Assessing the likelihood of having false positives caused by population stratification

Population stratification is always a concern in association analysis. There is a debate on the extent of the problem in less extreme situations (Thomas and Witte [1], Wacholder et al. [2]). Wacholder et al.[3] and Ardlie et al. [4] showed that hidden population structure is not a serious threat to case-control designs. We propose a method of assessing the seriousness of the population stratification before designing association studies. If population stratification is not a serious problem, one may consider using case-control study instead of family-based design to get more power. In a case-control design, we compare chi-square statistics from a structured population (a union of two subpopulations) and a homogeneous population with the same prevalence and allele frequencies. We provide an explicit formula to calculate the chi-square statistics from 17 parameters, such as proportions of subpopulation, allele frequencies in subpopulations, etc. We choose these factors because they have potential to cause false associations. Each parameter takes a random value in a chosen range. We then calculate the likelihood of getting opposite conclusions in the structured and the homogeneous populations. This is the likelihood of having false positives caused by population stratification. The advantage of this method is to provide a cost effective way to choose between using case-control data and using family data before actually collecting those data. We conclude that sample sizes have a significant effect on the likelihood of false positive caused by population stratification. The larger the sample size is, the more likely to have false positive if the population structure is ignored. If the sample size will be smaller than 200 by budget constraints, then case-control study may be a better choice because of its power

Weighted selective collapsing strategy for detecting rare and common variants in genetic association study

<p>Abstract</p> <p>Background</p> <p>Genome-wide association studies (GWAS) have been used successfully in detecting associations between common genetic variants and complex diseases. However, common SNPs detected by current GWAS only explain a small proportion of heritable variability. With the development of next-generation sequencing technologies, researchers find more and more evidence to support the role played by rare variants in heritable variability. However, rare and common variants are often studied separately. The objective of this paper is to develop a robust strategy to analyze association between complex traits and genetic regions using both common and rare variants.</p> <p>Results</p> <p>We propose a weighted selective collapsing strategy for both candidate gene studies and genome-wide association scans. The strategy considers genetic information from both common and rare variants, selectively collapses all variants in a given region by a forward selection procedure, and uses an adaptive weight to favor more likely causal rare variants. Under this strategy, two tests are proposed. One test denoted by <it>B_wSC</it>is sensitive to the directions of genetic effects, and it separates the deleterious and protective effects into two components. Another denoted by <it>B_wSCd</it>is robust in the directions of genetic effects, and it considers the difference of the two components. In our simulation studies, <it>B_wSC</it>achieves a higher power when the casual variants have the same genetic effect, while <it>B_wSCd</it>is as powerful as several existing tests when a mixed genetic effect exists. Both of the proposed tests work well with and without the existence of genetic effects from common variants.</p> <p>Conclusions</p> <p>Two tests using a weighted selective collapsing strategy provide potentially powerful methods for association studies of sequencing data. The tests have a higher power when both common and rare variants contribute to the heritable variability and the effect of common variants is not strong enough to be detected by traditional methods. Our simulation studies have demonstrated a substantially higher power for both tests in all scenarios regardless whether the common SNPs are associated with the trait or not.</p

Applications of density matrix in the fractional quantum mechanics

The many-body space fractional quantum system is studied using the density matrix method. We give the new results of the Thomas-Fermi model, and obtain the quantum pressure of the free electron gas. We also show the validity of the Hohenberg-Kohn theory in the space fractional quantum mechanics and generalize the density functional theory to the fractional quantum mechanics.Comment: 1 figur