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Let's suppose I perform two separate logistic regression models in two different subgroups of my dataset.

glm(death ~ age + ..... , data = female, family="binomial") #female population
glm(death ~ age + ..... , data = male, family="binomial") #male population

From these, I obtan an OR for age in the female group and one for the male group (numbers are just examples):

  • OR age in the female group: 1.88 (0.41-2.89); p>0.05
  • OR age in the male group: 1.45 (1.20-1.78); p<0.05 P interaction: 0.3

So the males OR is significant while the female's not. However, when I perform the interaction test, the p is >0.05. How do I interpret this? It means that there is no difference between the two ORs, so why one is significant and the other isn't? If there is no difference, then is the "true" OR < or >1?

user19745561
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    Could you please tell us what the "interaction test" is in this context? – whuber Apr 10 '23 at 23:02
  • @whuber Yes, I performed this test: 10.1136/bmj.326.7382.219 – user19745561 Apr 10 '23 at 23:07
  • Thank you. So if I understand your question correctly, you have found you cannot distinguish the male OR from 0; the female OR is around 1.2; and you cannot distinguish the male from the female OR. Would that be right? (If so, I suspect you haven't performed the interaction test correctly, because the lack of overlap in the two OR estimates indicates you can distinguish them.) – whuber Apr 10 '23 at 23:10
  • @whuber The numbers I put in the post are actually made up, I just wanted to express my question regarding the fact that sometimes one OR is significant and the other is not but the interaction is not significant. It is true that it happens when the 95%CI of the OR are almost overlapping, but then how do I interpret my results? – user19745561 Apr 10 '23 at 23:15
  • Exactly as you have. There's no inconsistency. It's possible that numbers A and B are indistinguishable, B and C are indistinguishable, but A is distinguishable from C because the gap between A and C is sufficiently large. But posing a question with fake numbers that don't reproduce your circumstances is a great way to mislead yourself and others. Why can't you quote your actual results? – whuber Apr 10 '23 at 23:23
  • @whuber: Sorry! I thought it would be the same. One example of results is OR 1.88 (0.41-2.89) for group A, while OR 1.45 (1.20-1.78) for group B. P interaction is 0.30. – user19745561 Apr 10 '23 at 23:27

1 Answers1

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A difference in significance does not indicate a significant difference. Males differ from 0, females do not. BUT, this does not necessarily mean that males and females differ from each other. Here is an example plot where group 1 does not differ from 0, but group 2 does (95% CI does not overlap 0). However, the two groups are not significantly different from each other, as their respective 95% CIs overlap.enter image description here

David B
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  • The basic idea is OK, but non-overlap of 95% CI is too stringent a requirement for a statistically significant difference between two groups at p < 0.05. See this answer; non-overlap is approximately equivalent to a statistically significant difference at p < 0.005, under some reasonable assumptions. A simple reproducible numerical example might be better to make your point. – EdM Apr 13 '23 at 14:31
  • @David B: thank you, however I have a remaining problem. Male = significant; Female = non significant; If P interaction is not significant, then it means that male = female --> significant = non significant? What are my results then? – user19745561 Apr 14 '23 at 15:43
  • You're making the error of conflating p-value with effect size. Non-significant is not the same as identical. – David B Apr 17 '23 at 14:01