I have been studying the subject of multiple imputation methods (such as multiple imputation by chained equations MICE) and I’m currently reading “Flexible Imputation of Missing Data” by the author of MICE in R. All was somewhat fine in my understanding until I hit this passage:

Complete case analysis can perform quite badly under MAR and some MNAR cases (Schafer and Graham, 2002), but there are two special cases where it can outperform multiple imputation.

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The second special case holds only if the complete data model is logistic regression. Suppose that the missing data are confined to either a dichotomous Y or to X, but not to both. Assuming that the model is correctly specified, the regression coefficients (except the intercept) are unbiased if only the complete cases are analyzed as long as the probability to be missing depends only on Y and not on X (Vach, 1994). This property provides the statistical basis of the estimation of the odds ratio from case-control studies in epidemiology. If missing data occur in both Y and X the property does not hold.

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The second special case holds only if the complete data model is logistic regression. Suppose that the missing data are confined to either a dichotomous Y or to X, but not to both. Assuming that the model is correctly specified, the regression coefficients (except the intercept) are unbiased if only the complete cases are analyzed as long as the probability to be missing depends only on Y and not on X (Vach, 1994). This property provides the statistical basis of the estimation of the odds ratio from case-control studies in epidemiology. If missing data occur in both Y and X the property does not hold.