I have what on the surface seems like a simple problem but I cannot figure out what is the appropriate test -- I am not a statistician...

I am trying to determine an appropriate metric to stratify patients in regards to getting toxicity (essentially trying to find a constraint so we can avoid it during treatment)

In group A, patients who met constraint A had a toxicity rate of 26% (5/19) vs 86% (12/14) for those who didn't.

In group B, patients who met constraint B had a toxicity rate of 55% (6/11) vs 72% (55/76) for those who didn't.

What test would I need to determine if constraint A was more effective stratifying patients (or reducing the proportion of patients with toxicity) versus constraint B.



1 Answer 1


This basically looks like a 2x2x2 table ([toxicity, non-toxicity] x [constraint, non-constraint] x [group A, group B]). This question is similar.

I'm not super familiar with this area (will delete this answer if a better one supersedes it), but you can do:

  • a chi-squared test with the expected values for the ([toxic, non-toxic] x [constraint, non-constraint]) combinations set equal to the average across groups
  • a binomial regression with glm(cbind(toxic, non-toxic) ~ constraint*group, family = binomial), testing the interaction for significance
  • an appropriate version of the Cochrane-Mantel-Haenszel test? (Based on the Wikipedia page it looks like this doesn't quite do what you wants - it tests the overall [toxicity x constraint] interaction across groups rather than comparing the groups ...)

If you feel like digging in there's probably something in Agresti's Categorical Data Analysis that covers this case ...

  • $\begingroup$ If the question is which constraint reduces the toxicity, then a test for association doesn't seem to be sufficient since it can test for a difference in the probability that toxicity = 1, but not for the direction of the difference? $\endgroup$
    – dipetkov
    Apr 2, 2023 at 12:20

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.