Background The case-only design is a powerful approach to identify gene <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12864_2025_11318_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$\times$</EquationSource> <EquationSource Format="MATHML"><math> <mo>×</mo> </math></EquationSource> </InlineEquation> gene and gene <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12864_2025_11318_Article_IEq2.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$\times$</EquationSource> <EquationSource Format="MATHML"><math> <mo>×</mo> </math></EquationSource> </InlineEquation> 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. Methods 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. Results For diseases with prevalence <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12864_2025_11318_Article_IEq3.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$<$</EquationSource> <EquationSource Format="MATHML"><math> <mo><</mo> </math></EquationSource> </InlineEquation> 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., <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12864_2025_11318_Article_IEq4.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$<$</EquationSource> <EquationSource Format="MATHML"><math> <mo><</mo> </math></EquationSource> </InlineEquation> 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. Conclusions 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.

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

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2025年3月6日

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Rui Dong,
Gao T. Wang,
Andrew T. DeWan,
Suzanne M. Leal

摘要

Background

The case-only design is a powerful approach to identify gene $\times$ $\times$ gene and gene $\times$ $\times$ 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.

Methods

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.

Results

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.

Conclusions

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.