Browsing Department of Biostatistics and Epidemiology by Title
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Classification Methods for CircularLinear Data Using Periodic FunctionsIn many fields such as medicine, agriculture and environmental studies, data are collected over time which can have some repeated pattern within a certain time period. Those data with the linear responses or measures such as blood pressure or solar energy with circular predictor, are called circularlinear data. The data having repeated measures over time are usually analyzed using longitudinal analysis methods. However, applying classical longitudinal data analysis to circularlinear data is generally inappropriate since the circular pattern of time would be treated as a simple continuous variable. Parametric approaches for circularlinear data have been developed using various modeling methods. We propose a Bayesian nonparametric MCMC circular smoothing splines approach, which is not only appropriate but also adds more flexibility for modeling and classification for circularlinear data. We first fit the circularlinear data on an estimated circle, to elicit functional pattern from the data, and then classify the patterns. In the development of the classification procedure, we use functional data analysis and some widely used dimension reduction classification methods such as the principal component analysis and support vector machine. We evaluate the performance of the proposed modelling and classification methods through extensive simulation, and demonstrate using the 20052006 NHANES physical activity monitor data on insomnia patients. In simulation study, the nonparametric Bayesian smoothing splines method coupled with support vector machine approach yields best performance in classification in terms of concordance rate. Our proposed nonparametric approach performed slightly better than the established parametric methods. Also, the initial data fitting procedures using a periodic regression function to reduce the noise in the data are shown to improve the performance in the classification problem. The result in the analysis of the NHANES data is consistent with simulation

Classifying Rheumatoid Arthritis Risk with Genetic Subgroups Using GenomeWide AssociationStructured genomewide association methods can be used to find population substructure, determine significant SNPs, and subsequently narrow down the field of SNPs to those most significant for determining disease risk. Beginning with more than 500,000 SNPs and rheumatoid arthritis (RA) phenotype data for cases and controls, we used a threepart clustering approach that found 684 SNPs significant for determining RA after accounting for clusters, and of those, 168 SNPs with differing odds across clusters. These 168 SNPs were used to create 16 population subgroups, each revealing a unique pattern of minor allele frequencies. The subgroups showed some commonality in multidimensional scaling plots, however, and were combined into five RA risk categories, each with odds differing from the other categories with pvalues less than 0.0001. Thus, based on SNP information from 168 SNPs it may be possible to assign an individual into one of five distinct RA risk categories.

COGA phenotypes and linkages on chromosome 2.An initial linkage analysis of the alcoholism phenotype as defined by DSMIIIR criteria and alcoholism defined by DSMIV criteria showed many, sometimes striking, inconsistencies. These inconsistencies are greatly reduced by making the definition of alcoholism more specific. We defined new phenotypes combining the alcoholism definitions and the latent variables, defining an individual as affected if that individual is alcoholic under one of the definitions (either DSMIIIR or DSMIV), and indicated having a symptom defined by one of the latent variables. This was done for each of the two alcoholism definitions and five latent variables, selected from a canonical discriminant analyses indicating they formed significant groupings using the electrophysiological variables. We found that linkage analyses utilizing these latent variables were much more robust and consistent than the linkage results based on DSMIIIR or DSMIV criteria for definition of alcoholism. We also performed linkage analyses on two first principal components derived phenotypes, one derived from the electrophysiological variables, and the other derived from the latent variables. A region on chromosome 2 at 250 cM was found to be linked to both of these derived phenotypes. Further examination of the SNPs in this region identified several haplotypes strongly associated with these derived phenotypes.

