Statistical Applications in Genetics and Molecular Biology

Published by De Gruyter

Volume 8 Issue 1

January 2009

Issue of Statistical Applications in Genetics and Molecular Biology

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Contents
Journal Overview

Article

January 6, 2009

Sparse Canonical Correlation Analysis with Application to Genomic Data Integration

Elena Parkhomenko, David Tritchler, Joseph Beyene

Abstract

Large scale genomic studies with multiple phenotypic or genotypic measures may require the identification of complex multivariate relationships. In multivariate analysis a common way to inspect the relationship between two sets of variables based on their correlation is canonical correlation analysis, which determines linear combinations of all variables of each type with maximal correlation between the two linear combinations. However, in high dimensional data analysis, when the number of variables under consideration exceeds tens of thousands, linear combinations of the entire sets of features may lack biological plausibility and interpretability. In addition, insufficient sample size may lead to computational problems, inaccurate estimates of parameters and non-generalizable results. These problems may be solved by selecting sparse subsets of variables, i.e. obtaining sparse loadings in the linear combinations of variables of each type. In this paper we present Sparse Canonical Correlation Analysis (SCCA) which examines the relationships between two types of variables and provides sparse solutions that include only small subsets of variables of each type by maximizing the correlation between the subsets of variables of different types while performing variable selection. We also present an extension of SCCA - adaptive SCCA. We evaluate their properties using simulated data and illustrate practical use by applying both methods to the study of natural variation in human gene expression.

January 13, 2009

Orthology-Based Multilevel Modeling of Differentially Expressed Mouse and Human Gene Pairs

Benjamin A Ogorek, Leonard A Stefanski

Abstract

There is great interest in finding human genes expressed through pharmaceutical intervention, thus opening a genomic window into benefit and side-effect profiles of a drug. Human insight gained from FDA-required animal experiments has historically been limited, but in the case of gene expression measurements, proposed biological orthologies between mouse and human genes provide a foothold for animal-to-human extrapolation. We have investigated a five-component, multilevel, bivariate normal mixture model that incorporates mouse, as well as human, gene expression data. The goal is two-fold: to increase human differential gene-finding power; and to find a subclass of gene pairs for which there is a direct exploitable relationship between animal and human genes. In simulation studies, the dual-species model boasted impressive gains in differential gene-finding power over a related marginal model using only human data. Bias in parameter estimation was problematic, however, and occasionally led to failures in control of the false discovery rate. Though it was considerably more difficult to find species-extrapolative gene-pairs (than differentially expressed human genes), simulation experiments deemed it to be possible, especially when traditional FDR controls are relaxed and under hypothetical parameter configurations.

January 21, 2009

Sequential Analysis for Microarray Data Based on Sensitivity and Meta-Analysis

Guillemette Marot, Claus-Dieter Mayer

Abstract

Motivation: Transcriptomic studies using microarray technology have become a standard tool in life sciences in the last decade. Nevertheless the cost of these experiments remains high and forces scientists to work with small sample sizes at the expense of statistical power. In many cases, little or no prior knowledge on the underlying variability is available, which would allow an accurate estimation of the number of samples (microarrays) required to answer a particular biological question of interest. We investigate sequential methods, also called group sequential or adaptive designs in the context of clinical trials, for microarray analysis. Through interim analyses at different stages of the experiment and application of a stopping rule a decision can be made as to whether more samples should be studied or whether the experiment has yielded enough information already.Results: The high dimensionality of microarray data facilitates the sequential approach. Since thousands of genes simultaneously contribute to the stopping decision, the marginal distribution of any single gene is nearly independent of the global stopping rule. For this reason, the interim analysis does not seriously bias the final p-values. We propose a meta-analysis approach to combining the results of the interim analyses at different stages. We consider stopping rules that are either based on the estimated number of true positives or on a sensitivity estimate and particularly discuss the difficulty of estimating the latter. We study this sequential method in an extensive simulation study and also apply it to several real data sets. The results show that applying sequential methods can reduce the number of microarrays without substantial loss of power. An R-package SequentialMA implementing the approach is available from the authors.

January 21, 2009

Dimension Reduction of Microarray Data in the Presence of a Censored Survival Response: A Simulation Study

Tuan S Nguyen, Javier Rojo

Abstract

An important aspect of microarray studies involves the prediction of patient survival based on their gene expression levels. To cope with the high dimensionality of the microarray gene expression data, it is customary to first reduce the dimension of the gene expression data via dimension reduction methods, and then use the Cox proportional hazards model to predict patient survival. In this paper, we propose a variant of Partial Least Squares, denoted as Rank-based Modified Partial Least Squares (RMPLS), that is insensitive to outlying values of both the response and the gene expressions. We assess the performance of RMPLS and several dimension reduction methods using a simulation model for gene expression data with a censored response. In particular, Principal Component Analysis (PCA), modified Partial Least Squares (MPLS), RMPLS, Sliced Inverse Regression (SIR), Correlation Principal Component Regression (CPCR), Supervised Principal Component Regression (SPCR) and Univariate Selection (UNIV) are compared in terms of mean squared error of the estimated survival function and the estimated coefficients of the covariates, and in terms of the bias of the estimated survival function. It turns out that RMPLS outperforms all other methods in terms of the mean squared error and the bias of the survival function in the presence of outliers in the response. In addition, RMPLS is comparable to MPLS in the absence of outliers. In this setting, both RMPLS and MPLS outperform all other methods considered in this study in terms of mean squared error and bias of the estimated survival function.

January 21, 2009

A Nonlinear Mixed-Effects Model for Estimating Calibration Intervals for Unknown Concentrations in Two-Color Microarray Data with Spike-Ins

Pushpike J Thilakarathne, Geert Verbeke, Kristof Engelen, Kathleen Marchal

Abstract

In this study, we propose a calibration method for preprocessing spiked-in microarray experiments based on nonlinear mixed-effects models. This method uses a spike-in calibration curve to estimate normalized absolute expression values. Moreover, using the asymptotic properties of the calibration estimate, 100(1-?)% confidence intervals for the estimated expression values can be constructed. Simulations are used to show that the approximations on which the construction of the confidence intervals are based are sufficiently accurate to reach the desired coverage probabilities. We illustrate applicability of our method, by estimating the normalized absolute expression values together with the corresponding confidence intervals for two publicly available cDNA microarray experiments (Hilson et al., 2004; Smets et al., 2008). This method can easily be adapted to preprocess one-color oligonucleotide microarray data with a slight adjustment to the mixed model.

