors to each other and to screening mammography. Conflicting hypotheses exist in the theoretic literature regarding the role and importance of subjective norms, a person's perceived social pressure to perform the behavior and his/her motivation to comply. The Theory of Reasoned Action (TRA) hypothesizes that subjective norms directly affect intention; while the Transtheoretical Model (TTM) hypothesizes that attitudes mediate the influence of subjective norms on stage of change. No one has examined which hypothesis best predicts the effect of subjective norms on mammography intention and stage of change. Two statistical methods are available for testing mediation, sequential regression analysis (SRA) and latent variable structural equation modeling (LVSEM); however, software to apply LVSEM to dichotomous variables like intention has only recently become available. No one has compared the methods to determine whether or not they yield similar results for dichotomous variables. ^ Study objectives were to: (1) determine whether the effect of subjective norms on mammography intention and stage of change are mediated by pros and cons; and (2) compare mediation results from the SRA and LVSEM approaches when the outcome is dichotomous. We conducted a secondary analysis of data from a national sample of women veterans enrolled in Project H.O.M.E. (H&barbelow;ealthy O&barbelow;utlook on the M&barbelow;ammography E&barbelow;xperience), a behavioral intervention trial. ^ Results showed that the TTM model described the causal pathways better than the TRA one; however, we found support for only one of the TTM causal mechanisms. Cons was the sole mediator. The mediated effect of subjective norms on intention and stage of change by cons was very small. These findings suggest that interventionists focus their efforts on reducing negative attitudes toward mammography when resources are limited. ^ Both the SRA and LVSEM methods provided evidence for complete mediation, and the direction, magnitude, and standard errors of the parameter estimates were very similar. Because SRA parameter estimates were not biased toward the null, we can probably assume negligible measurement error in the independent and mediator variables. Simulation studies are needed to further our understanding of how these two methods perform under different data conditions. ^

Nonlinear tests for genetic studies of complex disease

Linkage and association studies are major analytical tools to search for susceptibility genes for complex diseases. With the availability of large collection of single nucleotide polymorphisms (SNPs) and the rapid progresses for high throughput genotyping technologies, together with the ambitious goals of the International HapMap Project, genetic markers covering the whole genome will be available for genome-wide linkage and association studies. In order not to inflate the type I error rate in performing genome-wide linkage and association studies, multiple adjustment for the significant level for each independent linkage and/or association test is required, and this has led to the suggestion of genome-wide significant cut-off as low as 5 × 10 −7. Almost no linkage and/or association study can meet such a stringent threshold by the standard statistical methods. Developing new statistics with high power is urgently needed to tackle this problem. This dissertation proposes and explores a class of novel test statistics that can be used in both population-based and family-based genetic data by employing a completely new strategy, which uses nonlinear transformation of the sample means to construct test statistics for linkage and association studies. Extensive simulation studies are used to illustrate the properties of the nonlinear test statistics. Power calculations are performed using both analytical and empirical methods. Finally, real data sets are analyzed with the nonlinear test statistics. Results show that the nonlinear test statistics have correct type I error rates, and most of the studied nonlinear test statistics have higher power than the standard chi-square test. This dissertation introduces a new idea to design novel test statistics with high power and might open new ways to mapping susceptibility genes for complex diseases. ^

Functional data analysis approaches for genotype-phenotype association studies from next-generation sequencing

Next-generation DNA sequencing platforms can effectively detect the entire spectrum of genomic variation and is emerging to be a major tool for systematic exploration of the universe of variants and interactions in the entire genome. However, the data produced by next-generation sequencing technologies will suffer from three basic problems: sequence errors, assembly errors, and missing data. Current statistical methods for genetic analysis are well suited for detecting the association of common variants, but are less suitable to rare variants. This raises great challenge for sequence-based genetic studies of complex diseases.^ This research dissertation utilized genome continuum model as a general principle, and stochastic calculus and functional data analysis as tools for developing novel and powerful statistical methods for next generation of association studies of both qualitative and quantitative traits in the context of sequencing data, which finally lead to shifting the paradigm of association analysis from the current locus-by-locus analysis to collectively analyzing genome regions.^ In this project, the functional principal component (FPC) methods coupled with high-dimensional data reduction techniques will be used to develop novel and powerful methods for testing the associations of the entire spectrum of genetic variation within a segment of genome or a gene regardless of whether the variants are common or rare.^ The classical quantitative genetics suffer from high type I error rates and low power for rare variants. To overcome these limitations for resequencing data, this project used functional linear models with scalar response to develop statistics for identifying quantitative trait loci (QTLs) for both common and rare variants. To illustrate their applications, the functional linear models were applied to five quantitative traits in Framingham heart studies. ^ This project proposed a novel concept of gene-gene co-association in which a gene or a genomic region is taken as a unit of association analysis and used stochastic calculus to develop a unified framework for testing the association of multiple genes or genomic regions for both common and rare alleles. The proposed methods were applied to gene-gene co-association analysis of psoriasis in two independent GWAS datasets which led to discovery of networks significantly associated with psoriasis.^

