microsatellite analyser (MSA): a platform independent analysis tool for large microsatellite data sets

In molecular ecology the analysis of large microsatellite data sets is becoming increasingly popular. Here we introduce a new software tool, which is specifically designed to facilitate the analysis of large microsatellite data sets. All common microsatellite summary statistics and distances can be calculated. Furthermore, the microsatellite analyser (msa ) software offers an improved method to deal with inbred samples (such as Drosophila isofemale lines). Executables are available for Windows and Macintosh computers.     

On optimal selection of summary statistics for approximate Bayesian computation

How best to summarize large and complex datasets is a problem that arises in many areas of science. We approach it from the point of view of seeking data summaries that minimize the average squared error of the posterior distribution for a parameter of interest under approximate Bayesian computation (ABC). In ABC, simulation under the model replaces computation of the likelihood, which is convenient for many complex models. Simulated and observed datasets are usually compared using summary statistics, typically in practice chosen on the basis of the investigator's intuition and established practice in the field. We propose two algorithms for automated choice of efficient data summaries. Firstly, we motivate minimisation of the estimated entropy of the posterior approximation as a heuristic for the selection of summary statistics. Secondly, we propose a two-stage procedure: the minimum-entropy algorithm is used to identify simulated datasets close to that observed, and these are each successively regarded as observed datasets for which the mean root integrated squared error of the ABC posterior approximation is minimized over sets of summary statistics. In a simulation study, we both singly and jointly inferred the scaled mutation and recombination parameters from a population sample of DNA sequences. The computationally-fast minimum entropy algorithm showed a modest improvement over existing methods while our two-stage procedure showed substantial and highly-significant further improvement for both univariate and bivariate inferences. We found that the optimal set of summary statistics was highly dataset specific, suggesting that more generally there may be no globally-optimal choice, which argues for a new selection for each dataset even if the model and target of inference are unchanged.     

FLAGS: A Flexible and Adaptive Association Test for Gene Sets Using Summary Statistics

Genome-wide association studies (GWAS) have been widely used for identifying common variants associated with complex diseases. Despite remarkable success in uncovering many risk variants and providing novel insights into disease biology, genetic variants identified to date fail to explain the vast majority of the heritability for most complex diseases. One explanation is that there are still a large number of common variants that remain to be discovered, but their effect sizes are generally too small to be detected individually. Accordingly, gene set analysis of GWAS, which examines a group of functionally related genes, has been proposed as a complementary approach to single-marker analysis. Here, we propose a flexible and adaptive test for gene sets (FLAGS), using summary statistics. Extensive simulations showed that this method has an appropriate type I error rate and outperforms existing methods with increased power. As a proof of principle, through real data analyses of Crohn’s disease GWAS data and bipolar disorder GWAS meta-analysis results, we demonstrated the superior performance of FLAGS over several state-of-the-art association tests for gene sets. Our method allows for the more powerful application of gene set analysis to complex diseases, which will have broad use given that GWAS summary results are increasingly publicly available.     

Using cross-validation to evaluate predictive accuracy of survival risk classifiers based on high-dimensional data

Developments in whole genome biotechnology have stimulated statistical focus on prediction methods. We review here methodology for classifying patients into survival risk groups and for using cross-validation to evaluate such classifications. Measures of discrimination for survival risk models include separation of survival curves, time-dependent ROC curves and Harrell's concordance index. For high-dimensional data applications, however, computing these measures as re-substitution statistics on the same data used for model development results in highly biased estimates. Most developments in methodology for survival risk modeling with high-dimensional data have utilized separate test data sets for model evaluation. Cross-validation has sometimes been used for optimization of tuning parameters. In many applications, however, the data available are too limited for effective division into training and test sets and consequently authors have often either reported re-substitution statistics or analyzed their data using binary classification methods in order to utilize familiar cross-validation. In this article we have tried to indicate how to utilize cross-validation for the evaluation of survival risk models; specifically how to compute cross-validated estimates of survival distributions for predicted risk groups and how to compute cross-validated time-dependent ROC curves. We have also discussed evaluation of the statistical significance of a survival risk model and evaluation of whether high-dimensional genomic data adds predictive accuracy to a model based on standard covariates alone.     

