(outlier-) robust mmrm, similarly to robustlmm (based on lme4). A proposal to consider :)

[adrianolszewski]

Currently I'm working on a longitudinal study analysed via MMRM. There are a few influential observations and non-influential residual outliers. Situation is like below.

Coloured dots depict observations belonging to influential patients (Cook's distance on the subject level). Majority observations more/less follow the normal distribution and their Cook's are acceptable. For the few coloured one the discrepancies aren't that huge. Anyway, two independent statistical reviewers agreeably refused to accept the default parametric MMRM and asked me to use another method accounting for these observations. I am disallowed to exclude them (I'd need to exclude a whole patient, not just single observation; and neither is wrong, all are something that can be expected), or to use quantile-based methods. The only accepted solution was permutation testing or robust (weighting) approach.

One of them, luckily, proposed me with the robustlmm R package, which extends lme4 with robust estimation. In this very case lme4 can reproduce us() and cs() MMRM via 0+Timepoint|ID and 1|ID. And since robustlmm accepts the same syntax as lme4, I could use it. The obtained estimates, CIs and p-values are noticeably different, but fortunately consistent in terms of decisions. In other words, change of the method didn't change conclusions this time.

/ BTW, robustlmm doesn't provide p-values and degrees of freedom for the test statistic, so emmeans assigns infinity and uses normal approximation. I found an article, where authors took Satterthwaite from lme4 and reused it. This idea helped me, as in my case although the approximation at N=40 was close to N=Inf, taking N=Inf was rejected by the reviewers. /

And this also provoked me to ask - how about adding some options for robust estimation to MMRM?

I know, it's non-standard, moreover, there are lots of settings that can be controlled (but MMRM has some too :) ), but in the last 4 years I had 6 cases where it was formally requested in terms of the sensitivity analysis, to determine the impact of those discrepancies in assumptions and 2 where I was requested to change the main planned analysis to the robust one.

Honestly, I didn't thing about any technical details, but if you find it worthwhile, the robustlmm could be a good starter.

PS: I experimented a bit. Satterthwaite df from lmer4 + robustlmm seems to be a really good idea. But we could go even further: take the weights obtained from robustlmm and use them with mmrm? mmrm supports weighting, right? So why not feed it with these weights? It worked pretty well with lme4. I need to check it.

Happy new year!