# Interaction results in two datasets are concordant, but stratified analyses are not

Let's suppose I want to explore the relationship between a variable (SNP, {0,1,2}) and a disease outcome (D, continuous value such as blood pressure), knowing that this is different in two groups, let's say males and females (SEX).

I first explored this using an interaction model, in the form (using an R-based syntax):

D ~ SNP*SEX + covariates


This allows me to obtain not only a regression coefficient for the interaction term (β) but also its direction and significance (P-value).

Let's say that the P-value of my interaction is significant. Therefore, I want to further validate my finding in an independent cohort, where I get another significant interaction term and concordant directions of the effect (positive).

Let's now say that I want to explore more in details what is happening in the two strata (males/females). My questions are: "Are the direction of effects concordant in the two strata?", "Is the association significant in both strata?"

Since I have no idea how to extract this information from the interaction model (suggestions welcomed), let's say I run sex-stratified analyses in the two independent datasets.

In the first dataset I get significant results for both males and females, but opposite directions (negative and positive, respectively). In the second dataset, I get significant results only for males, and directions that are opposite to what I am observing in the first dataset (positive for males, negative for females). How is this possible, when the interaction term is concordant? How do I interpret this? What is the answer to my questions above?

I’m not very familiar with interaction models.