January 28, 2009

Composite Likelihood Modeling of Neighboring Site Correlations of DNA Sequence Substitution Rates

Ling Deng, Dirk F. Moore

Abstract

Sequence data from a series of homologous DNA segments from related organisms are typically polymorphic at many sites, and these polymorphisms are the result of evolutionary processes. Such data may be used to estimate the substitution rates as well as the variability of these rates. Careful characterization of the distribution of this variation is essential for accurate estimation of evolutionary distances and phylogeny reconstruction among these sequences. Many researchers have recognized the importance of the variability of substitution rates, which most have modeled using a discrete gamma distribution. Some have extended these methods to explicitly account for the correlation of substitution rates among sites using hidden Markov models; others have proposed context-dependent substitution rate schemes. We accommodate these correlations using a composite likelihood method based on a bivariate gamma distribution, which is more flexible than hidden Markov models in terms of correlation structure and more computationally tractable compared to the context-dependent schemes. We show that the estimates have good theoretical properties. We also use simulations to compare the maximum composite likelihood estimates to those obtained from maximum likelihood based on the independence assumption. We use data from the mitochondrial DNA of ten primates to obtain maximum composite likelihood estimates of the mean substitution rate, overdispersion, and correlation parameters, and use these estimates in a parametric phylogenetic bootstrap to assess the impact of serial correlation on the estimates of substitution rates and branch lengths.

January 28, 2009

A Multiple Testing Approach to High-Dimensional Association Studies with an Application to the Detection of Associations between Risk Factors of Heart Disease and Genetic Polymorphisms

José A. Ferreira, Johannes Berkhof, Olga Souverein, Koos Zwinderman

Abstract

We present an approach to association studies involving a dozen or so `response' variables and a few hundred `explanatory' variables which emphasizes transparency, simplicity, and protection against spurious results. The methods proposed are largely non-parametric, and they are systematically rounded-off by the Benjamini-Hochberg method of multiple testing. An application to the detection of associations between risk factors of heart disease and genetic polymorphisms using the REGRESS dataset provides ample illustration of our approach. Special attention is paid to book-keeping and information-management aspects of data analysis, which allow the creation of an informative and reasonably digestible `map of relationships'---the end-product of an association study as far as statistics is concerned.

February 4, 2009

Hypothesis Tests for Point-Mass Mixture Data with Application to `Omics Data with Many Zero Values

Sandra Taylor, Katherine Pollard

Abstract

Data composed of a continuous component plus a point-mass frequently arises in genomic studies. The distribution of this type of data is characterized by the proportion of observations in the point mass and the distribution of the continuous component. Standard statistical methods focus on one of these effects at a time and can fail to detect differences between experimental groups. We propose a novel empirical likelihood ratio test (LRT) statistic for simultaneously testing the null hypothesis of no difference in point-mass proportions and no difference in means of the continuous component. This study evaluates the performance of the empirical LRT and three existing point-mass mixture statistics: 1) Two-part statistic with a t-test for testing mean differences (Two-part t), 2) Two-part statistic with Wilcoxon test for testing mean differences (Two-part W), and 3) parametric LRT.Our investigations begin with an analysis of metabolomics data from Arabidopsis thaliana, which contains many metabolites with a large proportion of observed concentrations in a point-mass at zero. All four point-mass mixture statistics identify more significant differences than standard t-tests and Wilcoxon tests. The empirical LRT appears particularly effective. These findings motivate a large simulation study that assesses Type I and Type II error of the four test statistics with various choices of null distribution. The parametric LRT is frequently the most powerful test, as long as the model assumptions are correct. As is common in `omics data, the Arabidopsis metabolites have widely varying concentration distributions. A single parametric distribution cannot effectively represent all of these distributions, and individually selecting the optimal parametric distribution to use in the LRT for each metabolite is not practical. The empirical LRT, which does not require parametric assumptions, provides an attractive alternative to parametric and standard methods.

February 4, 2009

Inferring Dynamic Genetic Networks with Low Order Independencies

Sophie Lèbre

Abstract

In this paper, we introduce a novel inference method for dynamic genetic networks which makes it possible to face a number of time measurements n that is much smaller than the number of genes p. The approach is based on the concept of a low order conditional dependence graph that we extend here in the case of dynamic Bayesian networks. Most of our results are based on the theory of graphical models associated with the directed acyclic graphs (DAGs). In this way, we define a minimal DAG G which describes exactly the full order conditional dependencies given in the past of the process. Then, to face with the large p and small n estimation case, we propose to approximate DAG G by considering low order conditional independencies. We introduce partial qth order conditional dependence DAGs G(q) and analyze their probabilistic properties. In general, DAGs G(q) differ from DAG G but still reflect relevant dependence facts for sparse networks such as genetic networks. By using this approximation, we set out a non-Bayesian inference method and demonstrate the effectiveness of this approach on both simulated and real data analysis. The inference procedure is implemented in the R package 'G1DBN' freely available from the R archive (CRAN).

February 4, 2009

Normalization Method for Transcriptional Studies of Heterogeneous Samples - Simultaneous Array Normalization and Identification of Equivalent Expression

Li-Xuan Qin, Jaya M Satagopan

Abstract

Normalization is an important step in the analysis of microarray data of transcription profiles as systematic non-biological variations often arise from the multiple steps involved in any transcription profiling experiment. Existing methods for data normalization often assume that there are few or symmetric differential expression, but this assumption does not always hold. Alternatively, non-differentially expressed genes may be used for array normalization. However, it is unknown at the outset which genes are non-differentially expressed. In this paper we propose a hierarchical mixture model framework to simultaneously identify non-differentially expressed genes and normalize arrays using these genes. The Fisher's information matrix corresponding to array effects is derived, which provides useful intuition for guiding the choice of array normalization method. The operating characteristics of the proposed method are evaluated using simulated data. The simulations conducted under a wide range of parametric configurations suggest that the proposed method provides a useful alternative for array normalization. For example, the proposed method has better sensitivity than median normalization under modest prevalence of differentially expressed genes and when the magnitudes of over-expression and under-expression are not the same. Further, the proposed method has properties similar to median normalization when the prevalence of differentially expressed genes is very small. Empirical illustration of the proposed method is provided using a liposarcoma study from MSKCC to identify genes differentially expressed between normal fat tissue versus liposarcoma tissue samples.

February 4, 2009

A Bayesian Analysis Strategy for Cross-Study Translation of Gene Expression Biomarkers

Joseph Lucas, Carlos Carvalho, Mike West

Abstract

We describe a strategy for the analysis of experimentally derived gene expression signatures and their translation to human observational data. Sparse multivariate regression models are used to identify expression signature gene sets representing downstream biological pathway events following interventions in designed experiments. When translated into in vivo human observational data, analysis using sparse latent factor models can yield multiple quantitative factors characterizing expression patterns that are often more complex than in the controlled, in vitro setting. The estimation of common patterns in expression that reflect all aspects of covariation evident in vivo offers an enhanced, modular view of the complexity of biological associations of signature genes. This can identify substructure in the biological process under experimental investigation and improved biomarkers of clinical outcomes. We illustrate the approach in a detailed study from an oncogene intervention experiment where in vivo factor profiling of an in vitro signature generates biological insights related to underlying pathway activities and chromosomal structure, and leads to refinements of cancer recurrence risk stratification across several cancer studies.

