Multiple imputation analysis of Miettinen-Nurminen interval for difference in proportions

The standard multiple imputation technique focuses on parameter estimation and assumes that the parameter estimator is asymptotically normally distributed with a Wald-type confidence interval for the parameter of interest. On the other hand, the Miettinen-Nurminen (MN) method for difference in proportions (Miettinen O, Nurminen M. Stat Med. 1985;4:213-226) constructs the confidence interval using an asymptotic score method and hence is not directly amenable to the standard multiple imputation technique. We propose a multiple imputation analysis that is applicable to the MN method for difference in proportions. We use simulation studies to compare the proposed method with that of Li, Mehrotra and Barnard (LMB), which is based on effective sample sizes (Li X, Mehrotra DV, Barnard J. Stat Med. 2006;25:2107-2124). We show that both methods produce confidence intervals with adequate coverage, while the proposed method produces slightly shorter confidence intervals than the LMB method. In addition, the proposed method is evaluable for all datasets, while the LMB method cannot be used when the imputed cell counts are zero across imputations for a treatment group.