title: 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: OBJECTIVE
  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.
  
  
  CONCLUSIONS
  We suggest that causal principles should provide the basis for statistical modeling in genetics.
authors.affiliation: Department of Epidemiology, Mailman School of Public Health, Columbia University, New York, USA.
authors.forename: Ann M
authors.initials: AM
authors.lastname: Madsen
authors.forename: Ruth
authors.initials: R
authors.lastname: Ottman
authors.forename: Susan E
authors.initials: SE
authors.lastname: Hodge
mesh_terms: D003627:Data Interpretation, Statistical; D056726:Genetic Association Studies / Q000379:methods*; D030342:Genetic Diseases, Inborn / Q000453:epidemiology / Q000235:genetics*; D006801:Humans; D008957:Models, Genetic; D017720:Molecular Epidemiology / Q000379:methods*; D019683:Penetrance