February 4, 2009

Modified FDR Controlling Procedure for Multi-Stage Analyses

Catherine Tuglus, Mark J. van der Laan

Abstract

Multiple testing has become an integral component in genomic analyses involving microarray experiments where a large number of hypotheses are tested simultaneously. However, before applying more computationally intensive methods, it is often desirable to complete an initial truncation of the variable set using a simpler and faster supervised method such as univariate regression. Once such a truncation is completed, multiple testing methods applied to any subsequent analysis no longer control the appropriate Type I error rates. Here we propose a modified marginal Benjamini & Hochberg step-up FDR controlling procedure for multi-stage analyses (FDR-MSA), which correctly controls Type I error in terms of the entire variable set when only a subset of the initial set of variables is tested. The method is presented with respect to a variable importance application. As the initial subset size increases, we observe convergence to the standard Benjamini & Hochberg step-up FDR controlling multiple testing procedures. We demonstrate the power and Type I error control through simulation and application to the Golub Leukemia data from 1999.

February 11, 2009

Detecting Outlier Samples in Microarray Data

Albert D Shieh, Yeung Sam Hung

Abstract

In this paper, we address the problem of detecting outlier samples with highly different expression patterns in microarray data. Although outliers are not common, they appear even in widely used benchmark data sets and can negatively affect microarray data analysis. It is important to identify outliers in order to explore underlying experimental or biological problems and remove erroneous data. We propose an outlier detection method based on principal component analysis (PCA) and robust estimation of Mahalanobis distances that is fully automatic. We demonstrate that our outlier detection method identifies biologically significant outliers with high accuracy and that outlier removal improves the prediction accuracy of classifiers. Our outlier detection method is closely related to existing robust PCA methods, so we compare our outlier detection method to a prominent robust PCA method.

February 11, 2009

Survival Analysis with High-Dimensional Covariates: An Application in Microarray Studies

David Engler, Yi Li

Abstract

Use of microarray technology often leads to high-dimensional and low-sample size (HDLSS) data settings. A variety of approaches have been proposed for variable selection in this context. However, only a small number of these have been adapted for time-to-event data where censoring is present. Among standard variable selection methods shown both to have good predictive accuracy and to be computationally efficient is the elastic net penalization approach. In this paper, adaptations of the elastic net approach are presented for variable selection both under the Cox proportional hazards model and under an accelerated failure time (AFT) model. Assessment of the two methods is conducted through simulation studies and through analysis of microarray data obtained from a set of patients with diffuse large B-cell lymphoma where time to survival is of interest. The approaches are shown to match or exceed the predictive performance of a Cox-based and an AFT-based variable selection method. The methods are moreover shown to be much more computationally efficient than their respective Cox- and AFT-based counterparts.

February 12, 2009

Two-Stage Model-Based Clustering for Liquid Chromatography Mass Spectrometry Data Analysis

Marta ?uksza, Bogus?aw Kluge, Jerzy Ostrowski, Jakub Karczmarski, Anna Gambin

Abstract

Proteomic mass spectrometry is gaining an increasing role in diagnostics and in studies on protein complexes and biological systems. This experimental technology is producing high-throughput data which is inherently noisy and may contain various errors. Mathematical processing can help in removing them.In this paper we focus on the peak alignment problem in LC-MS spectra. As an alternative to heuristic approaches to the problem, we propose a mathematically sound method which exploits a model-based clustering. In this framework experiment errors are modeled as deviations from real values and mass spectra are regarded as finite Gaussian mixtures. The advantage of such an approach is that it provides convenient techniques for adjusting parameters and selecting solutions of best quality. The method can be parameterized by assuming various constraints. In this paper we investigate and compare different classes of models. We analyze the results in terms of statistically significant biomarkers that can be identified after the alignment of spectra. The study was conducted on a dataset of plasma samples of colorectal cancer patients and healthy donors.

February 12, 2009

Score Statistics for Mapping Quantitative Trait Loci

Myron N Chang, Rongling Wu, Samuel S Wu, George Casella

Abstract

We propose a method to detect the existence of quantitative trait loci (QTL) in a backcross population using a score test. Since the score test only uses the MLEs of parameters under the null hypothesis, it is computationally simpler than the likelihood ratio test (LRT). Moreover, because the location parameter of the QTL is unidentifiable under the null hypothesis, the distribution of the maximum of the LRT statistics, typically the statistic of choice for testing H0: no QTL, does not have the standard chi-square distribution asymptotically under the null hypothesis. From the simple structure of the score test statistics, the asymptotic null distribution can be derived for the maximum of the square of score test statistics. Numerical methods are proposed to compute the asymptotic null distribution and the critical thresholds can be obtained accordingly. We show that the maximum of the LR test statistics and the maximum of the square of score statistics are asymptotically equivalent. Therefore, the critical threshold for the score test can be used for the LR test also. A simple backcross design is used to demonstrate the application of the score test to QTL mapping.

February 12, 2009

Impact of Population Stratification on Family-Based Association Tests with Longitudinal Measurements

Xiao Ding, Scott Weiss, Benjamin Raby, Christoph Lange, Nan M Laird

Abstract

Several family-based approaches for testing genetic association with traits obtained from longitudinal or repeated measurement studies have been previously proposed. These approaches utilize the multivariate data more efficiently by using estimated optimal weights to combine univariate tests. We show that these FBAT approaches are still robust against hidden population stratification, but their power can be heavily affected since the estimated weights might provide poor approximation of the true theoretical optimal weights with the presence of population stratification. We introduce a permutation-based approach FBAT-MinP and an equal combination approach FBAT-EW, both of which do not involve the use of estimated weights. Through simulation studies, FBAT-MinP and FBAT-EW are shown to be powerful even in the presence of population stratification, when other approaches may substantially lose their power. An application of these approaches to the Childhood Asthma Management Program (CAMP) study data for testing an association between body mass index and a previously reported candidate SNP is given as an example.

February 26, 2009

A Multilocus Model for Constructing a Linkage Disequilibrium Map in Human Populations

Qin Li, Rongling Wu

Abstract

The extent and pattern of linkage disequilibrium (LD) determine the feasibility of association studies to map genes that underlie complex traits. Here we present a statistical algorithm for constructing a joint linkage-linkage disequilibrium map by simultaneously estimating the recombination fraction and linkage disequilibrium between different molecular markers in a natural human population. This algorithm was devised with a set of random unrelated families, each including a father, a mother and a varying number of offspring, sampled from a population at Hardy-Weinberg equilibrium. A two-level hierarchical mixture model framework was built, in which the likelihood of genotype data for the parents was formulated in terms of linkage disequilibrium at an upper level, whereas the likelihood of genetic transmission from the parents to offspring formulated in terms of the recombination fraction at a lower level. The EM algorithm was implemented to obtain a closed system of maximum likelihood estimates of marker co-segregation and co-transmission. The model allows a number of testable hypotheses about population genetic parameters, opening a broad gateway to understand the genetic structure and dynamics of an outcrossing population under natural selection. The new strategy will provide a platform for studying the genetic control of inherited diseases in which genetic material is accurately copied before being passed onto the offspring from a parent.

