I was wondering why, in a regression model including an interaction term, the confidence interval of one of the main effects becomes wider. Consider this Cox regression, where the variable IR_BMI27 is a categorical variable with four categories, which is why we see three categories (Hazard Ratios being expressed relative to the reference category), and the outcome is binary:
I added an interaction term between and the variable Age and, as you can see, while the point estimate of the HR of the fourth category of IR_BMI27 strongly increases and remains statistically significant, its confidence interval becomes wider (less so in the other categories):
Why would that happen? I am curious about the theoretical basis for that. I am familiar with the interpretation of a shift in effect size (or statistical significance) for a main effect when introducing an interaction term, but I wonder whether the sheer change in confidence interval size reflects the same principles. Does it mean that the distribution of age in that category is skewed? Or does it mean that the distribution of the outcome of interest across ages in that category is skewed? This is a table reporting the sample sizes and the CVD events (that is the binary outcome variable) per category of IR_BMI27, all stratified by Age in decennia (39 to 50, 51 to 60, 61 to 70, 71 to 80): I cannot see anything strange.