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

Comment on "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-STS244A the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Discovering influential variables: A method of partitions

A trend in all scientific disciplines, based on advances in technology, is the increasing availability of high dimensional data in which are buried important information. A current urgent challenge to statisticians is to develop effective methods of finding the useful information from the vast amounts of messy and noisy data available, most of which are noninformative. This paper presents a general computer intensive approach, based on a method pioneered by Lo and Zheng for detecting which, of many potential explanatory variables, have an influence on a dependent variable $Y$. This approach is suited to detect influential variables, where causal effects depend on the confluence of values of several variables. It has the advantage of avoiding a difficult direct analysis, involving possibly thousands of variables, by dealing with many randomly selected small subsets from which smaller subsets are selected, guided by a measure of influence $I$. The main objective is to discover the influential variables, rather than to measure their effects. Once they are detected, the problem of dealing with a much smaller group of influential variables should be vulnerable to appropriate analysis. In a sense, we are confining our attention to locating a few needles in a haystack.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS265 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

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

The authors suggest an interesting way to measure the fraction of missing information in the context of hypothesis testing. The measure seeks to quantify the impact of missing observations on the test between two hypotheses. The amount of impact can be useful information for applied research. An example is, in genetics, where multiple tests of the same sort are performed on different variables with different missing rates, and follow-up studies may be designed to resolve missing values in selected variables. In this discussion, we offer our prospective views on the use of relative information in a follow-up study. For studies where the impact of missing observations varies greatly across different variables and where the investigators have the flexibility of designing studies that can have different efforts on variables, an optimal design may be derived using relative information measures to improve the cost-effectiveness of the followup

A Robust Model-free Approach for Rare Variants Association Studies Incorporating Gene-Gene and Gene-Environmental Interactions

Recently more and more evidence suggest that rare variants with much lower minor allele frequencies play significant roles in disease etiology. Advances in next-generation sequencing technologies will lead to many more rare variants association studies. Several statistical methods have been proposed to assess the effect of rare variants by aggregating information from multiple loci across a genetic region and testing the association between the phenotype and aggregated genotype. One limitation of existing methods is that they only look into the marginal effects of rare variants but do not systematically take into account effects due to interactions among rare variants and between rare variants and environmental factors. In this article, we propose the summation of partition approach (SPA), a robust model-free method that is designed specifically for detecting both marginal effects and effects due to gene-gene (G×G) and gene-environmental (G×E) interactions for rare variants association studies. SPA has three advantages. First, it accounts for the interaction information and gains considerable power in the presence of unknown and complicated G×G or G×E interactions. Secondly, it does not sacrifice the marginal detection power; in the situation when rare variants only have marginal effects it is comparable with the most competitive method in current literature. Thirdly, it is easy to extend and can incorporate more complex interactions; other practitioners and scientists can tailor the procedure to fit their own study friendly. Our simulation studies show that SPA is considerably more powerful than many existing methods in the presence of G×G and G×E interactions

Coping with family structure in genome-wide association studies: a comparative evaluation

In this paper, a fully statistical investigation of the control of family structure as random effects is analyzed and discussed, using both the genome-wide association studies (GWAS) data and simulated data. Three modeling strategies are proposed and the analysis results suggest the hybrid use of results from all possible models should be combined in practice

Discovering interactions among BRCA1 and other candidate genes associated with sporadic breast cancer

Analysis of a subset of case-control sporadic breast cancer data, [from the National Cancer Institute's Cancer Genetic Markers of Susceptibility (CGEMS) initiative], focusing on 18 breast cancer-related genes with 304 SNPs, indicates that there are many interesting interactions that form two- and three-way networks in which BRCA1 plays a dominant and central role. The apparent interactions of BRCA1 with many other genes suggests the conjecture that BRCA1 serves as a protective gene and that some mutations in it or in related genes may prevent it from carrying out this protective function even if the patients are not carriers of known cancer-predisposing BRCA1 mutations. The method of analysis features the evaluation of the effect of a gene by averaging the effects of the SNPs covered by that gene. Marginal methods that test one gene at a time fail to show any effect. That may be related to the fact that each of these 18 genes adds very little to the risk of cancer. Analysis that relates the ratio of interactions to the maximum of the first-order effects discovers significant gene pairs and triplets. Breast cancer (MIM 114480) has complex causes. Known predisposition genes explain <15% of the breast cancer cases. It is generally believed that most sporadic breast cancers are triggered by unknown combined effects, possibly because of a large number of genes and other risk factors, each adding a small risk toward cancer etiology. Progress in seeking breast cancer genes other than BRCA1 and BRCA2 has been slow and limited because the individual risk due to each gene is small. This difficulty may be partly due to the fact that current methods rely largely on marginal information from genes studied one at a time and ignore potentially valuable information because of the interaction among multiple loci. Because each responsible gene may have a small marginal effect in causing disease, it is likely that such methods will fail to capture many responsible genes by studying a dataset where the disease may be due to a variety of different sources. The possible presence of many genes responsible for different subgroups of cancer patients may reduce the power of current methods to detect genes partly responsible for some forms of breast cancer. It is believed that methods effective in extracting interactive information from data should be developed. What should be done when marginal effects are too weak to be detected? Our methods use interactive information from multiple sites as well as marginal information, They provide power to detect interactive genes. To test this claim and to demonstrate the practical value of these methods in real applications, we apply them to an important study: a subset of a large dataset collected from a case-control sporadic breast cancer study, focusing on gene–gene-based analysis. This partial dataset comprises 18 genes with 304 SNP markers. The application results in a number of scientific findings. The message of this article is fourfold. First, if marginal methods fail, more powerful methods that take into account interactive information can be used effectively. We apply our proposed methods to this dataset to illustrate the detection of the interactions between genes. We point out that in our findings, none of the 18 selected genes show any detectable marginal effects that are significantly higher than those generated by random fluctuations. In other words, all of the 18 genes would be missed if only marginal methods were used. Second, we demonstrate how to carry out a gene-based analysis by treating each gene as a basic unit while incorporating relevant information from all SNPs within that gene. Two summary test scores are proposed to quantify the strength of interactions for each pair of genes. The pairwise interactions can be extended easily. We also provide results using third-order interactions. Third, to establish statistical significance, we generate a large number of permutations of the dependent variable (case or control) to see how the measures of interaction for the real data compare with those from the many permutations. Finally, when these procedures are applied to the data, they lead to a number of interesting findings. It is shown that there are a substantial number of significant interactions that form a network in which BRCA1 plays a dominant role. The interactions of BRCA1 with many of the other genes suggests the conjecture that BRCA1 serves as a protective gene and that some mutations in it or in related genes may prevent it from carrying out the protective function