February 26, 2009

Testing of Chromosomal Clumping of Gene Properties

Luciano Fernandez-Ricaud, Daniel Dalevi, Anders Blomberg, Olle Nerman

Abstract

Clumping of gene properties like expression or mutant phenotypes along chromosomes is commonly detected using completely random null-models where their location is equally likely across the chromosomes. Interpretation of statistical tests based on these assumptions may be misleading if dependencies exist that are unequal between chromosomes or in different chromosomal parts. One such regional dependency is the telomeric effect, observed in several studies of Saccharomyces cerevisiae, under which e.g. essential genes are less likely to reside near the chromosomal ends.In this study we demonstrate that standard randomisation test procedures are of limited applicability in the presence of telomeric effects. Several extensions of such standard tests are here suggested for handling clumping simultaneously with regional differences in essentiality frequencies in sub-telomeric and central gene positions. Furthermore, a general non-homogeneous discrete Markov approach for combining parametrically modelled position dependent probabilities of a dichotomous property with a simple single parameter clumping is suggested. This Markov model is adapted to the observed telomeric effects and then simulations are used to demonstrate properties of the suggested modified randomisation tests. The model is also applied as a direct alternative tool for statistical analysis of the S. cerevisiae genome for clumping of phenotypes.

April 7, 2009

Balanced Gradient Boosting from Imbalanced Data for Clinical Outcome Prediction

Reiji Teramoto

Abstract

In clinical outcome prediction, such as disease diagnosis and prognosis, it is often assumed that the class, e.g., disease and control, is equally distributed. However, in practice we often encounter biological or clinical data whose class distribution is highly skewed. Since standard supervised learning algorithms intend to maximize the overall prediction accuracy, a prediction model tends to show a strong bias toward the majority class when it is trained on such imbalanced data. Therefore, the class distribution should be incorporated appropriately to learn from imbalanced data. To address this practically important problem, we proposed balanced gradient boosting (BalaBoost) which reformulates gradient boosting to avoid the overfitting to the majority class and is sensitive to the minority class by making use of the equal class distribution instead of the empirical class distribution. We applied BalaBoost to cancer tissue diagnosis based on miRNA expression data, premature death prediction for diabetes patients based on biochemical and clinical variables and tumor grade prediction of renal cell carcinoma based on tumor marker expressions whose class distribution is highly skewed. Experimental results showed that BalaBoost outperformed the representative supervised learning algorithms, i.e., gradient boosting, Random Forests and Support Vector Machine. Our results led us to the conclusion that BalaBoost is promising for clinical outcome prediction from imbalanced data.

April 14, 2009

Univariate Shrinkage in the Cox Model for High Dimensional Data

Robert J. Tibshirani

Abstract

We propose a method for prediction in Cox's proportional model, when the number of features (regressors), p, exceeds the number of observations, n. The method assumes that the features are independent in each risk set, so that the partial likelihood factors into a product. As such, it is analogous to univariate thresholding in linear regression and nearest shrunken centroids in classification. We call the procedure Cox univariate shrinkage and demonstrate its usefulness on real and simulated data. The method has the attractive property of being essentially univariate in its operation: the features are entered into the model based on the size of their Cox score statistics. We illustrate the new method on real and simulated data, and compare it to other proposed methods for survival prediction with a large number of predictors.

April 14, 2009

Multilevel Comparison of Dendrograms: A New Method with an Application for Genetic Classifications

János Podani, Attila Engloner, Agnes Major

Abstract

Procedures are currently available for the evaluation of hierarchical classifications of produce tree dissimilarities or consensus dendrograms. Some tests of cluster validity operate by comparing all possible partitions from a tree with a reference partition. We propose an exhaustive search procedure to compare all partitions from one dendrogram with all partitions derived from the other to detect hierarchical levels at which the two dendrograms show maximum agreement. The method is illustrated using RAPD and microsatellite data in order to detect clones in reed populations. The utility of our approach is its ability to reveal extra information in different genetic data sets which would be hidden otherwise. The method is also useful in any field of science where hierarchical clustering is the main research tool and comparison of results is an objective. Artificial and actual dendrograms, together with randomly simulated trees were used to compare the performance of five classical coefficients of partition dissimilarity. The simulations showed that when meaningful group structure is lacking, then the five coefficients are in full disagreement, but they perform similarly otherwise.

April 16, 2009

Weighted Multiple Hypothesis Testing Procedures

Guolian Kang, Keying Ye, Nianjun Liu, David B. Allison, Guimin Gao

Abstract

Multiple hypothesis testing is commonly used in genome research such as genome-wide studies and gene expression data analysis (Lin, 2005). The widely used Bonferroni procedure controls the family-wise error rate (FWER) for multiple hypothesis testing, but has limited statistical power as the number of hypotheses tested increases. The power of multiple testing procedures can be increased by using weighted p-values (Genovese et al., 2006). The weights for the p-values can be estimated by using certain prior information. Wasserman and Roeder (2006) described a weighted Bonferroni procedure, which incorporates weighted p-values into the Bonferroni procedure, and Rubin et al. (2006) and Wasserman and Roeder (2006) estimated the optimal weights that maximize the power of the weighted Bonferroni procedure under the assumption that the means of the test statistics in the multiple testing are known (these weights are called optimal Bonferroni weights). This weighted Bonferroni procedure controls FWER and can have higher power than the Bonferroni procedure, especially when the optimal Bonferroni weights are used. To further improve the power of the weighted Bonferroni procedure, first we propose a weighted idák procedure that incorporates weighted p-values into the idák procedure, and then we estimate the optimal weights that maximize the average power of the weighted idák procedure under the assumption that the means of the test statistics in the multiple testing are known (these weights are called optimal idák weights). This weighted idák procedure can have higher power than the weighted Bonferroni procedure. Second, we develop a generalized sequential (GS) idák procedure that incorporates weighted p-values into the sequential idák procedure (Scherrer, 1984). This GS idák procedure is an extension of and has higher power than the GS Bonferroni procedure of Holm (1979). Finally, under the assumption that the means of the test statistics in the multiple testing are known, we incorporate the optimal idák weights and the optimal Bonferroni weights into the GS idák procedure and the GS Bonferroni procedure, respectively. Theoretical proof and/or simulation studies show that the GS idák procedure can have higher power than the GS Bonferroni procedure when their corresponding optimal weights are used, and that both of these GS procedures can have much higher power than the weighted idák and the weighted Bonferroni procedures. All proposed procedures control the FWER well and are useful when prior information is available to estimate the weights.

May 5, 2009

Incorporating Duplicate Genotype Data into Linear Trend Tests of Genetic Association: Methods and Cost-Effectiveness

Bryce Borchers, Marshall Brown, Brian McLellan, Airat Bekmetjev, Nathan L Tintle

Abstract

The genome-wide association (GWA) study is an increasingly popular way to attempt to identify the causal variants in human disease. Duplicate genotyping (or re-genotyping) a portion of the samples in a GWA study is common, though it is typical for these data to be ignored in subsequent tests of genetic association. We demonstrate a method for including duplicate genotype data in linear trend tests of genetic association which yields increased power. We also consider the cost-effectiveness of collecting duplicate genotype data and find that when the relative cost of genotyping to phenotyping and sample acquisition costs is less than or equal to the genotyping error rate it is more powerful to duplicate genotype the entire sample instead of spending the same money to increase the sample size. Duplicate genotyping is particularly cost-effective when SNP minor allele frequencies are low. Practical advice for the implementation of duplicate genotyping is provided. Free software is provided to compute asymptotic and permutation based tests of association using duplicate genotype data as well as to aid in the duplicate genotyping design decision.

