Number of imputations needed to stabilize estimated treatment difference in longitudinal data analysis

Multiple imputation procedures replace each missing value with a set of plausible values based on the posterior predictive distribution of missing data given observed data. In many applications, as few as five imputations are adequate to achieve high efficiency relative to an infinite number of imputations. However, substantially more imputations are often needed to stabilize imputation-based inference at the analysis stage. Imputation-based inference at the analysis stage is considered stable if the conditional variability of the multiple imputation estimator, half-width of 95% confidence interval, test statistic, and estimated fraction of missing information given observed data is within specified thresholds for simulation error. For the estimation of treatment difference at study end for normally distributed responses in longitudinal trials, we calculate the multiple imputation quantities for an infinite number of imputations analytically and use simulations to assess the variability of the number of imputations needed at the analysis stage in repeated sampling.