Generalized genomic distance-based regression methodology for multilocus association analysis

Large-scale, multilocus genetic association studies require powerful and appropriate statistical-analysis tools that are designed to relate genotype and haplotype information to phenotypes of interest. Many analysis approaches consider relating allelic, haplotypic, or genotypic information to a trait through use of extensions of traditional analysis techniques, such as contingency-table analysis, regression methods, and analysis-of-variance techniques. In this work, we consider a complementary approach that involves the characterization and measurement of the similarity and dissimilarity of the allelic composition of a set of individuals' diploid genomes at multiple loci in the regions of interest. We describe a regression method that can be used to relate variation in the measure of genomic dissimilarity (or "distance") among a set of individuals to variation in their trait values. Weighting factors associated with functional or evolutionary conservation information of the loci can be used in the assessment of similarity. The proposed method is very flexible and is easily extended to complex multilocus-analysis settings involving covariates. In addition, the proposed method actually encompasses both single-locus and haplotype-phylogeny analysis methods, which are two of the most widely used approaches in genetic association analysis. We showcase the method with data described in the literature. Ultimately, our method is appropriate for high-dimensional genomic data and anticipates an era when cost-effective exhaustive DNA sequence data can be obtained for a large number of individuals, over and above genotype information focused on a few well-chosen loci.     

Biological pathway selection through nonlinear dimension reduction

In the analysis of high-throughput biological data, it is often believed that the biological units such as genes behave interactively by groups, that is, pathways in our context. It is conceivable that utilization of priorly available pathway knowledge would greatly facilitate both interpretation and estimation in statistical analysis of such high-dimensional biological data. In this article, we propose a 2-step procedure for the purpose of identifying pathways that are related to and influence the clinical phenotype. In the first step, a nonlinear dimension reduction method is proposed, which permits flexible within-pathway gene interactions as well as nonlinear pathway effects on the response. In the second step, a regularized model-based pathway ranking and selection procedure is developed that is built upon the summary features extracted from the first step. Simulations suggest that the new method performs favorably compared to the existing solutions. An analysis of a glioblastoma microarray data finds 4 pathways that have evidence of support from the biological literature.     

A fast and reliable computational method for estimating population genetic parameters

The estimation of ancestral and current effective population sizes in expanding populations is a fundamental problem in population genetics. Recently it has become possible to scan entire genomes of several individuals within a population. These genomic data sets can be used to estimate basic population parameters such as the effective population size and population growth rate. Full-data-likelihood methods potentially offer a powerful statistical framework for inferring population genetic parameters. However, for large data sets, computationally intensive methods based upon full-likelihood estimates may encounter difficulties. First, the computational method may be prohibitively slow or difficult to implement for large data. Second, estimation bias may markedly affect the accuracy and reliability of parameter estimates, as suggested from past work on coalescent methods. To address these problems, a fast and computationally efficient least-squares method for estimating population parameters from genomic data is presented here. Instead of modeling genomic data using a full likelihood, this new approach uses an analogous function, in which the full data are replaced with a vector of summary statistics. Furthermore, these least-squares estimators may show significantly less estimation bias for growth rate and genetic diversity than a corresponding maximum-likelihood estimator for the same coalescent process. The least-squares statistics also scale up to genome-sized data sets with many nucleotides and loci. These results demonstrate that least-squares statistics will likely prove useful for nonlinear parameter estimation when the underlying population genomic processes have complex evolutionary dynamics involving interactions between mutation, selection, demography, and recombination.     

