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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.

Thanks

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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 ...

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  • $\begingroup$ 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

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