Causal inference and GWAS: Rubin, Pearl, and Mendelian randomization.

Although Genome Wide Analysis (GWAS) have been widely used to understand the genetic architecture of complex quantitative traits, interpreting their results in terms of the biological processes that determine those traits has been difficult or even lacking, because of the variability in responses to the tests of hypotheses within a trait, species, and breed or cross, and the lack of follow-up studies. It is then essential employing appropriate statistical tests that point out to the causal genes responsible of the relevant fraction of the genetic variability observed. We briefly review the main theoretical aspects of the two schools of causal inference (Rubin's Causal Model, RCM, and Pearl's causal inference, PCI). RCM approachs the hypothesis testing from a randomization perspective by considering a wider space of the observation, i.e. the "potential outcomes", rather than the narrower space that results from defining "treatment" effects after observing the data. Next, we discuss the assumptions involved to meet the requirements of randomization for RCM with observational data (non-designed experiments) with special emphasis on the Stable Unit Treatment Analysis (SUTVA). Due to the presence of "confounders" (i.e. systematic fixed effects, environmental permanent effects, interaction among genes, etc.), causal average treatment effects are viewed through the familiar lens of normal linear (or mixed) models. To overcome the difficulties of association analyses, a tests of causal effects is introduced using independent predicted residual breeding values from animal models of genetic evaluation that avoids the effects of population structure and confounder effects. An independent section discusses the issue of whether the additive effects defined at the "gene" level by R. A. Fisher and popularized in D. S. Falconer's textbook of quantitative genetics can be termed causal from either RCM or PCI.