Estimation in Longitudinal or Panel Data Models with Random‐Effect‐Based Missing Responses

Summary In studies with longitudinal or panel data, missing responses often depend on values of responses through a subject‐level unobserved random effect. Besides the likelihood approach based on parametric models, there exists a semiparametric method, the approximate conditional model (ACM) approach, which relies on the availability of a summary statistic and a linear or polynomial approximation to some random effects. However, two important issues must be addressed in applying ACM. The first is how to find a summary statistic and the second is how to estimate the parameters in the original model using estimates of parameters in ACM. Our study is to address these two issues. For the first issue, we derive summary statistics under various situations. For the second issue, we propose to use a grouping method, instead of linear or polynomial approximation to random effects. Because the grouping method is a moment‐based approach, the conditions we assumed in deriving summary statistics are weaker than the existing ones in the literature. When the derived summary statistic is continuous, we propose to use a classification tree method to obtain an approximate summary statistic for grouping. Some simulation results are presented to study the finite sample performance of the proposed method. An application is illustrated using data from the study of Modification of Diet in Renal Disease.     

Multiple regression methods show great potential for rare variant association tests

The investigation of associations between rare genetic variants and diseases or phenotypes has two goals. Firstly, the identification of which genes or genomic regions are associated, and secondly, discrimination of associated variants from background noise within each region. Over the last few years, many new methods have been developed which associate genomic regions with phenotypes. However, classical methods for high-dimensional data have received little attention. Here we investigate whether several classical statistical methods for high-dimensional data: ridge regression (RR), principal components regression (PCR), partial least squares regression (PLS), a sparse version of PLS (SPLS), and the LASSO are able to detect associations with rare genetic variants. These approaches have been extensively used in statistics to identify the true associations in data sets containing many predictor variables. Using genetic variants identified in three genes that were Sanger sequenced in 1998 individuals, we simulated continuous phenotypes under several different models, and we show that these feature selection and feature extraction methods can substantially outperform several popular methods for rare variant analysis. Furthermore, these approaches can identify which variants are contributing most to the model fit, and therefore both goals of rare variant analysis can be achieved simultaneously with the use of regression regularization methods. These methods are briefly illustrated with an analysis of adiponectin levels and variants in the ADIPOQ gene.     

Construction of a confidence set of markers for the location of a disease gene using affected sib pair data

We have previously proposed a confidence set approach for finding tightly linked genomic regions under the setting of parametric linkage analysis. In this article, we extend the confidence set approach to nonparametric linkage analysis of affected sib pair (ASP) data based on their identity-by-descent (IBD) information. Two well-known statistics in nonparametric linkage analysis, the Two-IBD test (proportion of ASPs sharing two alleles IBD), and the Mean test (average number of alleles shared IBD in the ASPs), are used for constructing confidence sets. Some numerical analyses as well as a simulation study were carried out to demonstrate the utility of the methods. Our results show that the fundamental advantages of the confidence set approach in parametric linkage analysis are retained when the method is generalized to nonparametric analysis. Our study on the accuracy of confidence sets, in terms of choice of tests, underlying disease incidence data, and amount of data available, leads us to conclude, among other things, that the Mean test outperforms the Two-IBD test in most situations, with the reverse being true only for traits with small additive variance. Although we describe how to construct confidence sets based on only two familiar tests, one can construct confidence sets similarly using other allele sharing statistics.     

Relative efficiency of using summary versus individual data in random-effects meta-analysis

Meta-analysis is a statistical methodology for combining information from diverse sources so that a more reliable and efficient conclusion can be reached. It can be conducted by either synthesizing study-level summary statistics or drawing inference from an overarching model for individual participant data (IPD) if available. The latter is often viewed as the “gold standard.” For random-effects models, however, it remains not fully understood whether the use of IPD indeed gains efficiency over summary statistics. In this paper, we examine the relative efficiency of the two methods under a general likelihood inference setting. We show theoretically and numerically that summary-statistics-based analysis is at most as efficient as IPD analysis, provided that the random effects follow the Gaussian distribution, and maximum likelihood estimation is used to obtain summary statistics. More specifically, (i) the two methods are equivalent in an asymptotic sense; and (ii) summary-statistics-based inference can incur an appreciable loss of efficiency if the sample sizes are not sufficiently large. Our results are established under the assumption that the between-study heterogeneity parameter remains constant regardless of the sample sizes, which is different from a previous study. Our findings are confirmed by the analyses of simulated data sets and a real-world study of alcohol interventions.     