Comparisons of mutation rate variation at genomewide microsatellites: evolutionary insights from two cultivated rice and their wild relatives.BACKGROUND: Mutation rate (mu) per generation per locus is an important parameter in the models of population genetics. Studies on mutation rate and its variation are of significance to elucidate the extent and distribution of genetic variation, further infer evolutionary relationships among closely related species, and deeply understand genetic variation of genomes. However, patterns of rate variation of microsatellite loci are still poorly understood in plant species. Furthermore, how their mutation rates vary in di, tri, and tetranucleotide repeats within the species is largely uninvestigated across related plant genomes. RESULTS: Genomewide variation of mutation rates was first investigated by means of the composite population parameter theta (theta = 4Nmu, where N is the effective population size and mu is the mutation rate per locus per generation) in four subspecies of Asian cultivated rice O. sativa and its three related species, O. rufipogon, O. glaberrima, and O. officinalis. On the basis of three data sets of microsatellite allele frequencies throughout the genome, population mutation rate (theta) was estimated for each locus. Our results reveal that the variation of population mutation rates at microsatellites within each studied species or subspecies of cultivated rice can be approximated with a gamma distribution. The mean population mutation rates of microsatellites do not significantly differ in motifs of di, tri, and tetranucleotide repeats for the studied rice species. The shape parameter was also estimated for each subspecies of rice as well as other related rice species. Of them, different subspecies of O. sativa possesses similar shape parameters (alpha) of the gamma distribution, while other species extensively vary in their population mutation rates. CONCLUSION: Through the analysis of genomewide microsatellite data, the population mutation rate can be approximately fitted with a gamma distribution in most of the studied species. In general, different population histories occurred along different lineages may result in the observed variation of population mutation rates at microsatellites among the studied Oryza species.

Correlation Coefficient Inference for LeftCensored Biomarker Data with Known Detection LimitsResearchers are often interested in the relationship between biological concentrations obtained using two different assays, both of which may be biomarkers. Despite the continuing advances in biotechnology, the value of a particular biomarker may fall below some known limit of detection (LOD). Data values such as these are referred to as nondetects (NDs) and can be treated as leftcensored observations. When attempting to measure the association between two concentrations, both of which are subject to NDs, serious complications can arise in the data analysis. Simple substitution, random imputation, and maximum likelihood estimation methods are just a few of the methods that have been proposed for handling NDs when estimating the correlation between two variables, both of which are subject to leftcensoring. Unfortunately, many of the popular methods require that the data follow a bivariate normal distribution or that only a small percentage of the data for each variable are below the LOD. These assumptions are often violated with biomarker data. In this paper, we evaluate the performance of several methods, including Spearman’s rho, when the data do not follow a bivariate normal distribution and when there are moderate to large censoring proportions in one or both of the variables. We evaluate the performance of seven methods for estimating the correlation, ρ, between two leftcensored variables using bias, median absolute deviation, 95% confidence interval width, and coverage probability under assumptions of various sample sizes, correlations, and censoring proportions. We show that using substitution and imputation methods yields biased estimates of ρ and less than nominal coverage probability under most of the simulation parameters we examined. We recommend the maximum likelihood method for general use even when the data significantly depart from bivariate normality.

Epigenetic Silencing of Nucleolar rRNA Genes in Alzheimer's DiseaseBackground: Ribosomal deficits are documented in mild cognitive impairment (MCI), which often represents an early stage Alzheimer's disease (AD), as well as in advanced AD. The nucleolar rRNA genes (rDNA), transcription of which is critical for ribosomal biogenesis, are regulated by epigenetic silencing including promoter CpG methylation.

False coverage rate  adjusted smoothed bootstrap simultaneous confidence intervals for selected parametersMany modern applications refer to a large number of populations with high dimensional parameters. Since there are so many parameters, researchers often draw inferences regarding the most significant parameters, which are called selected parameters. Benjamini and Yekutieli (2005) proposed the false coveragestatement rate (FCR) method for multiplicity correction when constructing confidence intervals for only selected parameters. FCR for the confidence interval method is parallel to the concept of the false discovery rate for multiple hypothesis testing. In practice, we typically construct FCRadjusted approximate confidence intervals for selected parameters either using the bootstrap method or the normal approximation method. However, these approximated confidence intervals show higher FCR for small and moderate sample sizes. Therefore, we suggest a novel procedure to construct simultaneous confidence intervals for the selected parameters by using a smoothed bootstrap procedure. We consider a smoothed bootstrap procedure using a kernel density estimator. A pertinent problem associated with the smoothed bootstrap approach is how to choose the unknown bandwidth in some optimal sense. We derive an optimal choice for the bandwidth and the resulting smoothed bootstrap confidence intervals asymptotically to give better control of the FCR than its competitors. We further show that the suggested smoothed bootstrap simultaneous confidence intervals are FCRconsistent if the dimension of data grows no faster than N^3/2. Finite sample performances of our method are illustrated based on empirical studies. Through these empirical studies, it is shown that the proposed method can be successfully applied in practice.

