title: How allele frequency and study design affect association test statistics with misrepresentation errors.
abstract: We evaluate the effect of genotyping errors on the type-I error of a general association test based on genotypes, showing that, in the presence of errors in the case and control samples, the test statistic asymptotically follows a scaled non-central $\chi ^2$ distribution. We give explicit formulae for the scaling factor and non-centrality parameter for the symmetric allele-based genotyping error model and for additive and recessive disease models. They show how genotyping errors can lead to a significantly higher false-positive rate, growing with sample size, compared with the nominal significance levels. The strength of this effect depends very strongly on the population distribution of the genotype, with a pronounced effect in the case of rare alleles, and a great robustness against error in the case of large minor allele frequency. We also show how these results can be used to correct $p$-values.
authors.affiliation: MRC Centre for Neuropsychiatric Genetics and Genomics, School of Medicine, Cardiff University, Cardiff CF14 4XN, UK.
authors.forename: Valentina
authors.initials: V
authors.lastname: Escott-Price
authors.forename: Mansoureh
authors.initials: M
authors.lastname: Ghodsi
authors.forename: Karl Michael
authors.initials: KM
authors.lastname: Schmidt
mesh_terms: D005787:Gene Frequency / Q000235:genetics*; D005838:Genotype; D060005:Genotyping Techniques / Q000592:standards*; D006801:Humans; D015233:Models, Statistical; D012107:Research Design / Q000592:standards*; D016008:Statistical Distributions
keywords: Case–control study; General association test; Genomic control; Genotyping errors; Non-central χ2 distribution; Type-I error