Dmitri V. Zaykin

Testing association of statistically inferred haplotypes with discrete and continuous traits in samples of unrelated individuals.

There have been increasing efforts to relate drug efficacy and disease predisposition with genetic polymorphisms. We present statistical tests for association of haplotype frequencies with discrete and continuous traits in samples of unrelated individuals. Haplotype frequencies are estimated through the expectation-maximization algorithm, and each individual in the sample is expanded into all possible haplotype configurations with corresponding probabilities, conditional on their genotype. A regression-based approach is then used to relate inferred haplotype probabilities to the response. The relationship of this technique to commonly used approaches developed for case-control data is discussed. We confirm the proper size of the test under H₀ and find an increase in power under the alternative by comparing test results using inferred haplotypes with single-marker tests using simulated data. More importantly, analysis of real data comprised of a dense map of single nucleotide polymorphisms spaced along a 12-cM chromosomal region allows us to confirm the utility of the haplotype approach as well as the validity and usefulness of the proposed statistical technique. The method appears to be successful in relating data from multiple, correlated markers to response.

Exact tests for association between alleles at arbitrary numbers of loci

Associations between allelic frequencies, within and between loci, can be tested for with an exact test. The probability of the set of multi-locus genotypes in a sample, conditional on the allelic counts, is calculated from multinomial theory under the hypothesis of no association. Alleles are then permuted and the conditional probability calculated for the permuted genotypic array. The proportion of arrays no more probable than the original sample provides the significance level for the test. An algorithm is provided for counting genotypes efficiently in the arrays, and the powers of the test presented for various kinds of association. The powers for the case when associations are generated by admixture of several populations suggest that exact tests are capable of detecting levels of association that would affect forensic calculations to a significant extent.

Selection of genetic markers for association analyses, using linkage disequilibrium and haplotypes.

The genotyping of closely spaced single-nucleotide polymorphism (SNP) markers frequently yields highly correlated data, owing to extensive linkage disequilibrium (LD) between markers. The extent of LD varies widely across the genome and drives the number of frequent haplotypes observed in small regions. Several studies have illustrated the possibility that LD or haplotype data could be used to select a subset of SNPs that optimize the information retained in a genomic region while reducing the genotyping effort and simplifying the analysis. We propose a method based on the spectral decomposition of the matrices of pairwise LD between markers, and we select markers on the basis of their contributions to the total genetic variation. We also modify Claytons haplotype tagging SNP selection method, which utilizes haplotype information. For both methods, we propose sliding window-based algorithms that allow the methods to be applied to large chromosomal regions. Our procedures require genotype information about a small number of individuals for an initial set of SNPs and selection of an optimum subset of SNPs that could be efficiently genotyped on larger numbers of samples while retaining most of the genetic variation in samples. We identify suitable parameter combinations for the procedures, and we show that a sample size of 50-100 individuals achieves consistent results in studies of simulated data sets in linkage equilibrium and LD. When applied to experimental data sets, both procedures were similarly effective at reducing the genotyping requirement while maintaining the genetic information content throughout the regions. We also show that haplotype-association results that Hosking et al. obtained near CYP2D6 were almost identical before and after marker selection.

GAW12: Simulated genome scan, sequence, and family data for a common disease

The Genetic Analysis Workshop (GAW) 12 simulated data involves a common disease defined by imposing a threshold on a quantitative liability distribution. Associated with the disease are five quantitative risk factors, a quantitative environmental exposure, and a dichotomous environmental variable. Age at disease onset and household membership were also simulated. Genotype data, including 2,855 microsatellites on 22 autosomes, were simulated for 1,497 individuals in 23 families. Phenotype data and sequence data for seven candidate genes were provided for 1,000 of these indiviudals who were “living” and available for study. Data were simulated for 50 replicate samples in each of two populations, a general population and a population isolate formed from a small group of founders.

Interval estimation of genetic susceptibility for retrospective case-control studies

BackgroundThis article describes classical and Bayesian interval estimation of genetic susceptibility based on random samples with pre-specified numbers of unrelated cases and controls.ResultsFrequencies of genotypes in cases and controls can be estimated directly from retrospective case-control data. On the other hand, genetic susceptibility defined as the expected proportion of cases among individuals with a particular genotype depends on the population proportion of cases (prevalence). Given this design, prevalence is an external parameter and hence the susceptibility cannot be estimated based on only the observed data. Interval estimation of susceptibility that can incorporate uncertainty in prevalence values is explored from both classical and Bayesian perspective. Similarity between classical and Bayesian interval estimates in terms of frequentist coverage probabilities for this problem allows an appealing interpretation of classical intervals as bounds for genetic susceptibility. In addition, it is observed that both the asymptotic classical and Bayesian interval estimates have comparable average length. These interval estimates serve as a very good approximation to the exact (finite sample) Bayesian interval estimates. Extension from genotypic to allelic susceptibility intervals shows dependency on phenotype-induced deviations from Hardy-Weinberg equilibrium.ConclusionsThe suggested classical and Bayesian interval estimates appear to perform reasonably well. Generally, the use of exact Bayesian interval estimation method is recommended for genetic susceptibility, however the asymptotic classical and approximate Bayesian methods are adequate for sample sizes of at least 50 cases and controls.

Association mapping: where we've been, where we're going

This paper provides a review of recent work in the area of marker-phenotype association studies, specifically as used for localizing – or mapping – genes affecting a trait of interest. We describe the basis of association mapping and discuss a number of the commonly used techniques. We have also included references to various papers that have evaluated the use of these methods.

Evolution of the simulated data problem.

The simulated data problem was designed via an interactive process by the Simulation Problem Organizing Committee and the selected data simulators. Based on discussions at the previous Genetic Analysis Workshop, many of the features of previous simulation problems, such as a complex disease, genome scan, and replication, were retained and in addition, a population genetics model was used to generate the simulated genes. We describe the process that was used to structure the problem and summarize the discussions about many of the scientific issues that were considered.

Identifying susceptibility genes using linkage and linkage disequilibrium analysis in large pedigrees.

Linkage and linkage disequilibrium tests are powerful tools for mapping complex disease genes. We investigated two approaches to identifying markers associated with disease. One method applied linkage analysis and then linkage disequilibrium tests to markers within linked regions. The other method looked for linkage disequilibrium with disease using all markers. Additionally, we investigated using Simes’ test to combine p‐values from linkage disequilibrium tests for nearby markers. We applied both approaches to all replicates of the Genetic Analysis Workshop 12 problem 2 isolated population data set. We reported results from the 25th replicate as if it were a real problem and assessed the power of our methods using all replicates. Using all replicates, we found that testing all markers for linkage disequilibrium with disease was more powerful than identifying markers that were in linkage with disease and then testing markers within those regions for linkage disequilibrium with the implementations that we chose. Using Simes’ test to combine p‐values for linkage disequilibrium tests on correlated markers seemed to be of marginal value.