Multiple imputation for longitudinal data in the presence of heteroscedasticity between treatment groups

Multiple imputation is a promising approach for handling of missing data. One uncertainty in applications of the multiple imputation to randomized controlled trials with longitudinal data is whether the imputation should be carried out across all subjects simultaneously or by treatment group separately, which leads to two different strategies for building imputation procedures and/or models. Indeed, it has not been sufficiently addressed and well-documented how the two imputation strategies work in the analysis of the longitudinal data. We consider situations in the presence of heteroscedasticity between treatment groups and conducted extensive simulation studies to examine how the choice of imputation strategy had impacts on the estimation of treatment effects under an assumption of missing at random mechanism. The choice of analysis model was also assessed. The simulation studies suggested that in the presence of heteroscedasticity, the separate imputation by treatment group was robust enough to provide unbiased and precise estimation of the treatment effects; in contrast, the simultaneous imputation, which is frequently used in applications, led to serious biases and poor coverage probabilities of 95% confidence interval for the treatment effects. The heteroscedasticity should be dealt with in more careful manners for the longitudinal data analysis, and if it could be the case in hand, we recommend using the separate imputation by treatment group, as well as applying unequal variance analysis methods for complete data with imputed values. The methods were illustrated with data from two real examples of pediatric research and mental health research.