# Different results with splitting data vs. adjusting

I have a question regarding the results that I have achieved from my analysis. I'm new to statistics and the understanding of epidemiology. Please, help me interpret this better. I know what a confounder is, but still, I don't know how to understand this. I have a big sample size with equal numbers of each gender. I have used logistic regression to understand the association (not prediction, but association!) between diabetes (dia) and a genetic mutation (GM). The outcome, Y is diabetes, and the X variable is a genetic mutation. I have been using R for this.

dia ~ GM


I get an OR = 2, and it is significant.

Then I add a confounder variable such as gender (GE) and gestational age (GA)

dia ~ GM + GA + GE


The OR is still 2 and significant. The confounders did nothing for the association.

Then I split my sample by gender, so I did this association for males and females separately.

dia ~ GM


In the female group, there was no significant association. The association is gone. But in the male group, the association was significant.

What exactly does this mean? Why did my OR not change when I added/adjusted for gender as a confounder, but when I did a gender-specific analysis, the results changed? How is this interpreted? I may have misunderstood the information about what a confounder is.

You write

In the female group, there was no significant association. The association is gone

The association not being significant is not the same as it being "gone". When you split your sample, you lowered N in each sample. This lowers power and, for the same effect size, raises the p value. What was the effect size (OR) in men and women?

I may have misunderstood the information about what a confounder is.

Yes, I think you have. From Wikipedia:

In causal inference, a confounder is a variable that influences both the dependent variable and independent variable, causing a spurious association.

That is different from what you think it is. What you are really asking about is not confounding or mediation, but moderation. That is, when you did the separate analysis, you found different relationships between GM and dia for men and women. To look at this in a single regression, you would add the interaction between GM and GE and run:

dia ~ GM + GE + GM*GE + GA

(Also, you have GA in some equations but not others, I hope that's just a typo).

• In addition, you can never compare p-values. Comparisons need to be head-to-head. Aug 11 at 13:15
• Thank you for your help! Yes you are right. it is a typo. GA had to be in the models for gender also. I meant what you wrote, that the association is not gone, but it is not significant. I'm new at using the language of epidemiology/statstics. Thanks for correcting me! Is moderation the same as effect modification/interaction analysis? Because I have seen the multiplication term between two variables before when reading about effect modification/interaction. So are all these words used interchangeably? OR_Women = 0.98, not significant. OR_Men = 3.2, is significant. Sample with both OR=2. Aug 11 at 13:27
• Yes, moderation is pretty much synonymous with interaction. And you clearly have interaction, based on what you write here. Aug 11 at 13:42
• I have one more question about the confounder. It is for my master thesis. Can I include my results as first showing a forest plot for dia ~ GM. and then a forest plot for dia ~ GM + GA + GE. or should I show the results like this, first dia ~GM, then dia ~GM + GA, and then dia ~GM + GA + GE. I want to hear your opinion on what will make most sense to do Aug 11 at 14:10
• Certainly for two p-vales $p_1$ and $p_2$ some comparisons such as $p_1 \leq p_2$ can be evaluated, however what one is supposed to interpret from that is not understood by me. Math will accommodate quite a lot, but can does not imply should. Aug 11 at 14:41