A hot-deck multiple imputation procedure for gaps in longitudinal data on recurrent events

Hot-deck imputation offers advantages in reflecting salient features of data distributions in missing-data problems, but previous implementations have lacked the appeal associated with modern Bayesian statistical-computing techniques. We outline a strategy of iterative hot-deck multiple imputation with distance-based donor selection. With distance defined as a monotonic function of the difference in predictive means between cases, donors are chosen with probability inversely proportional to their distance from the donee. This method retains the implementation ease of ad hoc techniques, while incorporating the desirable features of Bayesian approaches. Special cases of our method include nearest-neighbor imputation and a simple random hot-deck. Iterating the procedure provides an analogy to Markov Chain Monte Carlo methods and is intended to mitigate dependence on starting values. Results from imputing missing values in a longitudinal depression treatment trial as well as a simulation study are presented. We evaluate how different definitions of distance, choices of starting values, the order in which variables are chosen for imputation, and the number of iterations impact inferences. We show that our measure of distance controls the tradeoff between bias and variance of our estimates. We find that inferences from the depression treatment trial are not sensitive to most definitions of distance. In addition, while differences exist between 1 iteration and 10 iterations, there are no meaningful differences between inferences based on 10 iterations and those based on 500 iterations. The choice of starting value did not have an impact on inferences but the order in which the variables were chosen for imputation was significant even after iteration.