Guan Xing

Comparison of microsatellites, single-nucleotide polymorphisms (SNPs) and composite markers derived from SNPs in linkage analysis

There is growing evidence that a map of dense single-nucleotide polymorphisms (SNPs) can outperform a map of sparse microsatellites for linkage analysis. There is also argument as to whether a clustered SNP map can outperform an evenly spaced SNP map. Using Genetic Analysis Workshop 14 simulated data, we compared for linkage analysis microsatellites, SNPs, and composite markers derived from SNPs. We encoded the composite markers in a two-step approach, in which the maximum identity length contrast method was employed to allow for recombination between loci. A SNP map 2.3 times as dense as a microsatellite map (~2.9 cM compared to ~6.7 cM apart) provided slightly less information content (~0.83 compared to ~0.89). Most inheritance information could be extracted when the SNPs were spaced < 1 cM apart. Comparing the linkage results on using SNPs or composite markers derived from them based on both 3 cM and 0.3 cM resolution maps, we showed that the inter-SNP distance should be kept small (< 1 cM), and that for multipoint linkage analysis the original markers and the derived composite markers had similar power; but for single point linkage analysis the resulting composite markers lead to more power. Considering all factors, such as information content, flexibility of analysis method, map errors, and genotyping errors, a map of clustered SNPs can be an efficient design for a genome-wide linkage scan.

Blindly Using Wald's Test Can Miss Rare Disease-Causal Variants in Case-Control Association Studies

There are four tests – the likelihood ratio (LR) test, Walds test, the score test and the exact test – commonly employed in genetic association studies. On comparison of the four tests, we found that Walds test, popular in genome‐wide screens due to its low computational demands, exhibited a paradoxical behaviour in that the test statistic decreased as the effect size of the variant increased, resulting in a loss of power. The LR test always achieved the most significant P‐values, followed by the exact test. We further examined the results in a real data set composed of high‐ and low‐cholesterol subjects from the Dallas Heart Study (DHS). We also compared the single‐variant LR test with two multi‐variant analysis approaches – the burden test and the C‐alpha test – in analysing the sequencing data by simulation. Our results call for caution in using Walds test in genome‐wide case‐control association studies and suggest that the LR test is a better alternative in spite of its computational demands.

Adjusting for covariates in logistic regression models

To the Editor We read with interest the paper by Kuo and Feingold (henceforth K&F) ‘‘What’s the best statistic for a simple test of genetic association in a case-control study’’ [Kuo and Feingold, 2010], in which the authors compared the power of three logistic regression models to detect genetic effects, concluded that ‘‘the most commonly used approach to handle covariates—modeling covariate main effects but not interaction—is almost never a good idea,’’ and recommended modeling only the genetic factors without covariate adjustment in genome-scanning. We feel that the issue of covariate adjustment in logistic regression models was oversimplified and the conclusion was unjustified. In this letter, we attempt to explain the observations found by K&F using established results in the statistical literature, to confirm the theoretical results in the genetic association study scenario by mimicking and extending the simulation study performed by K&F, and to discuss their implication on covariate adjustment in genome-scanning. The impact of covariate adjustment on the precision of regression coefficient estimators in classic linear models depends on multiple correlations between variables; however, adjusting for covariates in logistic regression models always leads to a loss of precision. Denote by Y a quantitative trait, by G a genotype, and by E a covariate, e.g. an environmental factor. Suppose we fit to data two linear regression models E(Y|G) 5 a1b1G and EðYjG;EÞ 1⁄4 a01b1G1b 0 2E. The asymptotic relative precision (ARP) of the estimator b̂1 to b̂1 can be derived as

Power of selective genotyping in genome-wide association studies of quantitative traits

The selective genotyping approach in quantitative genetics means genotyping only individuals with extreme phenotypes. This approach is considered an efficient way to perform gene mapping, and can be applied in both linkage and association studies. Selective genotyping in association mapping of quantitative trait loci was proposed to increase the power of detecting rare alleles of large effect. However, using this approach, only common variants have been detected. Studies on selective genotyping have been limited to single-locus scenarios. In this study we aim to investigate the power of selective genotyping in a genome-wide association study scenario, and we specifically study the impact of minor allele frequency of variants on the power of this approach. We use the Genetic Analysis Workshop 16 rheumatoid arthritis whole-genome data from the North American Rheumatoid Arthritis Consortium. Two quantitative traits, anti-cyclic citrullinated peptide and rheumatoid factor immunoglobulin M, and one binary trait, rheumatoid arthritis affection status, are used in the analysis. The power of selective genotyping is explored as a function of three parameters: sampling proportion, minor allele frequency of single-nucleotide polymorphism, and test level. The results show that the selective genotyping approach is more efficient in detecting common variants than detecting rare variants, and it is efficient only when the level of declaring significance is not stringent. In summary, the selective genotyping approach is most suitable for detecting common variants in candidate gene-based studies.

A comparison of approaches to control for confounding factors by regression models.

