6533b7d5fe1ef96bd1264797

RESEARCH PRODUCT

Testing for goodness rather than lack of fit of an X–chromosomal SNP to the Hardy-Weinberg model

Stefan WellekStefan WellekAndreas ZieglerAndreas Ziegler

subject

HeredityNormal DistributionDistance MeasurementTrinomial01 natural sciencesLinkage Disequilibrium010104 statistics & probabilityStatisticsLack-of-fit sum of squaresMathematicsVenous ThrombosisMeasurement0303 health sciencesMultidisciplinaryQRSoftware EngineeringGenomicsHardy–Weinberg principleGenetic MappingPhysical SciencesEngineering and TechnologyMedicineResearch ArticleComputer and Information SciencesScienceGeometryAsymptotic distributionVariant GenotypesPolymorphism Single NucleotideMolecular Genetics03 medical and health sciencesGenome-Wide Association StudiesGeneticsTest statisticHumansComputer Simulation0101 mathematicsMolecular BiologyGenetic Association Studies030304 developmental biologyChromosomes Human XModels StatisticalModels GeneticSoftware ToolsBiology and Life SciencesComputational BiologyHuman GeneticsGenome AnalysisProbability TheoryProbability DistributionGenotype frequencyRadiiSample size determinationSample SizeBinomial proportion confidence intervalMathematics

description

The problem of checking the genotype distribution obtained for some diallelic marker for compatibility with the Hardy-Weinberg equilibrium (HWE) condition arises also for loci on the X chromosome. The possible genotypes depend on the sex of the individual in this case: for females, the genotype distribution is trinomial, as in the case of an autosomal locus, whereas a binomial proportion is observed for males. Like in genetic association studies with autosomal SNPs, interest is typically in establishing approximate compatibility of the observed genotype frequencies with HWE. This requires to replace traditional methods tailored for detecting lack of fit to the model with an equivalence testing procedure to be derived by treating approximate compatibility with the model as the alternative hypothesis. The test constructed here is based on an upper confidence bound and a simple to interpret combined measure of distance between true and HWE conforming genotype distributions in female and male subjects. A particular focus of the paper is on the derivation of the asymptotic distribution of the test statistic under null alternatives which is not of the usual Gaussian form. A closed sample size formula is also provided and shown to behave satisfactorily in terms of the approximation error.

https://doi.org/10.1371/journal.pone.0212344