Testing for linkage and Hardy-Weinberg disequilibrium

Turning Vice into Virtue: Using Batch-Effects to Detect Errors in Large Genomic Data Sets

It is often unavoidable to combine data from different sequencing centers or sequencing platforms when compiling data sets with a large number of individuals. However, the different data are likely to contain specific systematic errors that will appear as SNPs. Here, we devise a method to detect systematic errors in combined data sets. To measure quality differences between individual genomes, we study pairs of variants that reside on different chromosomes and co-occur in individuals. The abundance of these pairs of variants in different genomes is then used to detect systematic errors due to batch effects. Applying our method to the 1000 Genomes data set, we find that coding regions are enriched for errors, where ∼1% of the higher frequency variants are predicted to be erroneous, whereas errors outside of coding regions are much rarer (<0.001%). As expected, predicted errors are found less often than other variants in a data set that was generated with a different sequencing technology, indicating that many of the candidates are indeed errors. However, predicted 1000 Genomes errors are also found in other large data sets; our observation is thus not specific to the 1000 Genomes data set. Our results show that batch effects can be turned into a virtue by using the resulting variation in large scale data sets to detect systematic errors.

A Bivariate Hypothesis Testing Approach for Mapping the Trait-Influential Gene

The linkage disequilibrium (LD) based quantitative trait loci (QTL) model involves two indispensable hypothesis tests: the test of whether or not a QTL exists, and the test of the LD strength between the QTaL and the observed marker. The advantage of this two-test framework is to test whether there is an influential QTL around the observed marker instead of just having a QTL by random chance. There exist unsolved, open statistical questions about the inaccurate asymptotic distributions of the test statistics. We propose a bivariate null kernel (BNK) hypothesis testing method, which characterizes the joint distribution of the two test statistics in two-dimensional space. The power of this BNK approach is verified by three different simulation designs and one whole genome dataset. It solves a few challenging open statistical questions, closely separates the confounding between ‘linkage’ and ‘QTL effect’, makes a fine genome division, provides a comprehensive understanding of the entire genome, overcomes limitations of traditional QTL approaches, and connects traditional QTL mapping with the newest genotyping technologies. The proposed approach contributes to both the genetics literature and the statistics literature, and has a potential to be extended to broader fields where a bivariate test is needed.

Estimating Disequilibrium Coefficients

Gametic phase disequilibrium is the nonrandom association of alleles within gametes. Linkage disequilibrium (LD) describes the special case of deviation from independence between alleles at two linked genetic loci. Estimation of allelic LD requires knowledge of haplotypes. Genotype-based LD measures dispense with the haplotype estimation step and avoid bias in LD estimation. In this chapter, the most important measures for allelic and genotypic LD are introduced. The use of software packages for LD estimation is illustrated.

Exploiting Linkage Disequilibrium for Ultrahigh-Dimensional Genome-Wide Data with an Integrated Statistical Approach

Genome-wide data with millions of single-nucleotide polymorphisms (SNPs) can be highly correlated due to linkage disequilibrium (LD). The ultrahigh dimensionality of big data brings unprecedented challenges to statistical modeling such as noise accumulation, the curse of dimensionality, computational burden, spurious correlations, and a processing and storing bottleneck. The traditional statistical approaches lose their power due to [Formula: see text] (n is the number of observations and p is the number of SNPs) and the complex correlation structure among SNPs. In this article, we propose an integrated distance correlation ridge regression (DCRR) approach to accommodate the ultrahigh dimensionality, joint polygenic effects of multiple loci, and the complex LD structures. Initially, a distance correlation (DC) screening approach is used to extensively remove noise, after which LD structure is addressed using a ridge penalized multiple logistic regression (LRR) model. The false discovery rate, true positive discovery rate, and computational cost were simultaneously assessed through a large number of simulations. A binary trait of Arabidopsis thaliana, the hypersensitive response to the bacterial elicitor AvrRpm1, was analyzed in 84 inbred lines (28 susceptibilities and 56 resistances) with 216,130 SNPs. Compared to previous SNP discovery methods implemented on the same data set, the DCRR approach successfully detected the causative SNP while dramatically reducing spurious associations and computational time.

Testing for Hardy-Weinberg proportions: have we lost the plot?

Testing for Hardy-Weinberg proportions (HWP) is routine in almost all genetic studies of natural populations, but many researchers do not demonstrate a full understanding of the purposes of these tests or how to interpret the results. Common problems include a lack of understanding of statistical power and the difference between statistical significance and biological significance, how to interpret results of multiple tests, and how to distinguish between various factors that can cause statistically significant departures. In this perspective, which focuses on analysis of genetic data for nonmodel species, I 1) review factors that can cause departures from HWP at individual loci and linkage disequilibrium (LD) at pairs of loci; 2) discuss commonly used tests for HWP and LD, with an emphasis on multiple-testing issues; 3) show how to distinguish among possible causes of departures from HWP; and 4) outline some simple steps to follow when significant test results are found. Finally, I 5) identify some issues that merit particular attention as we move into an era in which analysis of genomics-scale datasets for nonmodel species is commonplace.