Justification for imputation with over 50% missing data

Question

I'm looking to get some advice/thoughts on the following situation: let's say I have a prospective, observational study that was designed to assess change in BMI over two years of follow-up (primary outcome) in a population that was administered drug A and Drug B per standard of care. The point is not to compare BMI between groups A and B but to assess BMI changes within each group.

Visits with height and weight collection were supposed to occur every six months (baseline, six months, 12 months, 18 months and 24 months) for 24 months. However, due to high dropout, only 40% of participants had the full 24 months of follow-up, so the sample size target for the primary outcome was not met.

I was thinking of using a mixed effects model, given the longitudinal nature of the study, to account for within-participant correlations with Fixed effects for time (months since baseline), drug group, and their interaction. Random Effects: random intercepts and slopes for each participant to account for individual variations.

However, the investigator is also pushing for missing data imputation, but I'm not sure if that's feasible or how to justify this to regulatory authorities, given that we'd have to impute more than 50% of the data.

How would you handle this situation? Is imputation warranted here, and if yes, what imputation method would be best suited (perhaps a pattern-mixture model, given that the missing data pattern is MNAR?)? Are there any articles you'd recommend I read about how others might have dealt with a similar problem and solved it?

Any advice/references would be greatly appreciated.

Thanks!

Answer 1

You are mentioning that some regulatory authority will assess the study report. Thus, your work will probably be evaluated in accordance with the standard statistical guidelines, that is, ICH E9. In its current version, section 5.3 states:

".. In reality, however, there will almost always be some missing data. A trial may be regarded as valid, nonetheless, provided the methods of dealing with missing values are sensible, and particularly if those methods are pre-defined in the protocol. Definition of methods may be refined by updating this aspect in the statistical analysis plan during the blind review. Unfortunately, no universally applicable methods of handling missing values can be recommended. An investigation should be made concerning the sensitivity of the results of analysis to the method of handling missing values, especially if the number of missing values is substantial."

Due to the required, but seemingly insufficient prespecification of the methods to handle missing data and the large proportion of missing data, it will probably become very difficult to convince any assessor of the robustness of any analysis - irrespective of the method you are going to use. Hence, my best recommendation is: Stick to your primary pre-specified analysis strategy and evaluate the sensitivity of those results against a large variety of MNAR scenarios.

The various scenarios proposed for reference-based multiple imputation might serve as a reasonable starting point to this end:

Carpenter J. R., Roger J. H., and Kenward M. G. 2013. Analysis of longitudinal trials with protocol deviation: A framework for relevant, accessible assumptions, and inference via multiple imputation. Journal of Biopharmaceutical Statistics 23: 1352–1371.

Answer 2

A mixed effects model also implicitly imputed, so if you're fine with that, why would you not be fine with making the imputation more explicitly clear?

The main question is what you intend to impute. Imputing im- or explicitly under MAR would suggest you believe patients stayed on their drugs and continued to receive the effects (if any). If dropping out = off drug, then that seems wrong. Imputing based on retrieved drop-outs might be more defensible. Although with so much missing data, your assumptions will clearly be very influential and people might question your results no matter what you do.