I would like to do just a simple imputation on my outcome, not having many other covariates and not wanting to make estimates on tens and datasets I would like to avoid multiple imputation. Assuming that one is supposed to be more like the group to which one belongs I would like to do a simple imputation (by the mean or the median) within one's own group, although this is not a common method. Are there any recommendations for this type of imputation? What is the disadvantage of such an imputation? Is it an overestimation of the treatment effect (I assume the missing data are MCAR)? And won't the opposite, i.e. imputing by the mean or the median of the whole sample, lead to an underestimation of the treatment effect?
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$\begingroup$ Imputation involves learning and learning is enhanced with larger sample sizes. So I would not separate the observations by treatment. And avoiding multiple imputation will create a bias, especially on the standard errors/confidence intervals/credible intervals. Single-value fill-in methods are only OK if the proportion of missings is tiny. More here. $\endgroup$– Frank HarrellCommented Sep 5, 2022 at 14:08
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Actually your sentiments on high order imputation is not original. Here is work by Caroline Svahn and Oleg Sysoev, "Selective Imputation of Covariates in High Dimensional Censored Data", that you may find valuable. Here is an abstract from the fully available article, to quote:
Our method allows for iterative, subject-wise selection of covariates to impute in order to achieve a fast and accurate predictive model. The algorithm furthermore selects values for imputation which are likely to provide important information if imputed. In contrast to previously proposed methods, our approach is fully nonparametric and therefore, very flexible. We demonstrate that, in comparison to previous work, our model achieves faster execution and often comparable accuracy in a simulated example as well as predicting signal strength in radio network data.
The authors also notes:
Ignoring the censoring can be problematic as valuable information may be missing and restoration of these censored values may significantly improve the quality of models...Strategies to handle censored data are plenty, however, little effort has been made to handle censored data of high dimension.
I hope you find this approach of value.
