Liability-scale heritability estimation for biobank studies of low-prevalence disease

Theory for liability-scale models of the underlying genetic basis of complex disease provides an important way to interpret, compare, and understand results generated from biological studies. In particular, through estimation of the liability-scale heritability (LSH), liability models facilitate an understanding and comparison of the relative importance of genetic and environmental risk factors that shape different clinically important disease outcomes. Increasingly, large-scale biobank studies that link genetic information to electronic health records, containing hundreds of disease diagnosis indicators that mostly occur infrequently within the sample, are becoming available. Here, we propose an extension of the existing liability-scale model theory suitable for estimating LSH in biobank studies of low-prevalence disease. In a simulation study, we find that our derived expression yields lower mean square error (MSE) and is less sensitive to prevalence misspecification as compared to previous transformations for diseases with =< 2% population prevalence and LSH of =< 0.45, especially if the biobank sample prevalence is less than that of the wider population. Applying our expression to 13 diagnostic outcomes of =< 3% prevalence in the UK Biobank study revealed important differences in LSH obtained from the different theoretical expressions that impact the conclusions made when comparing LSH across disease outcomes. This demonstrates the importance of careful consideration for estimation and prediction of low-prevalence disease outcomes and facilitates improved inference of the underlying genetic basis of =< 2% population prevalence diseases, especially where biobank sample ascertainment results in a healthier sample population.