A common technique to control for confounding factors in practice is by regression adjustment. There are various versions of regression modeling in the literature, and in this paper we considered four approaches often seen in genetic association studies. We carried out both analytical and simulation studies comparing the bias of effect size estimates and examining the test sizes under the null hypothesis of no association between an outcome and an exposure. Further, we compared the methods in a nonsynonymous genome-wide scan for plasma lipoprotein(a) levels using a dataset from the Dallas Heart Study. We found that a widely employed approach that models the covariate-adjusted outcome and the exposure leads to an infranominal test size and underestimation of the exposure effect size. In conclusion, we recommend either using multiple regression models or modeling the covariate-adjusted outcome and the covariate-adjusted exposure to control for confounding factors.

Distribution of model-based multipoint heterogeneity lod scores.

The distribution of two‐point heterogeneity lod scores (HLOD) has been intensively investigated because the conventional χ2 approximation to the likelihood ratio test is not directly applicable. However, there was no study investigating th e distribution of the multipoint HLOD despite its wide application. Here we want to point out that, compared with the two‐point HLOD, the multipoint HLOD essentially tests for homogeneity given linkage and follows a relatively simple limiting distribution , which can be obtained by established statistical theory. We further examine the theoretical result by simulation studies. Genet. Epidemiol. 34: 912‐916, 2010.© 2010 Wiley‐Liss, Inc.

Enhancing the Power to Detect Low-Frequency Variants in Genome-Wide Screens

In genetic association studies a conventional test statistic is proportional to the correlation coefficient between the trait and the variant, with the result that it lacks power to detect association for low-frequency variants. Considering the link between the conventional association test statistics and the linkage disequilibrium measure r2, we propose a test statistic analogous to the standardized linkage disequilibrium D′ to increase the power of detecting association for low-frequency variants. By both simulation and real data analysis we show that the proposed D′ test is more powerful than the conventional methods for detecting association for low-frequency variants in a genome-wide setting. The optimal coding strategy for the D′ test and its asymptotic properties are also investigated. In summary, we advocate using the D′ test in a dominant model as a complementary approach to enhancing the power of detecting association for low-frequency variants with moderate to large effect sizes in case-control genome-wide association studies.

A logistic mixture model for a family-based association study

A family-based association study design is not only able to localize causative genes more precisely than linkage analysis, but it also helps explain the genetic mechanism underlying the trait under study. Therefore, it can be used to follow up an initial linkage scan. For an association study of binary traits in general pedigrees, we propose a logistic mixture model that regresses the trait value on the genotypic values of markers under investigation and other covariates such as environmental factors. We first tested both the validity and power of the new model by simulating nuclear families inheriting a simple Mendelian trait. It is powerful when the correct disease model is specified and shows much loss of power when the dominance of a model is inversely specified, i.e., a dominant model is wrongly specified as recessive or vice versa. We then applied the new model to the Genetic Analysis Workshop (GAW) 15 simulation data to test the performance of the model when adjusting for covariates in the case of complex traits. Adjusting for the covariate that interacts with disease loci improves the power to detect association. The simplest version of the model only takes monogenic inheritance into account, but analysis of the GAW simulation data shows that even this simple model can be powerful for complex traits.

Differentiating the Cochran-Armitage Trend Test and Pearson's χ2 Test: Location and Dispersion

In genetic case‐control association studies, a standard practice is to perform the Cochran‐Armitage (CA) trend test with 1 degree‐of‐freedom (d.f.) under the assumption of an additive model. However, when the true genetic model is recessive or near recessive, it is outperformed by Pearsons χ2 test with 2 d.f. In this article, we analytically reveal the statistical basis that leads to the phenomenon. First, we show that the CA trend test examines the location shift between the case and control groups, whereas Pearsons χ2 test examines both the location and dispersion shifts between the two groups. Second, we show that under the additive model, the effect of location deviation outweighs that of the dispersion deviation and vice versa under a near recessive model. Therefore, Pearsons χ2 test is a more robust test than the CA trend test, and it outperforms the latter when the mode of inheritance evolves to the recessive end.

A comparison of the likelihood ratio test and the variance-stabilising transformation-based tests for detecting association of rare variants.

In a recent paper in this journal, the use of variance‐stabilising transformation techniques was proposed to overcome the problem of inadequacy in normality approximation when testing association for a low‐frequency variant in a case‐control study. It was shown that tests based on the variance‐stabilising transformations are more powerful than Fishers exact test while controlling for type I error rate. Earlier in the journal, another study had shown that the likelihood ratio test (LRT) is superior to Fishers exact test, Walds test, and Pearsons χ2 test in testing association for low‐frequency variants. Thus, it is of interest to make a direct comparison between the LRT and the tests based on the variance‐stabilising transformations. In this commentary, we show that the LRT and the variance‐stabilising transformation‐based tests have comparable power greater than Fishers exact test, Walds test, and Pearsons χ2 test.