# Multiple comparison in Multiple imputation

I am wondering if it is appropriate to use the term "multiple comparison problem" when applied to multiple imputation. I know that the multiple comparison problem arises when we have one set of data and ask many questions about it. Is this theoretically the same thing as having multiple data sets, and asking the same question on each dataset?

The reason I ask is because I have a MI dataset, and want to run a log rank test on each of the 50 datasets, but I don't believe that running the test on each dataset and then pooling is valid (because of the multiple comparison problem).

• What exactly do you impute? The group variable or something else? – Theodor Nov 2 '15 at 12:06
• Correct. In my original dataset, the survival time and censoring indicator are fully observed, but the treatment/group needs imputation. As well, in another instance, I have that same setup, but a variable is imputed that I subset on (ie coxph(Surv(time,cens)~treat,subset=(receptor==TRUE)) – RayVelcoro Nov 2 '15 at 14:20

• I am currently doing the Wald like test as you suggested in the second paragraph. My logic is that we want the pooled log rank test (from kaplan meier curves), but since this is not normally distributed, we can run a cox model (equivalent with no ties), and then to a Wald test, since the score test is the log rank test, and the wald test is asymptotically equivalent to it. I'm just afraid that. Besides, pooling on $\chi^2$ doesn't seem to work well. I'm just afraid of the theoretical soundness of this method. – RayVelcoro Nov 2 '15 at 16:38