Permutation testing in the presence of polygenic variation

Area of Science:

• Genetics
• Statistical genetics
• Bioinformatics

Background:

• Permutation testing is widely used to determine the statistical significance of complex genetic analyses, especially for gene mapping.
• Naive application of permutation tests can lead to invalid results, particularly in the presence of polygenic effects and structured populations.
• Complex trait mapping often involves challenges like polygenicity, family structures, cryptic relatedness, admixture, and population stratification.

Purpose of the Study:

• To identify problems with standard permutation testing for quantitative trait loci (QTL) in the context of polygenic effects.
• To propose and validate a new permutation-based algorithm, MVNpermute, for accurate statistical significance testing.
• To provide analytical derivations and conceptual understanding of why typical permutation procedures fail.

Main Methods:

• Analytical derivations to explain the failure of standard phenotype and genotype permutations in linear mixed models.
• Development of an alternative permutation-based algorithm, MVNpermute.
• Simulations to validate theoretical predictions of type 1 error rate inflation and confirm the correctness of the MVNpermute null distribution.

Main Results:

• Standard permutation procedures can inflate the type 1 error rate in QTL analysis when polygenic effects and population structure are present.
• A formula is derived to predict type 1 error rate inflation based on covariance structure misspecification and trait heritability.
• The MVNpermute algorithm successfully obtains the correct null distribution, ensuring valid statistical testing.

Conclusions:

• Careful consideration of polygenic effects and population structure is crucial for valid permutation testing in QTL analysis.
• The MVNpermute algorithm offers a reliable solution for accurate significance testing in complex trait mapping.
• The findings have implications for various test statistics and highlight the limitations of naive permutation approaches.