Multiple imputation approaches for the analysis of dichotomized responses in longitudinal studies with missing data

Often a binary variable is generated by dichotomizing an underlying continuous variable measured at a specific time point according to a prespecified threshold value. In the event that the underlying continuous measurements are from a longitudinal study, one can use the repeated-measures model to impute missing data on responder status as a result of subject dropout and apply the logistic regression model on the observed or otherwise imputed responder status. Standard Bayesian multiple imputation techniques (Rubin, 1987, in Multiple Imputation for Nonresponse in Surveys) that draw the parameters for the imputation model from the posterior distribution and construct the variance of parameter estimates for the analysis model as a combination of within- and between-imputation variances are found to be conservative. The frequentist multiple imputation approach that fixes the parameters for the imputation model at the maximum likelihood estimates and construct the variance of parameter estimates for the analysis model using the results of Robins and Wang (2000, Biometrika 87, 113-124) is shown to be more efficient. We propose to apply (Kenward and Roger, 1997, Biometrics 53, 983-997) degrees of freedom to account for the uncertainty associated with variance-covariance parameter estimates for the repeated measures model.