Familybased genomewide association study for simulated data of Framingham Heart Study.ABSTRACT : Genomewide association studies (GWAS) have quickly become the norm in dissecting the genetic basis of complex diseases. Familybased association approaches have the advantages of being robust to possible hidden population structure in samples. Most of these methods were developed with limited markers. Their applicability and performance for GWAS need to be examined. In this report, we evaluated the properties of the familybased association method implemented by ASSOC in the S.A.G.E package using the simulated data sets for the Framingham Heart Study, and found that ASSOC is a highly useful tool for GWAS.

A genebased approach for testing association of rare allelesRare genetic variants have been shown to be important to the susceptibility of common human diseases. Methods for detecting association of rare genetic variants are drawing much attention. In this report, we applied a genebased approach to the 200 simulated data sets of unrelated individuals. The test can detect the association of some genes with multiple rare variants.

Maternal Health Literacy Progression Among Rural Perinatal WomenThis research examined changes in maternal health literacy progression among 106 low income, high risk, rural perinatal African American and White women who received home visits by Registered Nurse Case Managers through the Enterprise Community Healthy Start Program. Maternal health literacy progression would enable women to better address intermediate factors in their lives that impacted birth outcomes, and ultimately infant mortality (Lu and Halfon in Mater Child Health J 7(1):1330, 2003; Sharma et al. in J Natl Med Assoc 86(11):857860, 1994). The Life Skills Progression Instrument (LSP) (Wollesen and Peifer, in Life skills progression. An outcome and intervention planning instrument for use with families at risk. Paul H. Brookes Publishing Co., Baltimore, 2006) measured changes in behaviors that represented intermediate factors in birth outcomes. Maternal Health Care Literacy (LSP/MHCL) was a woman's use of information, critical thinking and health care services; Maternal Self Care Literacy (LSP/MSCL) was a woman's management of personal and child health at home (Smith and Moore in Health literacy and depression in the context of home visitation. Mater Child Health J, 2011). Adequacy was set at a score of (≥4). Among 106 women in the study initial scores were inadequate (<4) on LSP/MHCL (83 %), and on LSP/MSCL (30 %). Significant positive changes were noted in maternal health literacy progression from the initial prenatal assessment to the first (p < .01) postpartum assessment and to the final (p < .01) postpartum assessment using McNemar's test of gain scores. Numeric comparison of first and last gain scores indicated women's scores progressed (LSP/MHCL; p < .0001) and (LSP/MSCL; p < .0001). Elevated depression scores were most frequent among women with <4 LSP/MHCL and/or <4 LSP/MSCL. Visit notes indicated lack or loss of relationship with the father of the baby and intimate partner discord contributed to higher depression scores.

Mathematical and Stochastic Modeling of HIV Immunology and EpidemiologyIn HIV virus dynamics, controlling of viral load and maintaining of CD4 value at a higher level are always primary goals for the providers. In recent years, a new molecule was discovered, namely, eCD4Ig, which mimics CD4 if introduced into the human body and has potential to change existing HIV virus dynamics. Thus, to understand dynamics of viral load, eCD4Ig, CD4 cells, we have developed mathematical models by incorporating interactions between this new molecule and other known immunological, virological information. We further investigated model based speculations for management, and obtained the level of eCD4Ig required for elimination of virus. Next, we built epidemiological model for HIV spread and control among discordant couple through dynamics of PrEP (Preexposure prophylaxis). For this, an actuarial assumptions based stochastic model is used to obtain the mean remaining time of couple to stay as discordant. We generalized single hookup/marriage stochastic model to multiple hookup/marriage model.

A modified bump hunting approach with correlationadjusted kernel weight for detecting differentially methylated regions on the 450K arrayDNA methylation plays an important role in the regulation of gene expression, as hypermethylation is associated with gene silencing. The general purpose of this dissertation is the development of a statistical method, called DMR Detector, for detecting differentially methylated regions (DMRs) on the 450K array. DMR Detector makes three key modifications to an existing method called Bumphunter. The first is what statistic to collect from the initial fitting for further analysis. The second is to perform kernel smoothing under the assumption of correlated errors using a newly proposed correlationadjusted kernel weight. The third is how to define regions of interest. In simulation, the method was shown to have high power comparable to Bumphunter, with consistently lower familywise type I error rate, controlled well below the 0.1 FDR. DMR Detector was applied to real data and was able to detect one DMR that was not detected by Bumphunter.