Posterior predictive checks of coalescent models: P2C2M,an R package

Bayesian inference operates under the assumption that the empirical data are a good statistical fit to the analytical model, but this assumption can be challenging to evaluate. Here, we introduce a novel r package that utilizes posterior predictive simulation to evaluate the fit of the multispecies coalescent model used to estimate species trees. We conduct a simulation study to evaluate the consistency of different summary statistics in comparing posterior and posterior predictive distributions, the use of simulation replication in reducing error rates and the utility of parallel process invocation towards improving computation times. We also test P2C2M on two empirical data sets in which hybridization and gene flow are suspected of contributing to shared polymorphism, which is in violation with the coalescent model: Tamias chipmunks and Myotis bats. Our results indicate that (i) probability‐based summary statistics display the lowest error rates, (ii) the implementation of simulation replication decreases the rate of type II errors, and (iii) our r package displays improved statistical power compared to previous implementations of this approach. When probabilistic summary statistics are used, P2C2M corroborates the assumption that genealogies collected from Tamias and Myotis are not a good fit to the multispecies coalescent model. Taken as a whole, our findings argue that an assessment of the fit of the multispecies coalescent model should accompany any phylogenetic analysis that estimates a species tree.     

High-Dimensional Heteroscedastic Regression with an Application to eQTL Data Analysis

We consider the problem of high-dimensional regression under non-constant error variances. Despite being a common phenomenon in biological applications, heteroscedasticity has, so far, been largely ignored in high-dimensional analysis of genomic data sets. We propose a new methodology that allows non-constant error variances for high-dimensional estimation and model selection. Our method incorporates heteroscedasticity by simultaneously modeling both the mean and variance components via a novel doubly regularized approach. Extensive Monte Carlo simulations indicate that our proposed procedure can result in better estimation and variable selection than existing methods when heteroscedasticity arises from the presence of predictors explaining error variances and outliers. Further, we demonstrate the presence of heteroscedasticity in and apply our method to an expression quantitative trait loci (eQTLs) study of 112 yeast segregants. The new procedure can automatically account for heteroscedasticity in identifying the eQTLs that are associated with gene expression variations and lead to smaller prediction errors. These results demonstrate the importance of considering heteroscedasticity in eQTL data analysis.     

Sparse Support Vector Machines with L_{p} Penalty for Biomarker Identification

The development of high-throughput technology has generated a massive amount of high-dimensional data, and many of them are of discrete type. Robust and efficient learning algorithms such as LASSO [1] are required for feature selection and overfitting control. However, most feature selection algorithms are only applicable to the continuous data type. In this paper, we propose a novel method for sparse support vector machines (SVMs) with L_{p} (p ≪ 1) regularization. Efficient algorithms (LpSVM) are developed for learning the classifier that is applicable to high-dimensional data sets with both discrete and continuous data types. The regularization parameters are estimated through maximizing the area under the ROC curve (AUC) of the cross-validation data. Experimental results on protein sequence and SNP data attest to the accuracy, sparsity, and efficiency of the proposed algorithm. Biomarkers identified with our methods are compared with those from other methods in the literature. The software package in Matlab is available upon request.     

Statistical analysis of personal radiofrequency electromagnetic field measurements with nondetects

Exposimeters are increasingly applied in bioelectromagnetic research to determine personal radiofrequency electromagnetic field (RF‐EMF) exposure. The main advantages of exposimeter measurements are their convenient handling for study participants and the large amount of personal exposure data, which can be obtained for several RF‐EMF sources. However, the large proportion of measurements below the detection limit is a challenge for data analysis. With the robust ROS (regression on order statistics) method, summary statistics can be calculated by fitting an assumed distribution to the observed data. We used a preliminary sample of 109 weekly exposimeter measurements from the QUALIFEX study to compare summary statistics computed by robust ROS with a naïve approach, where values below the detection limit were replaced by the value of the detection limit. For the total RF‐EMF exposure, differences between the naïve approach and the robust ROS were moderate for the 90th percentile and the arithmetic mean. However, exposure contributions from minor RF‐EMF sources were considerably overestimated with the naïve approach. This results in an underestimation of the exposure range in the population, which may bias the evaluation of potential exposure‐response associations. We conclude from our analyses that summary statistics of exposimeter data calculated by robust ROS are more reliable and more informative than estimates based on a naïve approach. Nevertheless, estimates of source‐specific medians or even lower percentiles depend on the assumed data distribution and should be considered with caution. Bioelectromagnetics. Bioelectromagnetics 29:471–478, 2008. © 2008 Wiley‐Liss, Inc.     

