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.
Highlights
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
We provide a strategy to estimate proportion of genetic variance explained on the liability scale from estimates of area under the ROC curve (AUC), disease prevalence, and heritability available as an online calculator
The maximum value of AUC when the test classifier is a genetic predictor depends on heritability and disease prevalence In Figure 1A we consider two diseases both with heritability of liability, h2L = 0.2, plotting probability of disease (i.e. G01) vs genetic liability (i.e. A)
Summary
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. Results from genome-wide association studies have provided empirical evidence that very few associated genetic variants with effect size greater than odds ratio of 1.5 exist [1,2] Reconciliation of these effect sizes with the, often sizeable, estimates of heritability for many complex diseases (Table 1) means that we must expect there to be many (perhaps thousands) of genetic variants underlying complex disease if the effect size of any one variant is very small. We define genetic risk as the risk of disease given an individual’s unique multi-locus genotype; genetic risk remains unchanged throughout an individual’s lifetime and so could be predicted at birth prior to exposure to many environmental risk factors Such risk predictions could be age specific, for example, risk of type 2 diabetes at 10 years, 20 years or 50 years if genomic profile sets based on empirical data were available for these scenarios which have age-specific genetic epidemiologies.
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