A Modified Information Criterion in the 1d Fused Lasso for DNA Copy Number Variant Detection using Next Generation Sequencing DataDNA Copy Number Variations (CNVs) are associated with many human diseases. Recently, CNV studies have been carried out using Next Generation Sequencing (NGS) technology that produces millions of short reads. With NGS reads ratio data, we use the 1d fused lasso regression for CNV detection. Given the number of copy number changes, the corresponding genomic locations are estimated by fitting the 1d fused lasso. Estimation of the number of copy number changes depends on a tuning parameter in the 1d fused lasso. In this dissertation, we propose a new modified Bayesian information criterion, called JMIC, to estimate the optimal tuning parameter in the 1d fused lasso. In theoretical studies, we prove that the number of change points estimated by JMIC converges the true number of changes. Also, our simulation studies show that JMIC outperforms the other criteria considered. Finally, we apply our proposed method to the reads ratio data from the breast tumor cell HCC1954 and its matched cell line provided by Chiang et al. (2009).

Multivariate Poisson Abundance Models for Analyzing Antigen Receptor DataAntigen receptor data is an important source of information for immunologists that is highly statistically challenging to analyze due to the presence of a huge number of Tcell receptors in mammalian immune systems and the severe undersampling bias associated with the commonly used data collection procedures. Many important immunological questions can be stated in terms of richness and diversity of Tcell subsets under various experimental conditions. This dissertation presents a class of parametric models and uses a special case of them to compare the richness and diversity of antigen receptor populations in mammalian Tcells. The parametric models are based on a representation of the observed receptor counts as a multivariate Poisson abundance model (mPAM). A Bayesian model tting procedure is developed which allows tting of the mPAM parameters with the help of the complete likelihood as opposed to its conditional version which was used previously. The new procedure is shown to be often considerably more e cient (as measured by the amount of Fisher information) in the regions of the mPAM parameter space relevant to modeling Tcell data. A richness estimator based on the special case of the mPAM is shown to be superior to several existing richness estimators from the statistical ecology literature under the severe undersampling conditions encountered in antigen receptor data collection. The comparative diversity analyses based on the mPAM special case yield biologically meaningful results when applied to the Tcell receptor repertoires in mice. It is also shown that the amount of time to implement the Bayesian model tting procedure for the mPAM special case scales well as the dimension increases and that the amount of computational resources required to conduct complete statistical analyses for the mPAM special case can be drastically lower for our Bayesian model tting procedure than for code based on the conditional likelihood approach.

A new measure of population structure using multiple single nucleotide polymorphisms and its relationship with FST.BACKGROUND: Largescale genomewide association studies are promising for unraveling the genetic basis of complex diseases. Population structure is a potential problem, the effects of which on genetic association studies are controversial. The first step to systematically quantify the effects of population structure is to choose an appropriate measure of population structure for human data. The commonly used measure is Wright's FST. For a set of subpopulations it is generally assumed to be one value of FST. However, the estimates could be different for distinct loci. Since population structure is a concept at the population level, a measure of population structure that utilized the information across loci would be desirable. FINDINGS: In this study we propose an adjusted C parameter according to the sample size from each subpopulation. The new measure C is based on the c parameter proposed for SNP data, which was assumed to be subpopulationspecific and common for all loci. In this study, we performed extensive simulations of samples with varying levels of population structure to investigate the properties and relationships of both measures. It is found that the two measures generally agree well. CONCLUSION: The new measure simultaneously uses the marker information across the genome. It has the advantage of easy interpretation as one measure of population structure and yet can also assess population differentiation.

A New Method For Analyzing 1:N Matched Case Control Studies With Incomplete Data1:n matched casecontrol studies are commonly used to evaluate the association between the exposure to a risk factor and a disease, where one case is matched to up till n controls. The odds ratio is typically used to quantify such association. Difficulties in estimating the true odds ratio arise, when the exposure status is unknown for at least one individual in a group. In the case where the exposure status is known for all individuals in a group, the true odds ratio is estimated as the ratio of the counts in the discordant cells of the observed twobytwo table. In the case where all data are independent, the odds ratio is estimated using the crossproduct ratio from the observed table. Conditional logistic regression estimates are used for incomplete matching data. In this dissertation we suggest a simple method for estimating the odds ratio when the sample consists of a combination of paired and unpaired observations, with 1:n matching. This method uses a weighted average of the odds ratio calculations described above. This dissertation compares the new method to existing methods via simulation.