May 7, 2009

Increase of Rejection Rate in Case-Control Studies with the Differential Genotyping Error Rates

Kwangmi Ahn, Derek Gordon, Stephen J Finch

Abstract

Genotyping error adversely affects the statistical power of case-control association studies and introduces bias in the estimated parameters when the same error mechanism and probabilities apply to both affected and unaffected individuals; that is, when there is non-differential genotype misclassification. Simulation studies have shown that differential genotype misclassification leads to a rejection rate that is higher than the nominal significance level (type I error rate) for some tests of association.This study extends previous work by examining this issue analytically using the non-centrality parameter of the asymptotic distribution of the chi-squared test and linear trend test (LTT) when there is no difference between case and control genotype frequencies, but there is differential misclassification with SNP data. The parameters examined are the minor allele frequency (MAF) and sample size.When MAF is less than 0.2, differential genotyping errors lead to a rejection rate much larger than the nominal significance level. As the MAF decreases to zero, the increase in the rejection rate becomes larger. The errors that most increase the rejection rate are differential recording of the more common homozygote as the other homozygote and differential recording of the more common homozygote as the heterozygote. The rejection rate increases as the sample size increases for fixed differential genotyping error rates and nominal significance level for each test.

June 2, 2009

A Parametric Model for Analyzing Anticipation in Genetically Predisposed Families

Klaus Larsen, Janne Petersen, Inge Bernstein, Mef Nilbert

Abstract

Anticipation, i.e. a decreasing age-at-onset in subsequent generations has been observed in a number of genetically triggered diseases. The impact of anticipation is generally studied in affected parent-child pairs. These analyses are restricted to pairs in which both individuals have been affected and are sensitive to right truncation of the data. We propose a normal random effects model that allows for right-censored observations and includes covariates, and draw statistical inference based on the likelihood function.We applied the model to the hereditary nonpolyposis colorectal cancer (HNPCC)/Lynch syndrome family cohort from the national Danish HNPCC register. Age-at-onset was analyzed in 824 individuals from 2-4 generations in 125 families with proved disease-predisposing mutations. A significant effect from anticipation was identified with a mean of 3 years earlier age-at-onset per generation. The suggested model corrects for incomplete observations and considers families rather than affected pairs and thereby allows for studies of large sample sets, facilitates subgroup analyses and provides generation effect estimates.

June 5, 2009

Bayesian Unsupervised Learning with Multiple Data Types

Phaedra Agius, Yiming Ying, Colin Campbell

Abstract

We propose Bayesian generative models for unsupervised learning with two types of data and an assumed dependency of one type of data on the other. We consider two algorithmic approaches, based on a correspondence model, where latent variables are shared across datasets. These models indicate the appropriate number of clusters in addition to indicating relevant features in both types of data. We evaluate the model on artificially created data. We then apply the method to a breast cancer dataset consisting of gene expression and microRNA array data derived from the same patients. We assume partial dependence of gene expression on microRNA expression in this study. The method ranks genes within subtypes which have statistically significant abnormal expression and ranks associated abnormally expressing microRNA. We report a genetic signature for the basal-like subtype of breast cancer found across a number of previous gene expression array studies. Using the two algorithmic approaches we find that this signature also arises from clustering on the microRNA expression data and appears derivative from this data.

June 9, 2009

Extensions of Sparse Canonical Correlation Analysis with Applications to Genomic Data

Daniela M Witten, Robert J. Tibshirani

Abstract

In recent work, several authors have introduced methods for sparse canonical correlation analysis (sparse CCA). Suppose that two sets of measurements are available on the same set of observations. Sparse CCA is a method for identifying sparse linear combinations of the two sets of variables that are highly correlated with each other. It has been shown to be useful in the analysis of high-dimensional genomic data, when two sets of assays are available on the same set of samples. In this paper, we propose two extensions to the sparse CCA methodology. (1) Sparse CCA is an unsupervised method; that is, it does not make use of outcome measurements that may be available for each observation (e.g., survival time or cancer subtype). We propose an extension to sparse CCA, which we call sparse supervised CCA, which results in the identification of linear combinations of the two sets of variables that are correlated with each other and associated with the outcome. (2) It is becoming increasingly common for researchers to collect data on more than two assays on the same set of samples; for instance, SNP, gene expression, and DNA copy number measurements may all be available. We develop sparse multiple CCA in order to extend the sparse CCA methodology to the case of more than two data sets. We demonstrate these new methods on simulated data and on a recently published and publicly available diffuse large B-cell lymphoma data set.

June 19, 2009

A Non-Homogeneous Hidden-State Model on First Order Differences for Automatic Detection of Nucleosome Positions

Pei Fen Kuan, Dana Huebert, Audrey Gasch, Sunduz Keles

Abstract

The ability to map individual nucleosomes accurately across genomes enables the study of relationships between dynamic changes in nucleosome positioning/occupancy and gene regulation. However, the highly heterogeneous nature of nucleosome densities across genomes and short linker regions pose challenges in mapping nucleosome positions based on high-throughput microarray data of micrococcal nuclease (MNase) digested DNA. Previous works rely on additional detrending and careful visual examination to detect low-signal nucleosomes, which may exist in a subpopulation of cells. We propose a non-homogeneous hidden-state model based on first order differences of experimental data along genomic coordinates that bypasses the need for local detrending and can automatically detect nucleosome positions of various occupancy levels. Our proposed approach is applicable to both low and high resolution MNase-Chip and MNase-Seq (high throughput sequencing) data, and is able to map nucleosome-linker boundaries accurately. This automated algorithm is also computationally efficient and only requires a simple preprocessing step. We provide several examples illustrating the pitfalls of existing methods, the difficulties of detrending the observed hybridization signals and demonstrate the advantages of utilizing first order differences in detecting nucleosome occupancies via simulations and case studies involving MNase-Chip and MNase-Seq data of nucleosome occupancy in yeast S. cerevisiae.

June 23, 2009

Adaptive Transmission Disequilibrium Test for Family Trio Design

Min Yuan, Xin Tian, Gang Zheng, Yaning Yang

Abstract

The transmission disequilibrium test (TDT) is a standard method to detect association using family trio design. It is optimal for an additive genetic model. Other TDT-type tests optimal for recessive and dominant models have also been developed. Association tests using family data, including the TDT-type statistics, have been unified to a class of more comprehensive and flexable family-based association tests (FBAT). TDT-type tests have high efficiency when the genetic model is known or correctly specified, but may lose power if the model is mis-specified. Hence tests that are robust to genetic model mis-specification yet efficient are preferred. Constrained likelihood ratio test (CLRT) and MAX-type test have been shown to be efficiency robust. In this paper we propose a new efficiency robust procedure, referred to as adaptive TDT (aTDT). It uses the Hardy-Weinberg disequilibrium coefficient to identify the potential genetic model underlying the data and then applies the TDT-type test (or FBAT for general applications) corresponding to the selected model. Simulation demonstrates that aTDT is efficiency robust to model mis-specifications and generally outperforms the MAX test and CLRT in terms of power. We also show that aTDT has power close to, but much more robust, than the optimal TDT-type test based on a single genetic model. Applications to real and simulated data from Genetic Analysis Workshop (GAW) illustrate the use of our adaptive TDT.

