Subsampling Technique to Estimate Variance Component for UK-Biobank Traits

The estimation of heritability has been an important question in statistical genetics. Due to the clear mathematical properties, the modified Haseman–Elston regression has been found a bridge that connects and develops various parallel heritability estimation methods. With the increasing sample size, estimating heritability for biobank-scale data poses a challenge for statistical computation, in particular that the calculation of the genetic relationship matrix is a huge challenge in statistical computation. Using the Haseman–Elston framework, in this study we explicitly analyzed the mathematical structure of the key term tr(KTK), the trace of high-order term of the genetic relationship matrix, a component involved in the estimation procedure. In this study, we proposed two estimators, which can estimate tr(KTK) with greatly reduced sampling variance compared to the existing method under the same computational complexity. We applied this method to 81 traits in UK Biobank data and compared the chromosome-wise partition heritability with the whole-genome heritability, also as an approach for testing polygenicity.

Mixed Model with Correction for Case-Control Ascertainment Increases Association Power

We introduce a Liability Threshold Mixed Linear Model (LTMLM) association statistic for ascertained case-control studies that increases power vs. existing mixed model methods, with a well-controlled false-positive rate. Recent work has shown that existing mixed model methods suffer a loss in power under case-control ascertainment, but no solution has been proposed. Here, we solve this problem using a chi-square score statistic computed from posterior mean liabilities (PML) under the liability threshold model. Each individual’s PML is conditional not only on that individual’s case-control status, but also on every individual’s case-control status and on the genetic relationship matrix obtained from the data. The PML are estimated using a multivariate Gibbs sampler, with the liability-scale phenotypic covariance matrix based on the genetic relationship matrix (GRM) and a heritability parameter estimated via Haseman-Elston regression on case-control phenotypes followed by transformation to liability scale. In simulations of unrelated individuals, the LTMLM statistic was correctly calibrated and achieved higher power than existing mixed model methods in all scenarios tested, with the magnitude of the improvement depending on sample size and severity of case-control ascertainment. In a WTCCC2 multiple sclerosis data set with >10,000 samples, LTMLM was correctly calibrated and attained a 4.1% improvement (P=0.007) in chi-square statistics (vs. existing mixed model methods) at 75 known associated SNPs, consistent with simulations. Larger increases in power are expected at larger sample sizes. In conclusion, an increase in power over existing mixed model methods is available for ascertained case-control studies of diseases with low prevalence.

Effect of service sire on litter size traits in Czech Large White and Landrace pigs

The proportion of variance for service sire effect was estimated for three litter size traits (numbers of piglets born, born alive, and weaned) in Czech Large White (89 231 litters) and Czech Landrace (28 320 litters) pigs. Each trait in the first parity was considered as one trait and that trait in the second and subsequent parities was treated as a repeated trait. Consequently, three two-trait animal models were evaluated for each litter size trait: (i) the service sire effect was included and the complete relationship matrix for all the animals (service sires and sows) was taken into account; (ii) the service sire effect was included as a random effect without inclusion of the relationship matrix; (iii) the service sire effect was omitted from the model. Using the residual variance as a criterion, both models including the service sire effect were slightly better than the model without this effect. Estimates of genetic parameters were very similar for the two models including the service sire effect. The proportion of variance for service sire was in the range from 2 to 3% (standard error approx. 0.2%) in Czech Large White and 2% (standard error approx. 0.3%) in Czech Landrace for all three litter size traits and all models. Models without service sire effect or models including service sire as a simple random effect and without inclusion of the genetic relationship matrix are recommended for genetic evaluation of litter size traits.