Statistical analysis model after multiple imputation

[Laure C]

To give a little background, I am in the context of clinical trials, my outcome is normal continuous and measured at several times. I am interested in knowing if there is a treatment difference on the last measurement of that outcome. My main analysis is a Mixed-effects Model for Repeated Measures (including the fixed categorical effects of treatment, visit, treatment-by-visit interaction, as well as the continuous fixed covariates of baseline and baseline-by-visit interaction and using an unstructured covariance matrix). I also perform multiple imputation using the outcome at every times by treatment groups (with mcmc command in sas proc MI) as sensitivity analysis.

I am wondering what statistical analysis model should be used after performing a multiple imputation. I thought MMRM would be more appropriate than an analysis of covariance, in term of standard error for instance. 

But I've run some tests on some real data and I get exactly the same results with the two models regarding my treatment difference at the end (both for estimates and standard errors).
Actually, I also observe the same thing when analysing complete cases. But those are only empirical results...

So is MMRM different from ANCOVA to evaluate a treatment difference at a final timepoint, when there are no missing data, either after imputing missing data with multiple imputation or by discarding patients with missing data?

[Jonathan Bartlett]

Good question Laure.

So long as the mixed model uses an unstructured covariance matrix, when there is no missing data the intermediate time points give no information about the treatment effect at the final time point. So an ANCOVA and mixed model will give identical estimates and standard errors.

If you've performed MI, then you are a back with complete data, so again, as you have found, you can use either approach, as they are equivalent.

Of course if you hadn't performed MI, they would not be equivalent - the ANCOVA would drop anyone who is missing at the final time point, whereas the mixed model would implicitly impute those missing values based on any intermediate measurements of outcome.

Which brings us to one additional point - unless the imputation model makes use of auxiliary variables which aren't in the analysis model, the mixed model is optimal in terms of efficiency, and there is no point in doing MI (from an efficiency perspective).

Jonathan

www.thestatsgeek.com

www.missingdata.org.uk