The genetic interpretation of area under the ROC curve in genomic profiling

Abstract

Genome-wide association studies in human populations have facilitated the creation of genomic profiles which combine the effects of many associated genetic variants to predict risk of disease. The area under the receiver operator characteristic (ROC) curve is a well established measure for determining the efficacy of tests in correctly classifying diseased and non-diseased individuals. We use quantitative genetics theory to provide insight into the genetic interpretation of the area under the ROC curve (AUC) when the test classifier is a predictor of genetic risk. Even when the proportion of genetic variance explained by the test is 100%, there is a maximum value for AUC that depends on the genetic epidemiology of the disease, i.e. either the sibling recurrence risk or heritability and disease prevalence. We derive an equation relating maximum AUC to heritability and disease prevalence. The expression can be reversed to calculate the proportion of genetic variance explained given AUC, disease prevalence, and heritability. We use published estimates of disease prevalence and sibling recurrence risk for 17 complex genetic diseases to calculate the proportion of genetic variance that a test must explain to achieve AUC = 0.75; this varied from 0.10 to 0.74. We provide a genetic interpretation of AUC for use with predictors of genetic risk based on genomic profiles. We provide a strategy to estimate proportion of genetic variance explained on the liability scale from estimates of AUC, disease prevalence, and heritability (or sibling recurrence risk) available as an online calculator.

Figure 1. The dependence of maximum AUC (AUC_max) from a genomic profile on heritability and disese prevalence.

(A,B) Probability of disease versus genetic liability. (C,D) ROC curve .

Figure 2. Relationship between maximum AUC (AUC_max) from a genomic profile and heritability on the liability scale .

For different disease prevalences (A–D) from simulation (dashed line) and from equation 3 (solid line).

Figure 3. The relationship between maximum AUC (AUC_max) from a genomic profile and heritability on the liability scale (dashed line) or heritability on the observed scale (solid line), for disease prevalences in order from top left, K = 0.001, 0.01, 0.1, 0.3.