In applying multiple imputations to deal with missing values in a clinical trial, we are struggling to find an appropriate strategy. In this trial we are interested in the effect of an intervention to the primary outcome (depression severity, measured at several time points), and on those of a set of secondary outcome variables (severity of other symptoms and derived outcomes). Examples of derived outcomes are ‘response’, i.e. at least a 50% reduction of depression severity and ‘remission’ that is based on having any diagnosis at follow-up of a fixed set of diagnoses. For these derived outcomes we found that the choice between impute-then-transform (separate pre- and post treatment scores and diagnoses) or transform-then-impute (directly impute response or remission scores) leads to substantial differences. We use MICE to impute the variables. Averaging over 100 imputed data set we found:  

Impute-then-transform (Passive imputation)  

* Remission: 36.1%

* Response 50% depression severity: 22.9%

* Response 50% anxiety serverity: 26.2%

Transform-then-impute (Just-another-variable)

* Remission: 45.3%

* Response 50% depression severity 31.1%

* Response 50% anxiety severity: 32.8%

Question 1: We collected from the literature (van Hippel (2009), White, Royston, Wood (2011)) that the Transform-then-impute or Just-Another-Variable approach is recommended over the other strategy. Therefore, we added these derived variables as separate variables in the imputation model. Interestingly, the result between the two strategies differ substantially, as shown above. Would you agree that the Just-Another-Variable is the preferred strategy?

Question 2: The number of variables to be imputed (41) reaches the number of patients in one of the two treatment arms (45 patients). Is the fact that the number of variables to be imputed reaches the number of patients in one of the treatment arms in-itself worrisome?

REFERENCES

- Von Hippel PT (2009) “How to Impute Interactions, Squares, and Other Transformed Variables.” Sociological Methodology 39 (1): 265–91.

- White IR, Royston P, Wood AM (2011) “Multiple Imputation Using Chained Equations: Issues and Guidance for Practice.” Statistics in Medicine 30 (4): 377–99.