Distribution of quality adjusted life expectancy: A systems approach

Statistical methods are developed which assess survival data for two attributes; (1) prolongation of life, (2) quality of life. Health state transition probabilities correspond to prolongation of life and are modeled as a discrete-time semi-Markov process. Imbedded within the sojourn time of a particular health state are the quality of life transitions. They reflect events which differentiate perceptions of pain and suffering over a fixed time period. Quality of life transition probabilities are derived from the assumptions of a simple Markov process. These probabilities depend on the health state currently occupied and the next health state to which a transition is made. Utilizing the two forms of attributes the model has the capability to estimate the distribution of expected quality adjusted life years (in addition to the distribution of expected survival times). The expected quality of life can also be estimated within the health state sojourn time making more flexible the assessment of utility preferences. The methods are demonstrated on a subset of follow-up data from the Beta Blocker Heart Attack Trial (BHAT). This model contains the structure necessary to make inferences when assessing a general survival problem with a two dimensional outcome. ^

THE USE OF MULTIVARIATE ANALYSIS OF COVARIANCE IN EVALUATING THE COMPARABILITY OF LABORATORY DETERMINATIONS IN COOPERATIVE STUDIES

The role of clinical chemistry has traditionally been to evaluate acutely ill or hospitalized patients. Traditional statistical methods have serious drawbacks in that they use univariate techniques. To demonstrate alternative methodology, a multivariate analysis of covariance model was developed and applied to the data from the Cooperative Study of Sickle Cell Disease.^ The purpose of developing the model for the laboratory data from the CSSCD was to evaluate the comparability of the results from the different clinics. Several variables were incorporated into the model in order to control for possible differences among the clinics that might confound any real laboratory differences.^ Differences for LDH, alkaline phosphatase and SGOT were identified which will necessitate adjustments by clinic whenever these data are used. In addition, aberrant clinic values for LDH, creatinine and BUN were also identified.^ The use of any statistical technique including multivariate analysis without thoughtful consideration may lead to spurious conclusions that may not be corrected for some time, if ever. However, the advantages of multivariate analysis far outweigh its potential problems. If its use increases as it should, the applicability to the analysis of laboratory data in prospective patient monitoring, quality control programs, and interpretation of data from cooperative studies could well have a major impact on the health and well being of a large number of individuals. ^

SEVERE HEAD TRAUMA, EMERGENCY TRANSPORT, AND PATIENT OUTCOME

Trauma and severe head injuries are important issues because they are prevalent, because they occur predominantly in the young, and because variations in clinical management may matter. Trauma is the leading cause of death for those under age 40. The focus of this head injury study is to determine if variations in time from the scene of accident to a trauma center hospital makes a difference in patient outcomes.^ A trauma registry is maintained in the Houston-Galveston area and includes all patients admitted to any one of three trauma center hospitals with mild or severe head injuries. A study cohort, derived from the Registry, includes 254 severe head injury cases, for 1980, with a Glasgow Coma Score of 8 or less.^ Multiple influences relate to patient outcomes from severe head injury. Two primary variables and four confounding variables are identified, including time to emergency room, time to intubation, patient age, severity of injury, type of injury and mode of transport to the emergency room. Regression analysis, analysis of variance, and chi-square analysis were the principal statistical methods utilized.^ Analysis indicates that within an urban setting, with a four-hour time span, variations in time to emergency room do not provide any strong influence or predictive value to patient outcome. However, data are suggestive that at longer time periods there is a negative influence on outcomes. Age is influential only when the older group (55-64) is included. Mode of transport (helicopter or ambulance) did not indicate any significant difference in outcome.^ In a multivariate regression model, outcomes are influenced primarily by severity of injury and age which explain 36% (R('2)) of variance. Inclusion of time to emergency room, time to intubation, transport mode and type injury add only 4% (R('2)) additional contribution to explaining variation in patient outcome.^ The research concludes that since the group most at risk to head trauma is the young adult male involved in automobile/motorcycle accidents, more may be gained by modifying driving habits and other preventive measures. Continuous clinical and evaluative research are required to provide updated clinical wisdom in patient management and trauma treatment protocols. A National Institute of Trauma may be required to develop a national public policy and evaluate the many medical, behavioral and social changes required to cope with the country's number 3 killer and the primary killer of young adults.^

Black/white disparities in infant mortality rates in the U.S.: A quality of care perspective

