Causal Models for Investigating Complex Genetic Disease: II. What Causal Models Can Tell Us about Penetrance for Additive, Heterogeneity, and Multiplicative Two-Locus Models

Abstract

Background/Aims: Statistical geneticists commonly use certain two-locus penetrance models because these models are familiar and mathematically tractable. We investigate whether and under what circumstances these two-locus penetrance models correspond to models of causation. Methods: We describe a sufficient component cause model for a hypothetical disease with two genetic causes. We then use the potential outcomes framework to determine the expected two-locus penetrances from this causal model and contrast them with commonly used two-locus penetrance models (additive, heterogeneity, and multiplicative penetrance models, as formulated by Risch [Am J Hum Genet 1990;46:222–228]). Results: Conventional additive and multiplicative models can correspond to any two-locus causal model only when certain very specific algebraic relationships hold. The heterogeneity model corresponds to a two-locus causal model only if the model stipulates that no disease cases are caused by the combined presence of the causal genotypes at both loci (i.e. only when there is no causal gene-gene interaction). Hence the heterogeneity model provides a valid test of the null hypothesis of no gene-gene interaction, whereas the additive and multiplicative models do not. Conclusion: We suggest that causal principles should provide the basis for statistical modeling in genetics.