June 25, 2009

Model Selection Based on FDR-Thresholding Optimizing the Area under the ROC-Curve

Alexandra C. Graf, Peter Bauer

Abstract

We evaluate variable selection by multiple tests controlling the false discovery rate (FDR) to build a linear score for prediction of clinical outcome in high-dimensional data. Quality of prediction is assessed by the receiver operating characteristic curve (ROC) for prediction in independent patients. Thus we try to combine both goals: prediction and controlled structure estimation. We show that the FDR-threshold which provides the ROC-curve with the largest area under the curve (AUC) varies largely over the different parameter constellations not known in advance. Hence, we investigated a new cross validation procedure based on the maximum rank correlation estimator to determine the optimal selection threshold. This procedure (i) allows choosing an appropriate selection criterion, (ii) provides an estimate of the FDR close to the true FDR and (iii) is simple and computationally feasible for rather moderate to small sample sizes. Low estimates of the cross validated AUC (the estimates generally being positively biased) and large estimates of the cross validated FDR may indicate a lack of sufficiently prognostic variables and/or too small sample sizes. The method is applied to an oncology dataset.

June 30, 2009

Estimation of Selection Intensity under Overdominance by Bayesian Methods

Erkan Ozge Buzbas, Paul Joyce, Zaid Abdo

Abstract

A balanced pattern in the allele frequencies of polymorphic loci is a potential sign of selection, particularly of overdominance. Although this type of selection is of some interest in population genetics, there exists no likelihood based approaches specifically tailored to make inference on selection intensity. To fill this gap, we present Bayesian methods to estimate selection intensity under k-allele models with overdominance. Our model allows for an arbitrary number of loci and alleles within a locus. The neutral and selected variability within each locus are modeled with corresponding k-allele models. To estimate the posterior distribution of the mean selection intensity in a multilocus region, a hierarchical setup between loci is used. The methods are demonstrated with data at the Human Leukocyte Antigen loci from world-wide populations.

July 1, 2009

A Multivariate Growth Curve Model for Ranking Genes in Replicated Time Course Microarray Data

Jemila S Hamid, Joseph Beyene

Abstract

Gene ranking problem in time course microarray experiments is challenging since gene expression levels between different time points are correlated. This is because, expression values at successive time points are usually taken from the same organism, tissue or culture. Moreover, time dependency of gene expression values is usually of interest and often is the biological problem that motivates the experiment. We propose a multivariate growth curve model for ranking genes and estimating mean gene expression profiles in replicated time course microarray data. The approach takes the within individual correlation as well as the temporal ordering into consideration. Moreover, time is incorporated as a continuous variable in the model to account for the temporal pattern. Polynomial profiles are assumed to describe the time dependence and a transformation incorporating information across the genes is used. A moderated likelihood ratio test is then applied to the transformed data to get a statistic for ranking genes according to the difference in expression profiles among biological groups. The methodology is presented in a general setup and could be used for one sample as well as more than one sample problem. The estimation is done in a multivariate framework in which information from all the groups involved is used for better inference. Moreover, the within individual correlation as well as information across genes entered in the estimation through a moderated covariance matrix. We assess the performance of our method using simulation studies and illustrate the results with publicly available real time course microarray data.

July 27, 2009

Rotation Testing in Gene Set Enrichment Analysis for Small Direct Comparison Experiments

Guro Dørum, Lars Snipen, Margrete Solheim, Solve Sæbø

Abstract

Gene Set Enrichment Analysis (GSEA) is a method for analysing gene expression data with a focus on a priori defined gene sets. The permutation test generally used in GSEA for testing the significance of gene set enrichment involves permutation of a phenotype vector and is developed for data from an indirect comparison design, i.e. unpaired data. In some studies the samples representing two phenotypes are paired, e.g. samples taken from a patient before and after treatment, or if samples representing two phenotypes are hybridised to the same two-channel array (direct comparison design). In this paper we will focus on data from direct comparison experiments, but the methods can be applied to paired data in general. For these types of data, a standard permutation test for paired data that randomly re-signs samples can be used. However, if the sample size is very small, which is often the case for a direct comparison design, a permutation test will give very imprecise estimates of the p-values. Here we propose using a rotation test rather than a permutation test for estimation of significance in GSEA of direct comparison data with a limited number of samples. Our proposed rotation test makes GSEA applicable to direct comparison data with few samples, by depending on rotations of the data instead of permutations. The rotation test is a generalisation of the permutation test, and can in addition be used on indirect comparison data and for testing significance of other types of test statistics outside the GSEA framework.

September 9, 2009

Ancestral Recombination Graphs under Non-Random Ascertainment, with Applications to Gene Mapping

Ola Hössjer, Linda Hartman, Keith Humphreys

Abstract

Consider a sample of apparently unrelated individuals, for which marker genotype and phenotype data is available. When individuals are sampled on phenotypes, we propose an ascertained ancestral recombination graph (ARG) that models shared ancestry of the sample chromosomes given phenotype data along a region that possibly harbors a disease susceptibility gene. The ascertained ARG is used to define a gene mapping algorithm by means of a lod score and associated p-values based on permutation testing. Under certain modeling simplifications, the lod score and p-values can be computed exactly, without any Monte Carlo approximations, even for unphased chromosome genotype data. Our method handles incomplete penetrance, varying marker allele frequencies and neutral mutations, and is based on a Hidden Markov algorithm for subsets of disease mutated chromosomes. The performance of the method is investigated in a simulation study and for a real data set from a case-control study of breast cancer.

September 9, 2009

Prediction of Motifs Based on a Repeated-Measures Model for Integrating Cross-Species Sequence and Expression Data

Elizabeth A Siewert, Katerina J Kechris

Abstract

De novo identification of transcription factor binding sites (TFBS) is a challenging computational problem because TFBSs are relatively short sequences buried in long genomic regions. Earlier methods incorporated genome-wide expression data and promoter sequences into a linear-model framework, regressing expression on counts of putative TFBSs in promoters for a single species. More recently, it has been shown that examining sequence data across multiple species improves the prediction of TFBSs. In this work, we describe an extension of the single-species, linear-model framework for the analysis of paired cross-species sequence and expression data. A repeated measures model for gene-expression measurements across species is used, accounting for phylogenetic relationships among species through the error covariance structure. This multiple-species algorithm is applied to a data set of four yeast species grown under heat-shock conditions and comparisons are made to the single species algorithm. Using evaluations based on transcription factor binding strength and an independent source of expression data, we find the multiple species results show an improvement in the prediction of TFBS.