The infant mortality rate for non-Hispanic Black infants in the U.S. is 13.63 deaths per 1,000 live births while the IMR for non-Hispanic White persons in the U.S. is 5.76 deaths per 1,000 live births. Black women are 2 times as likely as White women to deliver preterm infants and Black women are 2 times as likely as White women to deliver low birth weight infants (weighing less than 2,500 grams at birth). Differential underlying risk factors among mothers of different racial/ethnic groups for delivering pre-term and low birth weight infants have been historically accepted as the cause of racial disparities in IMRs. However, differential underlying risk status may not be the only major causative factor. Differential or unequal access to and provision of care is widely speculated to be a leading contributing factor to the wide racial disparity in infant mortality.2 This paper conducts a systematic review of existing literature investigating racial disparities in obstetrical care provided by healthcare practitioners to evaluate whether inequities in healthcare services provided to pregnant mothers and their neonates exist. The search terms "racial disparities obstetrical care," "racial differences quality of prenatal care," and "infant mortality racial disparities" were entered into the EBSCO Medline, Ovid Medline, PubMed, and Academic Search Complete databases, and articles between years 1990–2011 were selected for abstract review. The only articles included were those that used statistical methods to assess whether racial inequalities were present in the obstetrical services provided to pregnant women. My literature search returned 5 articles. Four of the five studies yielded significant racial differences in obstetrical care. However, the one study that used a large, nationally representative valid sample did not represent significant differences. Thus, this review provides initial evidence for racial disparities in obstetrical care, but concludes that more studies are needed in this area. Not all of the studies reviewed were consistent in the use and measurement of services, and not all studies were significant. The policy and public health implications of possible racial disparities in obstetrical care include the need to develop standard of care protocols for ALL obstetrical patients across the United States to minimize and/or eliminate the inequities and differences in obstetrical services provided.^

A hybrid method in combining treatment effects from matched and unmatched studies

In the biomedical studies, the general data structures have been the matched (paired) and unmatched designs. Recently, many researchers are interested in Meta-Analysis to obtain a better understanding from several clinical data of a medical treatment. The hybrid design, which is combined two data structures, may create the fundamental question for statistical methods and the challenges for statistical inferences. The applied methods are depending on the underlying distribution. If the outcomes are normally distributed, we would use the classic paired and two independent sample T-tests on the matched and unmatched cases. If not, we can apply Wilcoxon signed rank and rank sum test on each case. ^ To assess an overall treatment effect on a hybrid design, we can apply the inverse variance weight method used in Meta-Analysis. On the nonparametric case, we can use a test statistic which is combined on two Wilcoxon test statistics. However, these two test statistics are not in same scale. We propose the Hybrid Test Statistic based on the Hodges-Lehmann estimates of the treatment effects, which are medians in the same scale.^ To compare the proposed method, we use the classic meta-analysis T-test statistic on the combined the estimates of the treatment effects from two T-test statistics. Theoretically, the efficiency of two unbiased estimators of a parameter is the ratio of their variances. With the concept of Asymptotic Relative Efficiency (ARE) developed by Pitman, we show ARE of the hybrid test statistic relative to classic meta-analysis T-test statistic using the Hodges-Lemann estimators associated with two test statistics.^ From several simulation studies, we calculate the empirical type I error rate and power of the test statistics. The proposed statistic would provide effective tool to evaluate and understand the treatment effect in various public health studies as well as clinical trials.^

Classification of cellular malignancy associated changes in cervical cancer

Cervical cancer is the leading cause of death and disease from malignant neoplasms among women in developing countries. Even though the Pap smear has significantly decreased the number of deaths from cervical cancer in the past years, it has its limitations. Researchers have developed an automated screening machine which can potentially detect abnormal cases that are overlooked by conventional screening. The goal of quantitative cytology is to classify the patient's tissue sample based on quantitative measurements of the individual cells. It is also much cheaper and potentially can take less time. One of the major challenges of collecting cells with a cytobrush is the possibility of not sampling any existing dysplastic cells on the cervix. Being able to correctly classify patients who have disease without the presence of dysplastic cells could improve the accuracy of quantitative cytology algorithms. Subtle morphologic changes in normal-appearing tissues adjacent to or distant from malignant tumors have been shown to exist, but a comparison of various statistical methods, including many recent advances in the statistical learning field, has not previously been done. The objective of this thesis is to use different classification methods applied to quantitative cytology data for the detection of malignancy associated changes (MACs). In this thesis, Elastic Net is the best algorithm. When we applied the Elastic Net algorithm to the test set, we combined the training set and validation set as "training" set and used 5-fold cross validation to choose the parameter for Elastic Net. It has a sensitivity of 47% at 80% specificity, an AUC 0.52, and a partial AUC 0.10 (95% CI 0.09-0.11).^