Imputation, single/multiple

FIGURE 9.1 Performance of the conditional multiple imputation and fractional single multiple imputation (LLOQ/ ) methods under the fourth scenario (i.e., assuming 45% interindividual variability and 25% residual variability) for the following parameters (A) AUCo-inf, (B) %AUC extrapolated, and (C) terminal half-life (Lambda Z HL). 

Traditionally, incomplete (missing) data have been handled by deletion from analysis of cases that contain missing values (single imputation) and most recently by using multiple imputation techniques. In this section single imputation techniques are discussed. Multiple imputation and the paradigm for multiple imputation are discussed in separate sections because of the broad scope of these topics. 

If the data are collected at fixed time intervals then one trick to generate imputed values that would account for within-subject correlations is to transform the data into a columnar format with one row of data per subject. So if the data were collected at Visits 2, 3, and 4, then three new variables would be generated. Variable 1 would correspond to Visit 2, Variable 2 to Visit 3, etc. In this manner then each row of data would correspond to a single individual. Now any of the imputation techniques introduced in the chapter on Linear Regression and Modeling could be used to impute the missing data based on the new variables. Once the data are imputed, the data set can be reformatted to multiple rows per subject and the analysis proceeds with the imputed data. This approach assumes that all samples are collected at the same time interval for all subjects, i.e., assumes that all samples were assumed at Visits 1-4 in this case. 

Multiple imputation is not, in fact, always necessary to produce correct variance estimates. It depends on the analysis strategy following single imputation. A simple example is given in the technical appendix. 

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