Implementing Multiple Imputation for Missing Data in Longitudinal Studies When Models are Not Feasible: An Example Using the Random Hot Deck Approach

Chinchin Wang; Tyrel Stokes; Russell J Steele; Niels Wedderkopp; Ian Shrier

doi:10.2147/CLEP.S368303

Implementing Multiple Imputation for Missing Data in Longitudinal Studies When Models are Not Feasible: An Example Using the Random Hot Deck Approach

Clin Epidemiol. 2022 Nov 15:14:1387-1403. doi: 10.2147/CLEP.S368303. eCollection 2022.

Authors

Chinchin Wang^{1

2}, Tyrel Stokes³, Russell J Steele³, Niels Wedderkopp⁴, Ian Shrier¹

Affiliations

¹ Centre for Clinical Epidemiology, Lady Davis Institute, Jewish General Hospital, McGill University, Montreal, Quebec, H3T 1E2, Canada.
² Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montreal, Quebec, H3A 1A2, Canada.
³ Department of Mathematics and Statistics, McGill University, Montreal, Quebec, H3A 0B9, Canada.
⁴ Orthopedic Department University Hospital of South West Denmark, Department of Regional Health Research, University of Southern Denmark, Odense, Denmark.

Abstract

Purpose: Researchers often use model-based multiple imputation to handle missing at random data to minimize bias. However, constraints within the data may sometimes result in implausible values, making model-based imputation infeasible. In these contexts, we illustrate how random hot deck imputation can allow for plausible multiple imputation in longitudinal studies.

Patients and methods: Our motivating example is the Childhood Health, Activity, and Motor Performance School Study Denmark (CHAMPS-DK), a prospective cohort study that measured weekly sports participation for 1700 Danish schoolchildren. Using observed data on 4 variables (pain, activity frequency, sport, sport counts), we created a gold-standard data set without missing data. We then created a synthetic data set by setting some variable values to missing based on a prediction model that mimicked real-data missingness patterns. To create 5 imputed data sets, we matched each record with missing data to several fully observed records, generated probabilities from matched records, and sampled from these records based on the probability of each occurring. We assessed variability and agreement (kappa) between the imputed data sets and the gold-standard data set. We compare results to common model-based imputation methods.

Results: Variability across data sets appeared reasonable. The range of kappa for the random hot deck approach was moderate for activity frequency (0.65 to 0.71) and sport (0.59 to 0.85), and poor for common model-based approaches (range 0.00 to 0.11). The range of kappas for sport count was strong (0.87 to 0.97) for random hot deck imputation and weak to moderate (0.55 to 0.71) for common model-based imputation. Agreement was higher when more information was present, and when prevalence was higher for our binary variable sport.

Conclusion: Random hot deck imputation should be considered as an alternative method when model-based approaches are infeasible, specifically where there are constraints within and between covariates.

Keywords: hot deck imputation; longitudinal studies; missing at random; missing data; multiple imputation; random hot deck imputation.

Grants and funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.