Constructing gene association networks for rheumatoid arthritis using the backward genotype-trait association (BGTA) algorithm

Rheumatoid arthritis (RA, MIM 180300) is a common and complex inflammatory disorder. The North American Rheumatoid Arthritis Consortium (NARAC) data, as part of the Genetic Analysis Workshop 15 data, consists of both genome scan and candidate gene studies on RA patients. We applied the backward genotype-trait association (BGTA) algorithm to capture marginal and gene × gene interaction effects of multiple susceptibility loci on RA disease status. A two-stage screening approach was used for the genome scan, whereas a comprehensive study of all possible subsets was conducted for the candidate genes. For the genome scan, we constructed an association network among 39 genetic loci that demonstrated strong signals, 19 of which have been reported in the RA literature. For the candidate genes, we found strong signals for PTPN22 and SUMO4. Based on significant association evidence, we built an association network among the loci of PTPN22, PADI4, DLG5, SLC22A4, SUMO4, and CARD15. To control for false positives, we used permutation tests to constrain the family-wise type I error rate to 1%. Using the BGTA algorithm, we identified genetic loci and candidate genes that were associated with RA susceptibility and association networks among them. For the first time, we report possible interactions between single-nucleotide polymorphisms/genes, which may be useful for biological interpretation

New insights into old methods for identifying causal rare variants

The advance of high-throughput next-generation sequencing technology makes possible the analysis of rare variants. However, the investigation of rare variants in unrelated-individuals data sets faces the challenge of low power, and most methods circumvent the difficulty by using various collapsing procedures based on genes, pathways, or gene clusters. We suggest a new way to identify causal rare variants using the F-statistic and sliced inverse regression. The procedure is tested on the data set provided by the Genetic Analysis Workshop 17 (GAW17). After preliminary data reduction, we ranked markers according to their F-statistic values. Top-ranked markers were then subjected to sliced inverse regression, and those with higher absolute coefficients in the most significant sliced inverse regression direction were selected. The procedure yields good false discovery rates for the GAW17 data and thus is a promising method for future study on rare variants

Joint study of genetic regulators for expression traits related to breast cancer

The mRNA expression levels of genes have been shown to have discriminating power for the classification of breast cancer. Studying the heritability of gene expression levels on breast cancer related transcripts can lead to the identification of shared common regulators and inter-regulation patterns, which would be important for dissecting the etiology of breast cancer. We applied multilocus association genome-wide scans to 18 breast cancer related transcripts and combined the results with traditional linkage scans. Regulatory hotspots for these transcripts were identified and some inter-regulation patterns were observed. We also derived evidence on interacting genetic regulatory loci shared by a number of these transcripts. In this paper, by restricting to a set of related genes, we were able to employ a more detailed multilocus approach that evaluates both marginal and interaction association signals at each single-nucleotide polymorphism. Interesting inter-regulation patterns and significant overlaps of genetic regulators between transcripts were observed. Interaction association results returned more expression quantitative trait locus hotspots that are significant

Identifying influential regions in extremely rare variants using a fixed-bin approach

In this study, we analyze the Genetic Analysis Workshop 17 data to identify regions of single-nucleotide polymorphisms (SNPs) that exhibit a significant influence on response rate (proportion of subjects with an affirmative affected status), called the affected ratio, among rare variants. Under the null hypothesis, the distribution of rare variants is assumed to be uniform over case (affected) and control (unaffected) subjects. We attempt to pinpoint regions where the composition is significantly different between case and control events, specifically where there are unusually high numbers of rare variants among affected subjects. We focus on private variants, which require a degree of “collapsing” to combine information over several SNPs, to obtain meaningful results. Instead of implementing a gene-based approach, where regions would vary in size and sometimes be too small to achieve a strong enough signal, we implement a fixed-bin approach, with a preset number of SNPs per region, relying on the assumption that proximity and similarity go hand in hand. Through application of 100-SNP and 30-SNP fixed bins, we identify several most influential regions, which later are seen to contain some of the causal SNPs. The 100- and 30-SNP approaches detected seven and three causal SNPs among the most significant regions, respectively, with two overlapping SNPs located in the ELAVL4 gene, reported by both procedures