The PPLD has advantages over conventional regression methods in application to moderately sized genome-wide association studies

In earlier work, we have developed and evaluated an alternative approach to the analysis of GWAS data, based on a statistic called the PPLD. More recently, motivated by a GWAS for genetic modifiers of the X-linked Mendelian disorder Duchenne Muscular Dystrophy (DMD), we adapted the PPLD for application to time-to-event (TE) phenotypes. Because DMD itself is relatively rare, this is a setting in which the very large sample sizes generally assembled for GWAS are simply not attainable. For this reason, statistical methods specially adapted for use in small data sets are required. Here we explore the behavior of the TE-PPLD via simulations, comparing the TE-PPLD with Cox Proportional Hazards analysis in the context of small to moderate sample sizes. Our results will help to inform our approach to the DMD study going forward, and they illustrate several respects in which the TE-PPLD, and by extension the original PPLD, offer advantages over regression-based approaches to GWAS in this context.

Exploiting gene x gene interaction in linkage analysis

When two genes interact to cause a clinically important phenotype, it would seem reasonable to expect that we could leverage genotypic information at one of the loci in order to improve our ability to detect the other. We were therefore interested in extending the posterior probability of linkage (PPL), a class of linkage statistics we have been developing over the past decade, in order to explicitly allow for gene × gene interaction. In this report we utilize a new implementation of the PPL incorporating liability classes (LCs), which provide a direct parameterization of gene × gene interaction by allowing the penetrances at the locus being evaluated to depend upon measured genotypes at a known locus. With knowledge of the generating model for the simulated rheumatoid arthritis (RA) data, we selected two loci for examination: Locus A, which in interaction with the HLA-DR antigen locus affects risk of the dichotomous RA phenotype; and Locus E, which in interaction with DR affects quantitative levels of the anti-CCP phenotype. The data comprised nuclear families of two parents and an affected sib pair (ASP). Our results confirm theoretical work suggesting that gene × gene interactions CANNOT be leveraged to improve linkage detection for dichotomous traits based on affecteds-only data structures. However, incorporation of DR-based LCs did lead to appreciably higher quantitative trait PPLs. This suggests that gene × gene interactions could be effectively used in quantitative trait analyses even when families have been ascertained as ASPs for a related dichotomous trait.

Accumulating quantitative trait linkage evidence across multiple datasets using the posterior probability of linkage

Genome scans for complex disorders are frequently inconclusive, prompting researchers to increase sample size in an effort to obtain stronger evidence. However, increasing sample size in the presence of locus heterogeneity may actually, on average, decrease the linkage signal at a true susceptibility gene. The posterior probability of linkage, or PPL, was specifically designed to address this issue in the context of categorical trait analysis, by appropriately accumulating evidence either for or against linkage as new data are added. We now formulate a quantitative trait (QT) analog, the QT-PPL, which directly measures the evidence that a QT is linked to a genetic marker or location. The new QT-PPL is based on a classical single-locus QT likelihood with the trait parameters (allele frequency, genotypic means and variances) integrated out. We show using simulations that the QT-PPL is robust to two key modeling violations (multiple trait loci and non-normality in the form of excess kurtosis), as well as being inherently ascertainment corrected, and illustrate the advantages of the QT-PPL for accumulating linkage evidence across multiple sets of data compared to other QT linkage methods.

Discussing gene-gene interaction: warning--translating equations to English may result in jabberwocky

Interest in mapping susceptibility alleles for complex diseases, which do not follow a classic single-gene segregation pattern, has driven interest in methods that account for, or use information from one locus when mapping another. Our discussion group examined methods related to epistasis or gene x gene interaction. The goal of modeling gene x gene interaction varied across groups; some papers tried to detect gene x gene interaction while others tried to exploit it to map genes. Most of the 10 papers summarized here applied newly created or newly modified statistical methods related to gene x gene interaction, while two groups primarily examined computational issues. As is often the case, comparisons are complicated by little overlap in the data used across the papers, and further complicated by the fact that the available data may not have been ideal for some gene x gene interaction methods. However, the main difficulty in comparing and contrasting methods across the papers is the lack of a consistent statistical definition of gene x gene interaction. But despite these issues, two clear trends emerged across the analyses: First, the methods for quantitative trait gene x gene interaction appeared to perform very well, even in families initially ascertained as affected sib pairs; and second, dichotomous trait gene x gene interaction methods failed to produce consistent results. The difficulty of using (primarily) affected sib pair data in a gene x gene interaction analysis is explored.

Application of logistic regression to case-control association studies involving two causative loci

Models in which two susceptibility loci jointly influence the risk of developing disease can be explored using logistic regression analysis. Comparison of likelihoods of models incorporating different sets of disease model parameters allows inferences to be drawn regarding the nature of the joint effect of the loci. We have simulated case-control samples generated assuming different two-locus models and then analysed them using logistic regression. We show that this method is practicable and that, for the models we have used, it can be expected to allow useful inferences to be drawn from sample sizes consisting of hundreds of subjects. Interactions between loci can be explored, but interactive effects do not exactly correspond with classical definitions of epistasis. We have particularly examined the issue of the extent to which it is helpful to utilise information from a previously identified locus when investigating a second, unknown locus. We show that for some models conditional analysis can have substantially greater power while for others unconditional analysis can be more powerful. Hence we conclude that in general both conditional and unconditional analyses should be performed when searching for additional loci.

Mathematical assumptions versus biological reality: myths in affected sib pair linkage analysis

Affected sib pair (ASP) analysis has become common ever since it was shown that, under very specific assumptions, ASPs afford a powerful design for linkage analysis. In 2003, Vieland and Huang, on the basis of a "fundamental heterogeneity equation," proved that heterogeneity and epistasis are confounded in ASP linkage analysis. A much more serious limitation of ASP linkage analysis is the implicit assumption that randomly sampled sib pairs share half their alleles identical by descent at any locus, whereas a critical assumption underlying Vieland and Huang's proof is that of joint Hardy-Weinberg equilibrium proportions at two trait loci. These are considered as examples of mathematical assumptions that may not always reflect biological reality. More-robust sib-pair designs and appropriate methods for their analysis have long been available.