Abstract
BackgroundPresence of interaction between a genotype and certain factor in determination of a trait's value, it is expected that the trait's variance is increased in the group of subjects having this genotype. Thus, test of heterogeneity of variances can be used as a test to screen for potentially interacting single-nucleotide polymorphisms (SNPs). In this work, we evaluated statistical properties of variance heterogeneity analysis in respect to the detection of potentially interacting SNPs in a case when an interaction variable is unknown.ResultsThrough simulations, we investigated type I error for Bartlett's test, Bartlett's test with prior rank transformation of a trait to normality, and Levene's test for different genetic models. Additionally, we derived an analytical expression for power estimation. We showed that Bartlett's test has acceptable type I error in the case of trait following a normal distribution, whereas Levene's test kept nominal Type I error under all scenarios investigated. For the power of variance homogeneity test, we showed (as opposed to the power of direct test which uses information about known interacting factor) that, given the same interaction effect, the power can vary widely depending on the non-estimable direct effect of the unobserved interacting variable. Thus, for a given interaction effect, only very wide limits of power of the variance homogeneity test can be estimated. Also we applied Levene's approach to test genome-wide homogeneity of variances of the C-reactive protein in the Rotterdam Study population (n = 5959). In this analysis, we replicate previous results of Pare and colleagues (2010) for the SNP rs12753193 (n = 21, 799).ConclusionsScreening for differences in variances among genotypes of a SNP is a promising approach as a number of biologically interesting models may lead to the heterogeneity of variances. However, it should be kept in mind that the absence of variance heterogeneity for a SNP can not be interpreted as the absence of involvement of the SNP in the interaction network.
Highlights
Presence of interaction between a genotype and certain factor in determination of a trait’s value, it is expected that the trait’s variance is increased in the group of subjects having this genotype
Genome-wide association (GWA) study has become the tool of choice for the identification of loci associated with complex traits
The analysis of variances of the trait is based on single-nucleotide polymorphisms (SNPs) information only, as the interacting factor is assumed to be unknown in such analysis aimed to identify potentially interacting SNPs without knowledge of an interacting variable
Summary
Each column presents one distribution of residual error, each group of columns represents one variance homogeneity test For both figures, the interacting allele frequency PB = 10%. Additional file 1, Figure S1 shows distribution of a trait for each genotype before and after transformation in case of SNP effect presence, explaining 5% of total variance. Additional file 2, Table S1, S2, and S3 present type I error in case there is SNP effect explaining correspondingly 0%, 1%, 5% of total traits’s variance Each of these tables present result for different interacting allele frequency PB = 5%, 10%, 25%, and 50%. The notable difference from two degrees of freedom test is that even in absence of SNP effect Bartlett’s test with prior rank transformation of a trait has increased type I error. Power We have derived an expression for dependence of trait’s variances on model parameters for each genotype of a SNP
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