September 9, 2009

Identifying Individuals in a Complex Mixture of DNA with Unknown Ancestry

Joshua Sampson, Hongyu Zhao

Abstract

A new test was recently developed that could use a high-density set of single nucleotide polymorphisms (SNPs) to determine whether a specific individual contributed to a mixture of DNA. The test statistic compared the genotype for the individual to the allele frequencies in the mixture and to the allele frequencies in a reference group. This test requires the ancestries of the reference group to be nearly identical to those of the contributors to the mixture. Here, we first quantify the bias, the increase in type I and type II error, when the ancestries are not well matched. Then, we show that the test can also be biased if the number of subjects in the two groups differ or if the platforms used to measure SNP intensities differ. We then introduce a new test statistic and a test that only requires the ancestries of the reference group to be similar to the individual of interest, and show that this test is not only robust to the number of subjects and platform, but also has increased power of detection. The two tests are compared on both HapMap and simulated data.

September 9, 2009

A Statistical Model for Genetic Mapping of Viral Infection by Integrating Epidemiological Behavior

Yao Li, Arthur Berg, Myron N Chang, Ping Du, Kwangmi Ahn, David Mauger, Duanping Liao, Rongling Wu

Abstract

Large-scale studies of genetic variation may be helpful for understanding the genetic control mechanisms of viral infection and, ultimately, predicting and eliminating infectious disease outbreaks. We propose a new statistical model for detecting specific DNA sequence variants that are responsible for viral infection. This model considers additive, dominance and epistatic effects of haplotypes from three different genomes, recipient, transmitter and virus, through an epidemiological process. The model is constructed within the maximum likelihood framework and implemented with the EM algorithm. A number of hypothesis tests about population genetic structure and diversity and the pattern of genetic control are formulated. A series of closed forms for the EM algorithm to estimate haplotype frequencies and haplotype effects in a network of genetic interactions among three genomes are derived. Simulation studies were performed to test the statistical properties of the model, recommending necessary sample sizes for obtaining reasonably good accuracy and precision of parameter estimation. By integrating, for the first time, the epidemiological principle of viral infection into genetic mapping, the new model shall find an immediate application to studying the genetic architecture of viral infection.

September 17, 2009

Calculating Asymptotic Significance Levels of the Constrained Likelihood Ratio Test with Application to Multivariate Genetic Linkage Analysis

Nathan J Morris, Robert Elston, Catherine M Stein

Abstract

The asymptotic distribution of the multivariate variance component linkage analysis likelihood ratio test has provoked some contradictory accounts in the literature. In this paper we confirm that some previous results are not correct by deriving the asymptotic distribution in one special case. It is shown that this special case is a good approximation to the distribution in many situations. We also introduce a new approach to simulating from the asymptotic distribution of the likelihood ratio test statistic in constrained testing problems. It is shown that this method is very efficient for small p-values, and is applicable even when the constraints are not convex. The method is related to a multivariate integration problem. We illustrate how the approach can be applied to multivariate linkage analysis in a simulation study. Some more philosophical issues relating to one-sided tests in variance components linkage analysis are discussed.

September 22, 2009

Modeling Dependence in Methylation Patterns with Application to Ovarian Carcinomas

Michelle R Lacey, Melanie Ehrlich

Abstract

Changes in cytosine methylation at CpG nucleotides are observed in many cancers and offer great potential for translational research. Diseases such as ovarian cancer that are especially challenging to diagnose and treat are of particular interest, and abnormal methylation in the tandem repeats Sat2 and NBL2 has been observed in a collection of ovarian carcinomas. In earlier analyses of double-stranded methylation patterns in 0.2 kb regions of Sat2 and NBL2, we detected clusters of identically methylated sites in close proximity. These clusters could not be explained by random variation, and our findings suggested a high degree of site-to-site dependence. However, previously developed stochastic models for methylation change have either treated CpG sites independently or employed a context dependent approach to adjust model parameters according to regional methylation levels. In this paper, we introduce a novel neighboring sites model as an alternative methodology for considering dependence in methylation patterns, and we compare the three models in their ability to generate simulated sequences statistically similar to our Sat2 and NBL2 carcinoma samples.

September 22, 2009

M-quantile Regression Analysis of Temporal Gene Expression Data

Veronica Vinciotti, Keming Yu

Abstract

In this paper, we explore the use of M-quantile regression and M-quantile coefficients to detect statistical differences between temporal curves that belong to different experimental conditions. In particular, we consider the application of temporal gene expression data. Here, the aim is to detect genes whose temporal expression is significantly different across a number of biological conditions. We present a new method to approach this problem. Firstly, the temporal profiles of the genes are modelled by a parametric M-quantile regression model. This model is particularly appealing to small-sample gene expression data, as it is very robust against outliers and it does not make any assumption on the error distribution. Secondly, we further increase the robustness of the method by summarising the M-quantile regression models for a large range of quantile values into an M-quantile coefficient. Finally, we fit a polynomial M-quantile regression model to the M-quantile coefficients over time and employ a Hotelling T2-test to detect significant differences of the temporal M-quantile coefficients profiles across conditions. Extensive simulations show the increased power and robustness of M-quantile regression methods over standard regression methods and over some of the previously published methods. We conclude by applying the method to detect differentially expressed genes from time-course microarray data on muscular dystrophy.

October 1, 2009

MC-Normalization: A Novel Method for Dye-Normalization of Two-Channel Microarray Data

Mattias Landfors, Jessica Fahlén, Patrik Rydén

Abstract

Pre-processing plays a vital role in two-color microarray data analysis. An analysis is characterized by its ability to identify differentially expressed genes (its sensitivity) and its ability to provide unbiased estimators of the true regulation (its bias). It has been shown that microarray experiments regularly underestimate the true regulation of differentially expressed genes. We introduce the MC-normalization, where C stands for channel-wise normalization, with considerably lower bias than the commonly used standard methods.The idea behind the MC-normalization is that the channels' individual intensities determine the correction, rather than the average intensity which is the case for the widely used MA-normalization. The two methods were evaluated using spike-in data from an in-house produced cDNA-experiment and a publicly available Agilent-experiment. The methods were applied on background corrected and non-background corrected data. For the cDNA-experiment the methods were either applied separately on data from each of the print-tips or applied on the complete array data. Altogether 24 analyses were evaluated. For each analysis the sensitivity, the bias and two variance measures were estimated.We prove that the MC-normalization has lower bias than the MA-normalization. The spike-in data confirmed the theoretical result and suggest that the difference is significant. Furthermore, the empirical data suggest that the MC-and MA-normalization have similar sensitivity. A striking result is that print-tip normalizations did have considerably higher sensitivity than analyses using the complete array data.

October 8, 2009

Characterizing the D2 Statistic: Word Matches in Biological Sequences

Sylvain Forêt, Susan R Wilson, Conrad J Burden

Abstract

Word matches are often used in sequence comparison methods, either as a measure of sequence similarity or in the first search steps of algorithms such as BLAST or BLAT. The D2 statistic is the number of matches of words of k letters between two sequences. Recent advances have been made in the characterization of this statistic and in the approximation of its distribution. Here, these results are extended to the case of approximate word matches.We compute the exact value of the variance of the D2 statistic for the case of a uniform letter distribution, and introduce a method to provide accurate approximations of the variance in the remaining cases. This enables the distribution of D2 to be approximated for typical situations arising in biological research. We apply these results to the identification of cis-regulatory modules, and show that this method detects such sequences with a high accuracy.The ability to approximate the distribution of D2 for both exact and approximate word matches will enable the use of this statistic in a more precise manner for sequence comparison, database searches, and identification of transcription factor binding sites.

