Multiple imputation methods for handling missing values in a longitudinal categorical variable with restrictions on transitions over time: a simulation study

Background Longitudinal categorical variables are sometimes restricted in terms of how individuals transition between categories over time. For example, with a time-dependent measure of smoking categorised as never-smoker, ex-smoker, and current-smoker, current-smokers or ex-smokers cannot transition to a never-smoker at a subsequent wave. These longitudinal variables often contain missing values, however, there is little guidance on whether these restrictions need to be accommodated when using multiple imputation methods. Multiply imputing such missing values, ignoring the restrictions, could lead to implausible transitions. Methods We designed a simulation study based on the Longitudinal Study of Australian Children, where the target analysis was the association between (incomplete) maternal smoking and childhood obesity. We set varying proportions of data on maternal smoking to missing completely at random or missing at random. We compared the performance of fully conditional specification with multinomial and ordinal logistic imputation, and predictive mean matching, two-fold fully conditional specification, indicator based imputation under multivariate normal imputation with projected distance-based rounding, and continuous imputation under multivariate normal imputation with calibration, where each of these multiple imputation methods were applied, accounting for the restrictions using a semi-deterministic imputation procedure. Results Overall, we observed reduced bias when applying multiple imputation methods with restrictions, and fully conditional specification with predictive mean matching performed the best. Applying fully conditional specification and two-fold fully conditional specification for imputing nominal variables based on multinomial logistic regression had severe convergence issues. Both imputation methods under multivariate normal imputation produced biased estimates when restrictions were not accommodated, however, we observed substantial reductions in bias when restrictions were applied with continuous imputation under multivariate normal imputation with calibration. Conclusion In a similar longitudinal setting we recommend the use of fully conditional specification with predictive mean matching, with restrictions applied during the imputation stage.