Rejoinder: Quantifying the Fraction of Missing Information for Hypothesis Testing in Statistical and Genetic Studies

Rejoinder to "Quantifying the Fraction of Missing Information for Hypothesis Testing in Statistical and Genetic Studies" [arXiv:1102.2774]Comment: Published in at http://dx.doi.org/10.1214/08-STS244REJ the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Quantifying the Fraction of Missing Information for Hypothesis Testing in Statistical and Genetic Studies

Many practical studies rely on hypothesis testing procedures applied to data sets with missing information. An important part of the analysis is to determine the impact of the missing data on the performance of the test, and this can be done by properly quantifying the relative (to complete data) amount of available information. The problem is directly motivated by applications to studies, such as linkage analyses and haplotype-based association projects, designed to identify genetic contributions to complex diseases. In the genetic studies the relative information measures are needed for the experimental design, technology comparison, interpretation of the data, and for understanding the behavior of some of the inference tools. The central difficulties in constructing such information measures arise from the multiple, and sometimes conflicting, aims in practice. For large samples, we show that a satisfactory, likelihood-based general solution exists by using appropriate forms of the relative Kullback--Leibler information, and that the proposed measures are computationally inexpensive given the maximized likelihoods with the observed data. Two measures are introduced, under the null and alternative hypothesis respectively. We exemplify the measures on data coming from mapping studies on the inflammatory bowel disease and diabetes. For small-sample problems, which appear rather frequently in practice and sometimes in disguised forms (e.g., measuring individual contributions to a large study), the robust Bayesian approach holds great promise, though the choice of a general-purpose "default prior" is a very challenging problem.Comment: Published in at http://dx.doi.org/10.1214/07-STS244 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Study of CNVs As Trait-Associated Polymorphisms and As Expression Quantitative Trait Loci

We conducted a comprehensive study of copy number variants (CNVs) well-tagged by SNPs (r2≥0.8) by analyzing their effect on gene expression and their association with disease susceptibility and other complex human traits. We tested whether these CNVs were more likely to be functional than frequency-matched SNPs as trait-associated loci or as expression quantitative trait loci (eQTLs) influencing phenotype by altering gene regulation. Our study found that CNV–tagging SNPs are significantly enriched for cis eQTLs; furthermore, we observed that trait associations from the NHGRI catalog show an overrepresentation of SNPs tagging CNVs relative to frequency-matched SNPs. We found that these SNPs tagging CNVs are more likely to affect multiple expression traits than frequency-matched variants. Given these findings on the functional relevance of CNVs, we created an online resource of expression-associated CNVs (eCNVs) using the most comprehensive population-based map of CNVs to inform future studies of complex traits. Although previous studies of common CNVs that can be typed on existing platforms and/or interrogated by SNPs in genome-wide association studies concluded that such CNVs appear unlikely to have a major role in the genetic basis of several complex diseases examined, our findings indicate that it would be premature to dismiss the possibility that even common CNVs may contribute to complex phenotypes and at least some common diseases.</p

A Study of CNVs As Trait-Associated Polymorphisms and As Expression Quantitative Trait Loci

We conducted a comprehensive study of copy number variants (CNVs) well-tagged by SNPs (r2≥0.8) by analyzing their effect on gene expression and their association with disease susceptibility and other complex human traits. We tested whether these CNVs were more likely to be functional than frequency-matched SNPs as trait-associated loci or as expression quantitative trait loci (eQTLs) influencing phenotype by altering gene regulation. Our study found that CNV–tagging SNPs are significantly enriched for cis eQTLs; furthermore, we observed that trait associations from the NHGRI catalog show an overrepresentation of SNPs tagging CNVs relative to frequency-matched SNPs. We found that these SNPs tagging CNVs are more likely to affect multiple expression traits than frequency-matched variants. Given these findings on the functional relevance of CNVs, we created an online resource of expression-associated CNVs (eCNVs) using the most comprehensive population-based map of CNVs to inform future studies of complex traits. Although previous studies of common CNVs that can be typed on existing platforms and/or interrogated by SNPs in genome-wide association studies concluded that such CNVs appear unlikely to have a major role in the genetic basis of several complex diseases examined, our findings indicate that it would be premature to dismiss the possibility that even common CNVs may contribute to complex phenotypes and at least some common diseases

An Evolutionary Framework for Association Testing in Resequencing Studies

Sequencing technologies are becoming cheap enough to apply to large numbers of study participants and promise to provide new insights into human phenotypes by bringing to light rare and previously unknown genetic variants. We develop a new framework for the analysis of sequence data that incorporates all of the major features of previously proposed approaches, including those focused on allele counts and allele burden, but is both more general and more powerful. We harness population genetic theory to provide prior information on effect sizes and to create a pooling strategy for information from rare variants. Our method, EMMPAT (Evolutionary Mixed Model for Pooled Association Testing), generates a single test per gene (substantially reducing multiple testing concerns), facilitates graphical summaries, and improves the interpretation of results by allowing calculation of attributable variance. Simulations show that, relative to previously used approaches, our method increases the power to detect genes that affect phenotype when natural selection has kept alleles with large effect sizes rare. We demonstrate our approach on a population-based re-sequencing study of association between serum triglycerides and variation in ANGPTL4.</p