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Table 1 Relationships among the coefficients of the Multi-Logistic Model and the type of interaction.

From: A novel approach to simulate gene-environment interactions in complex diseases

Interaction model Constraints
Genetic Model α1α2α3 and β1 = β2 = β3 = 0
Environmental Model α1 = α2 = α3 and β1 = β2 = β3 = β ≠ 0
Gene Environment interaction Model α1 = α2 = α3 and β1β2β3
Additive Model α1α2α3 and β1 = β2 = β3 = β ≠ 0
  1. Type of gene-environment interactions are expressed as constraints among coefficients of the Multi-Logistic Model. This approach allows to specify the type of interaction to simulate in a simple manner. Another interesting consequence is that for each type of interaction only a subset of coefficients needs to be specified.