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This question follows-up on the post: What is the difference between McNemar's test and the chi-squared test, and how do you know when to use each?

I am examining a pre- and post- intervention data on two disease conditions. The above post described the use of McNemar's test for 1 disease before and after an intervention was administered to a sample.

I have two contingency tables, which look like:

            **Disease A**

                After   
                   |no  |yes|
        Before|No  |41  |11 |
              |Yes |32  |39 |

              **Disease B**

               After   
                   |no  |yes|
        Before|No  |41  |11 |
              |Yes |32  |39 |

Question: I would like to compare the proportions of:

(1) Those that went from "Yes" to "No" pre to post for Disease A vs. Disease B

(2) Those that are "Yes" after treatment ("After Yes"/"Total N") vs. those that are "No" after treatment for Disease A vs. Disease B.

How do I compare the two proportions in the above two questions ?

Again, the data is drawn from the same sample and anyone with Disease A could also be positive for Disease B at the same time. The same intervention is used to treat both A and B.

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  • $\begingroup$ What question are you trying to answer by doing that? $\endgroup$ – Björn Feb 4 at 5:54
  • $\begingroup$ For Q(1), I'd like to know whether the rates of remission (going from yes to no post intervention) are significantly different for disease A and disease B. In other words, if disease A shows 40% remission and disease B shows 60% remission, are these rates significantly different? $\endgroup$ – user81715 Feb 5 at 16:42
  • $\begingroup$ What is that trying to answer? Whether the intervention is more effective in one disease or another? $\endgroup$ – Björn Feb 5 at 17:36
  • $\begingroup$ exactly. whether one of the two diseases responds less well to intervention when compared to the other. $\endgroup$ – user81715 Feb 5 at 20:35
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A comparison of how well a drug works in two different conditions is always implicitly versus a control group (e.g. if patients had not received any treatment, or best supportive care without additional drug therapy, or whatever is appropriate as a comparison). Thus, just having pre- and post-intervention data in isolation is not what is needed to assess this question. Having a concurrently recruited control group within the trial to which some patients are randomized would let you try to address this question much more easily (assuming the pre-/post-intervention status options truly mean the same thing in both conditions). As it is, the limits of the experimental design lead to much more complications at the analysis/interpretation stage.

With this type of data, one way of realistically approaching this is to get prior information on the outcomes for each level of the pre-intervention status (e.g. from trials that included an appropriate control group) for each condition and then to look at a (Bayesian) logistic regression model that has an intercept that is different for each pre-intervention and condition combination (perhaps easiest to specify this way, but you can also think of it as condition and pre-intervention status main effects, as well as the interaction of these), and also has a treatment main effect, as well as a treatment by condition interaction. There are quite a few different approaches for doing this including the (robust) meta-analytic predictive approach (see e.g. Schmidli, H., Gsteiger, S., Roychoudhury, S., O'Hagan, A., Spiegelhalter, D., & Neuenschwander, B. (2014). Robust meta‐analytic‐predictive priors in clinical trials with historical control information. Biometrics, 70(4), 1023-1032.), but also e.g. the power prior approach. One problem is that a single arm trial does not give information on whether the prior fits the data or not.

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