Understanding the potential bias of variance components estimators when using genomic models

Abstract

Abstract Background Genomic models that link phenotypes to dense genotype information are increasingly being used for infering variance parameters in genetics studies. The variance parameters of these models can be inferred using restricted maximum likelihood, which produces consistent, asymptotically normal estimates of variance components under the true model. These properties are not guaranteed to hold when the covariance structure of the data specified by the genomic model differs substantially from the covariance structure specified by the true model, and in this case, the likelihood of the model is said to be misspecified. If the covariance structure specified by the genomic model provides a poor description of that specified by the true model, the likelihood misspecification may lead to incorrect inferences. Results This work provides a theoretical analysis of the genomic models based on splitting the misspecified likelihood equations into components, which isolate those that contribute to incorrect inferences, providing an informative measure, defined as $$\varvec{\kappa }$$ κ , to compare the covariance structure of the data specified by the genomic and the true models. This comparison of the covariance structures allows us to determine whether or not bias in the variance components estimates is expected to occur. Conclusions The theory presented can be used to provide an explanation for the success of a number of recently reported approaches that are suggested to remove sources of bias of heritability estimates. Furthermore, however complex is the quantification of this bias, we can determine that, in genomic models that consider a single genomic component to estimate heritability (assuming SNP effects are all i.i.d.), the bias of the estimator tends to be downward, when it exists.