A method to detect single-nucleotide polymorphisms accounting for a linkage signal using covariate-based affected relative pair linkage analysis
© Song et al; licensee BioMed Central Ltd. 2011
Published: 29 November 2011
We evaluate an approach to detect single-nucleotide polymorphisms (SNPs) that account for a linkage signal with covariate-based affected relative pair linkage analysis in a conditional-logistic model framework using all 200 replicates of the Genetic Analysis Workshop 17 family data set. We begin by combining the multiple known covariate values into a single variable, a propensity score. We also use each SNP as a covariate, using an additive coding based on the number of minor alleles. We evaluate the distribution of the difference between LOD scores with the propensity score covariate only and LOD scores with the propensity score covariate and a SNP covariate. The inclusion of causal SNPs in causal genes increases LOD scores more than the inclusion of noncausal SNPs either within causal genes or outside causal genes. We compare the results from this method to results from a family-based association analysis and conclude that it is possible to identify SNPs that account for the linkage signals from genes using a SNP-covariate-based affected relative pair linkage approach.
Owing to the complexity of the genetic models underlying complex traits, model-free linkage methods, which do not require the specification of a disease model, are a popular choice. With these methods, inclusion of covariates increases the power to detect linkage , provided that the covariates reflect underlying locus heterogeneity. The method allows the genetic relative risk to depend on the covariate so that, in effect, the allele sharing at the marker locus differs for different values of the covariate. A general conditional-logistic model developed by Olson  provides a unified framework to incorporate covariates, and this model is implemented in LODPAL (SAGE, version 6.1.0) . A modified one-parameter model has been proposed , so that only one additional parameter per covariate is required.
To identify single-nucleotide polymorphisms (SNPs) that may explain the observed linkage signals, several researchers have developed methods for an affected pair analysis [5–10] and for quantitative trait linkage analysis . Among these studies, Houwing-Duistermaat et al.  proposed using Olson’s conditional-logistic model with a genotype-based covariate to explain the linkage signals. They applied the method to three SNPs and five markers in the Genetic Analysis Workshop 14 data, and they confirmed a SNP that explained a linkage peak. However, the statistical properties of this method still need to be studied. The large numbers of SNPs from exome sequencing data, along with the identical-by-descent (IBD) allele sharing from fully informative markers in the Genetic Analysis Workshop 17 (GAW17) data set , provide a good opportunity to evaluate this approach; hence our purpose here is to evaluate this new method in depth.
We analyzed all 200 replicates of the GAW17 family data set. The binary affected status was analyzed as the main trait of interest, and the affected relative pairs from all eight extended pedigrees were used.
Based on the knowledge of the underlying simulating model, we included Age, Sex, and Smoking status as covariates in all analyses. Using the method of Doan et al. , we combined these three covariates into a single variable, a propensity score (PS), as a means of allowing for multiple covariates with the addition of only 1 degree of freedom (df). In each replicate, the PS values were estimated by taking the predicted probability of being affected, given the set of covariates, after fitting a logistic regression of affection status on the given covariates with all 698 individuals using R, version 2.10.1 .
We used the IBD sharing values for the 3,205 genes from 22 autosomal chromosomes. After removing the SNPs with no variability in the data set or with no LOD score result from LODPAL, the average number of SNPs remaining for the analysis in each replicate was 9,069 out of 24,487 total SNPs. Among these 9,069 SNPs, 8,912 were in noncausal genes, 126 were noncausal SNPs in causal genes, and 31 were causal SNPs in causal genes. Each gene contained 1 to 231 SNPs. Using an additive coding based on the number of minor alleles, we recoded each SNP as 0, 1, or 2.
where the δ ij are the parameters associated with the covariate x j , with β0 and δ0 = 0. We use a one-parameter model so that only one additional parameter is estimated for each included covariate. The asymptotic distribution of the LR statistics (i.e., 4.605 × LOD score) for the one-parameter model is a 50:50 mixture of a chi-square distribution with K df and a chi-square distribution with K + 1 df when there are K covariates in the model and the relative pairs are independent.
We evaluate the LOD score increases from the first model to the second model (LodDiff) to detect SNPs that differentially account for the linkage signals.
In each replicate, the LodDiff values are calculated for all available SNPs. Then, the mean LodDiff values are calculated for three different groups of SNPs: SNPs in noncausal genes, noncausal SNPs in causal genes, and causal SNPs in causal genes. The distributions of these mean LodDiff values over 200 replicates are compared. Again in each replicate, all SNPs are sorted and divided into 10 equal partitions (deciles) according to their LodDiff values, and the proportion of true causal SNPs within each partition is checked. We report the mean proportion values over 200 replicates.
To conduct family-based association analysis using the residuals obtained from the logistic regression model with Age, Sex, and Smoking as covariates, we use the ASSOC program in SAGE (version 6.1.0). ASSOC performs a likelihood-based regression unconditional on parental genotype. The analysis model includes a SNP as a fixed effect and a polygenic component as a random effect. To account for the nonnormal distribution of the residuals, we apply the George-Elston transformation. The –log(p-value) is summarized in the same way as the LodDiff value was from 200 replicates.
Results and discussion
Causal SNPs within the top 5% of SNPs
Minor allele frequency
In addition, we checked the correlations between LodDiff and other properties of SNPs. The correlation between the LodDiff values and the number of additional SNPs in the gene being considered was 0.05. The correlation with the minor allele frequency of the SNP included was 0.07 and 0.19 with the effect size. Our analysis did not consider the linkage disequilibrium structure. Linkage disequilibrium between SNPs within a gene and SNPs in different genes might affect the effectiveness of LodDiff. Further work is needed to investigate this matter.
We investigated the possibility of identifying SNPs that account for the linkage signals coming from genes using a covariate-based affected relative pair linkage approach. Further research is needed to study the statistical properties and the empirical null distribution to evaluate the significance of any result.
The Genetic Analysis Workshop is supported by National Institutes of Health grant R01 GM031575. Some of the results in this paper were obtained by using the program package SAGE, which is supported by a U.S. Public Health Service Resource Grant (RR03655) from the National Center for Research Resources.
This article has been published as part of BMC Proceedings Volume 5 Supplement 9, 2011: Genetic Analysis Workshop 17. The full contents of the supplement are available online at http://www.biomedcentral.com/1753-6561/5?issue=S9.
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