October 8, 2009

Transmission Disequilibrium Test Power and Sample Size in the Presence of Locus Heterogeneity

Chuanwen Chen, Guang Yang, Steven Buyske, Tara Matise, Stephen J Finch, Derek Gordon

Abstract

Locus heterogeneity is one of the most important issues in gene mapping and can cause significant reductions in statistical power for gene mapping, yet no research to date has provided power and sample size calculations for family-based association methods in the presence of locus heterogeneity. The purpose of this research is three-fold: (i) to provide an analytic solution to the incorporation of locus heterogeneity into power and sample size calculations for the TDT statistic; (ii) to verify our analytic solution with simulations; and (iii) to study how different factors affect sample size requirement for the TDT in the presence of locus heterogeneity.The detection of association in the presence of locus heterogeneity requires a greater sample size than in its absence. This increase is independent of the prevalence of the disease. In addition, as the proportion of families unlinked to the disease locus increases, the sample size necessary to maintain constant power increases. Finally, as the effect size of the disease locus increases, the sample size necessary to detect association decreases in the presence of locus heterogeneity. We provide freely available software that can perform these calculations.

October 23, 2009

A Regularized Regression Approach for Dissecting Genetic Conflicts that Increase Disease Risk in Pregnancy

Shaoyu Li, Qing Lu, Wenjiang Fu, Roberto Romero, Yuehua Cui

Abstract

Human diseases developed during pregnancy could be caused by the direct effects of both maternal and fetal genes, and/or by the indirect effects caused by genetic conflicts. Genetic conflicts exist when the effects of fetal genes are opposed by the effects of maternal genes, or when there is a conflict between the maternal and paternal genes within the fetal genome. The two types of genetic conflicts involve the functions of different genes in different genomes and are genetically distinct. Differentiating and further dissecting the two sets of genetic conflict effects that increase disease risk during pregnancy present statistical challenges, and have been traditionally pursued as two separate endeavors. In this article, we develop a unified framework to model and test the two sets of genetic conflicts via a regularized regression approach. Our model is developed considering real situations in which the paternal information is often completely missing; an assumption that fails most of the current family-based studies. A mixture model-based penalized logistic regression is proposed for data sampled from a natural population. We develop a variable selection procedure to select significant genetic features. Simulation studies show that the model has high power and good false positive control under reasonable sample sizes and disease allele frequency. A case study of small for gestational age (SGA) is provided to show the utility of the proposed approach. Our model provides a powerful tool for dissecting genetic conflicts that increase disease risk during pregnancy, and offers a testable framework for the genetic conflict hypothesis previously proposed.

November 4, 2009

Statistical Screening Method for Genetic Factors Influencing Susceptibility to Common Diseases in a Two-Stage Genome-Wide Association Study

Yasunori Sato, Nan Laird, Hideki Suganami, Chikuma Hamada, Naoto Niki, Isao Yoshimura, Teruhiko Yoshida

Abstract

A genome-wide association study (GWAS) is a standard strategy for detecting disease susceptibility genes, despite unsettled controversies on many aspects, including optimal study design and statistical analysis. As for study design, a two-stage design has been applied to maximize cost-effectiveness. However, there has been little consensus on appropriate statistical analysis for two-stage design. Thereby perplexing the researchers as to which statistical measures should be applied at the first stage, and how to determine the significance level of the differences at the second stage. Here, using simulation studies, we compared statistical operating characteristics of the screening in a two-stage GWAS by taking into consideration the proper balance of false-positive and false-negative error. As a result, the lower bound of confidence interval for odds ratios is recommended as the first stage measure, and then the second stage criteria should primarily depend on the purpose of the genome screen or its role in the overall gene-hunting scheme. Based on the simulation study, we suggest rules of thumb about which statistics to use in a given situation. An application of all operating characteristics of the screening method to an actual GWAS for gastric cancer illustrates the practical relevance of our discussion.

November 7, 2009

A Unified Mixed Effects Model for Gene Set Analysis of Time Course Microarray Experiments

Lily Wang, Xi Chen, Russell D Wolfinger, Jeffrey L Franklin, Robert J Coffey, Bing Zhang

Abstract

Methods for gene set analysis test for coordinated changes of a group of genes involved in the same biological process or molecular pathway. Higher statistical power is gained for gene set analysis by combining weak signals from a number of individual genes in each group. Although many gene set analysis methods have been proposed for microarray experiments with two groups, few can be applied to time course experiments. We propose a unified statistical model for analyzing time course experiments at the gene set level using random coefficient models, which fall into the more general class of mixed effects models. These models include a systematic component that models the mean trajectory for the group of genes, and a random component (the random coefficients) that models how each gene's trajectory varies about the mean trajectory.We show that the proposed model (1) outperforms currently available methods at discriminating gene sets differentially changed over time from null gene sets; (2) provides more stable results that are less affected by sampling variations; (3) models dependency among genes adequately and preserves type I error rate; and (4) allows for gene ranking based on predicted values of the random effects. We describe simulation studies using gene expression data with "real life" correlations and we demonstrate the proposed random coefficient model using a mouse colon development time course dataset. The agreement between results of the proposed random coefficient model and the previous reports for this proof-of-concept trial further validates this methodology, which provides a unified statistical model for systems analysis of microarray experiments with complex experimental designs when re-sampling based methods are difficult to apply.

About this journal

Objective
Statistical Applications in Genetics and Molecular Biology seeks to publish significant research on the application of statistical ideas to problems arising from computational biology. The focus of the papers should be on the relevant statistical issues but should contain a succinct description of the relevant biological problem being considered. The range of topics is wide and will include topics such as linkage mapping, association studies, gene finding and sequence alignment, protein structure prediction, design and analysis of microarray data, molecular evolution and phylogenetic trees, DNA topology, and data base search strategies. Both original research and review articles will be warmly received.

What scholars are saying about Statistical Applications in Genetics and Molecular Biology

“This journal will keep statisticians up to date on the thinking behind the development and validation of molecular biology based classifiers for diagnostic testing for use in such areas as early detection of disease or recurrence, risk stratification, prognosis, prediction of treatment response, monitoring, and drug dosing.”

Gene Pennello, Ph.D., Center for Devices and Radiological Health, FDA

“Statistical applications in Genetics and Genomics are very important areas of research. This journal is one of the high-quality journals that I use, and that my students use as well.”

Carl Lee, Professor of Mathematics, Central Michigan University

Topics

Linkage mapping
Association studies
Gene regulatory networks
Protein structure prediction
High-throughput data analysis
Molecular evolution and phylogenetic trees
Multi-omics data integration
Genetic and epigenetic data modelling

Article formats
Original Research Articles, Review Articles, Software Application Notes.