Implementing Multiple Imputation for Missing Data in Longitudinal Studies When Models are Not Feasible: An Example Using the Random Hot Deck Approach
Bibliographic record
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.188 | 0.314 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.005 |
| Bibliometrics | 0.002 | 0.006 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.004 | 0.003 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.004 | 0.006 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".