Required sample size for multiple imputation?

[Brad Anderson]

Some colleagues did a pilot study to evaluate feasibility and potentially support a larger grant application. They randomized 23 subjects to 2 arms (n1 = 12, n2 = 11). They lost 3 subjects to follow-up so n1 = 10 and n2 = 9. They wanted to publish the results as a pilot RCT and feasibility study. They received a revise and resubmitt. One reviewer says they need to do something to impute the missing cases. I've used multiple imputation by chained equations and EM in the past, so I'm familiar with the basics. I just balk at the idea of using something like MICE to impute missing observations with such a small sample size. I just don't feel the limited data support the use of impuation methods in which the equations make fairly strong assumptions. I originally analyzed the data reporting simple measures of substantive effect size and then used nonparametric methods for null hypothesis testing. I wouldn't even do the later but reviewers seem to want p-values. I don't know of any suggested guides or rules of thumb that would either refute or support the use of MI in our example. Any guidance would be much appreciated.

[Carlo Lazzaro]

Brad:
welcome to the list-
Each reviewer has her/his own preferences: missing values may well be one of these. Set aside the evidence that, with such a small sample size it is hard to envisage something beyond descriptive statistics, the reviewer is probably interested in the type of the missingness (informative or not).
Maybe some scenario analyses via -mi- as a top-off of the baseline findings would satisfy reviewer's curiosity.