DivStat: A User-Friendly Tool for Single Nucleotide Polymorphism Analysis of Genomic Diversity

Recent developments have led to an enormous increase of publicly available large genomic data, including complete genomes. The 1000 Genomes Project was a major contributor, releasing the results of sequencing a large number of individual genomes, and allowing for a myriad of large scale studies on human genetic variation. However, the tools currently available are insufficient when the goal concerns some analyses of data sets encompassing more than hundreds of base pairs and when considering haplotype sequences of single nucleotide polymorphisms (SNPs). Here, we present a new and potent tool to deal with large data sets allowing the computation of a variety of summary statistics of population genetic data, increasing the speed of data analysis.     

Exploring massive, genome scale datasets with the GenometriCorr package

We have created a statistically grounded tool for determining the correlation of genomewide data with other datasets or known biological features, intended to guide biological exploration of high-dimensional datasets, rather than providing immediate answers. The software enables several biologically motivated approaches to these data and here we describe the rationale and implementation for each approach. Our models and statistics are implemented in an R package that efficiently calculates the spatial correlation between two sets of genomic intervals (data and/or annotated features), for use as a metric of functional interaction. The software handles any type of pointwise or interval data and instead of running analyses with predefined metrics, it computes the significance and direction of several types of spatial association; this is intended to suggest potentially relevant relationships between the datasets. AVAILABILITY AND IMPLEMENTATION: The package, GenometriCorr, can be freely downloaded at http://genometricorr.sourceforge.net/. Installation guidelines and examples are available from the sourceforge repository. The package is pending submission to Bioconductor.     

msABC: a modification of Hudson's ms to facilitate multi-locus ABC analysis

With the availability of whole-genome sequence data biologists are able to test hypotheses regarding the demography of populations. Furthermore, the advancement of the Approximate Bayesian Computation (ABC) methodology allows the demographic inference to be performed in a simple framework using summary statistics. We present here msABC, a coalescent-based software that facilitates the simulation of multi-locus data, suitable for an ABC analysis. msABC is based on Hudson's ms algorithm, which is used extensively for simulating neutral demographic histories of populations. The flexibility of the original algorithm has been extended so that sample size may vary among loci, missing data can be incorporated in simulations and calculations, and a multitude of summary statistics for single or multiple populations is generated. The source code of msABC is available at http://bio.lmu.de/~pavlidis/msabc or upon request from the authors.     

Comparative phylogeographic summary statistics for testing simultaneous vicariance

Testing for simultaneous vicariance across comparative phylogeographic data sets is a notoriously difficult problem hindered by mutational variance, the coalescent variance, and variability across pairs of sister taxa in parameters that affect genetic divergence. We simulate vicariance to characterize the behaviour of several commonly used summary statistics across a range of divergence times, and to characterize this behaviour in comparative phylogeographic datasets having multiple taxon-pairs. We found Tajima's D to be relatively uncorrelated with other summary statistics across divergence times, and using simple hypothesis testing of simultaneous vicariance given variable population sizes, we counter-intuitively found that the variance across taxon pairs in Nei and Li's net nucleotide divergence (pi(net)), a common measure of population divergence, is often inferior to using the variance in Tajima's D across taxon pairs as a test statistic to distinguish ancient simultaneous vicariance from variable vicariance histories. The opposite and more intuitive pattern is found for testing more recent simultaneous vicariance, and overall we found that depending on the timing of vicariance, one of these two test statistics can achieve high statistical power for rejecting simultaneous vicariance, given a reasonable number of intron loci (> 5 loci, 400 bp) and a range of conditions. These results suggest that components of these two composite summary statistics should be used in future simulation-based methods which can simultaneously use a pool of summary statistics to test comparative the phylogeographic hypotheses we consider here.