A new transmission test for affected sibpair families.Familybased association approaches such as the transmissiondisequilibrium test (TDT) are used extensively in the study of genetic traits because they are generally robust to the presence of population structure. However, these approaches necessarily involve recruitment of families, which is more costly and timeconsuming than sampling unrelated individuals in the populationbased approaches. Therefore, a familybased approach, which has high power, would be appealing because of the gain in time and cost due to the reduced sample size that is required to attain adequate power. Here we introduce a new familybased transmission test using the joint transmission status from affected sib pairs. We show that by including the transmission status of both siblings, our method gives higher power than the TDT design, while maintaining the correct type I error rate. We use the simulated data from affected sibpair families with rheumatoid arthritis provided by Genetic Analysis Workshop 15 to illustrate our approach.

Penalized Least Squares and the Algebraic Statistical Model for Biochemical Reaction NetworksSystems biology seeks to understand the formation of macro structures such as cellular processes and higher level cellular phenomena by investigating the interactions of systems’ individual components. For cellular biology, this goal is to understand the dynamic behavior of biological materials within the cell, a container consisting of smaller materials such as mRNA, proteins, enzymes and other intermediates necessary for regulating intracellular functions and chemical species levels. Understanding these cellular dynamics is needed to help develop new drug therapies, which can be targeted to specific molecules or specific genes, in order to perturb the system for a desired result. In this work we develop inferential procedures to estimate reaction rate coefficients in cellular systems of ordinary differential equations (ODEs) from noisy data arising from realizations of molecular trajectories. It is assumed that these systems obey the so called chemical mass action law of kinetics, with corresponding deterministic mass action limit as the system size becomes infinite. The estimation and inference is based on the penalized least squares estimates, where the covariance structure of these estimates corresponds to the solution of a system of coupled nonautonomuous ODEs. Another topic discussed here is that of network topology estimation. The algebraic statistical model (ASM) offers a means of performing this topological inference for the special class of conic networks. We prove that the ASM recovers the true network topology as the number of samples grows without bound, a property known in the literature as sparsistency. We propose a method to extend the ASM to a wider class of networks that are decomposable into multiple cones.

Ranking analysis of Fstatistics for microarray data.BACKGROUND: Microarray technology provides an efficient means for globally exploring physiological processes governed by the coordinated expression of multiple genes. However, identification of genes differentially expressed in microarray experiments is challenging because of their potentially high type I error rate. Methods for largescale statistical analyses have been developed but most of them are applicable to twosample or twocondition data. RESULTS: We developed a largescale multiplegroup Ftest based method, named ranking analysis of Fstatistics (RAF), which is an extension of ranking analysis of microarray data (RAM) for twosample ttest. In this method, we proposed a novel random splitting approach to generate the null distribution instead of using permutation, which may not be appropriate for microarray data. We also implemented a twosimulation strategy to estimate the false discovery rate. Simulation results suggested that it has higher efficiency in finding differentially expressed genes among multiple classes at a lower false discovery rate than some commonly used methods. By applying our method to the experimental data, we found 107 genes having significantly differential expressions among 4 treatments at <0.7% FDR, of which 31 belong to the expressed sequence tags (ESTs), 76 are unique genes who have known functions in the brain or central nervous system and belong to six major functional groups. CONCLUSION: Our method is suitable to identify differentially expressed genes among multiple groups, in particular, when sample size is small.

A resampling method of time course gene expression data for gene network inferenceManipulation of cellular functions may aid in treatment and/or cure of a disease. Thus, identifying the topology of a gene regulatory network (GRN) and the molecular role of each gene is essential. Discovering GRNs from gene expression data is hampered by intrinsic attributes of the data: small sample size n, large number of variables (genes) p, and unknown error structure. Numerous theoretical approaches for GRN inference attempt to overcome these difficulties; however, most solutions utilized in these methods are to provide either point estimators such as coefficient estimators or make numerous assumptions which are often incompatible with the data. Furthermore, the different solutions cause GRN inference methods to provide inconsistent results. This dissertation proposes a resampling method for timecourse gene expression data which can provide interval estimators for existing GRN inference methods without any distributional assumptions via bootstrapping and a statistical model that considers the various components of the data structure such as trend of gene expressions, errors of timecourse data, and correlation between genes, etc. This method will produce more precise GRNs that are consistent with observed gene expression data. Furthermore, by applying our method to multiple existing GRN inference methods, the resulting networks obtained from different inference methods could be combined using the joint confidence region for their parameters. Thus, this method can be used for the validation of identified networks and GRN inference methods.