The case-only design is a powerful approach to detect interactions but should be used with caution

The case-only design is a powerful approach to identify gene $\times$ gene and gene $\times$ environment interactions for complex traits. It has been demonstrated that for the case-only design to be valid the genetic and environmental factors must be independent in the population. Additionally, there is a rare disease assumption for the case-only design, but the impact of disease prevalence and other factors, e.g., size of main effects, on type I and II error rates has not been investigated.

Through theoretical and extensive simulation studies, we investigated type I error, power, and bias of interaction term for a wide variety of disease prevalences, main and interaction effect sizes, sample sizes, and variant and environmental exposure frequencies.

For diseases with prevalence $<$ 4%, the case-only design usually has well controlled type I error rates and is substantially more powerful to detect interactions than the case-control design, but for higher disease prevalences both type I and II error rates can be inflated and the estimate of interaction term biased. However, when one or both main effects are large there can be inflated type I error rate even for low disease prevalences, e.g., $<$ 1%, but if there is no or only one main effect, type I error rate is controlled regardless of the disease prevalence. Additionally, type I error rate can increase with sample size.

We determined the upper bound of the disease prevalence in order not to violate the rare disease assumption for the case-only design. To verify that a case-only design study does not have increased type I error rate, the bias of the interaction term should be estimated. Although the case-only design is a powerful method to detect interactions, prevalences for some complex traits are too high to implement this method without increasing type I error rates.