In Genome Wide Association Studies the relationship between a phenotype, with discrete outcome levels, and a genotype is typically assessed via linear regression, which necessarily ignores the non-normality of the outcome. Motivated by this, we consider a transformation that connects the linear effects to the non-linear scale. The approach improves on current transformations by maintaining small bias, of the non-linear genetic effect estimate, when variation in the outcome is explained mainly by additional covariates, e.g. age and gender.

As an example, we consider a binary trait and several genetic and non-genetic predictors connected via a logit link-function. The method, however, is applicable to a wide class of non-normal phenotypes and link-functions.