Longitudinal data with nonrandom missing values I'm working on experiment where two types of terminally ill mice are treated with two different drugs. Then physiological measurements are taken in four time points. Due to the disease some mice dropout during the experiment. My question is if I should treat this absence of data as missing at random or not missing at random? Eventually the drop out ratio is equal between the groups but obviously not equal between time points (i.e. if mouse is removed in time point 2 then it misses time point 3 and 4.
If I can treat this as missing at random I'd use mixed effect model. Otherwise I cannot see the way how to treat this lack of data.
For some clarity below is the data snippet.
ID Drug Time Value
1 D1 T1 20.1
1 D1 T2 17.5
1 D1 T3 17.4
1 D1 T4 16.2
2 D1 T1 24.5
2 D1 T2 14.3
2 D1 T3 NA
2 D1 T4 NA


This is a situation where the estimand (that which is to be estimated by as suitable estimator to get an estimate for the specific dataset) concept is useful. What would we even want, if we had the complete data?
Since it's the actual measurements including the ones after the "intercurrent event" of death (I assume the measurement is still possible after death, otherwise the situation is even more complicated and e.g. composite or other approaches may be needed), the question would be whether the trends on the data would be extrapolated sensibly into that situation by a mixed effects model. If you don't have any data in that situation, you'd have to base such a decision on judgment.
You could instead of a mixed effects model for repeated measures (MMRM) with an unstructured covariance matrix (which would implicitly impute missing data under an assumption that not much changes after data become missing and that extrapolates the trends in the data) use multiple imputation (MI) to see what a MMRM implicitly imputes (with a suitable setup including the right interactions in the MMRM, it behaves almost exactly like MI with a very large number of imputations). If those imputations don't look sensible/don't capture what should change after the intercurrent event, then you know that a mixed effects model will not behave sensibly.
Instead, a common strategy is then to set-up an imputation model that imputes in some sensible way. One typical idea in clinical trials in humans (if one is interested in a treatment policy estimand of "what really happened irrespective of whether patients stayed on their assigned treatment) would be to impute data after patients discontinue treatment and leave the trial either based on those that discontinued treatment and stayed in the trial, or based on what happens without treatment such as in a placebo group. Instead, a MMRM applied to on-treatment data would in this situation estimate what would happen, if hypothetically everyone had stayed on the treatment (while using MMRM with a mix of on- and off-treatment data results in an uninterpretable mess).
It's a little less clear how to impute what happens after death (which one would assume to be a major event that could really change what happens to the mouse's body thereafter), if you don't have data on that from any of the mice (but perhaps there's literature on that?).
