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 Monte Carlo test of linkage disequilibrium for single nucleotide polymorphisms

<p>Abstract</p> <p>Background</p> <p>Genetic association studies, especially genome-wide studies, make use of linkage disequilibrium(LD) information between single nucleotide polymorphisms (SNPs). LD is also used for studying genome structure and has been valuable for evolutionary studies. The strength of LD is commonly measured by <it>r</it>², a statistic closely related to the Pearson's <it>χ</it>²statistic. However, the computation and testing of linkage disequilibrium using <it>r</it>²requires known haplotype counts of the SNP pair, which can be a problem for most population-based studies where the haplotype phase is unknown. Most statistical genetic packages use likelihood-based methods to infer haplotypes. However, the variability of haplotype estimation needs to be accounted for in the test for linkage disequilibrium.</p> <p>Findings</p> <p>We develop a Monte Carlo based test for LD based on the null distribution of the <it>r</it>²statistic. Our test is based on <it>r</it>²and can be reported together with <it>r</it>². Simulation studies show that it offers slightly better power than existing methods.</p> <p>Conclusions</p> <p>Our approach provides an alternative test for LD and has been implemented as a R program for ease of use. It also provides a general framework to account for other haplotype inference methods in LD testing.</p