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Identification and Estimation for Nonignorable Missing Data: A Data Fusion Approach
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Proposes a data-fusion approach that identifies the mean of an MNAR outcome in a primary domain by pooling it with an auxiliary MAR domain, giving two identification models and IPW estimators, illustrated on NYS COVID-19 hospitalization data.
Problem
Parameter identification and estimation when an outcome is missing not at random (MNAR) and cannot be identified from the MNAR data alone, without strong missing-data model assumptions.
Approach
Augment the MNAR primary dataset with an auxiliary MAR dataset via selection-at-random across domains; under two complementary sets of assumptions (Model 1: missingness depends on a potentially missing covariate; Model 2: missingness depends on the outcome, using a shadow-variable odds-ratio approach), the outcome mean becomes identified from pooled data, and an IPW estimator is derived.
Key results
- In simulation Model 1 (T), the bootstrap estimate at n=2000 was 1.767 vs true 1.8 (bias -0.033, 95% CI [1.598, 1.930]).
- On the COVID-19 data, Model 1 estimated NYS hospitalization rate at 0.7396 (95% CI [0.7190, 0.7570]) and Model 2 at 0.7836 (95% CI [0.7558, 0.8071]), versus an MCAR estimate of 0.7533.
- MAR estimates (0.7337) were clearly biased relative to the IPW estimates in the simulations and application.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the Model 1 IPW estimator instead of the MAR estimator | Hospitalization-rate estimation for NYS March 2020 · COVID-19 NYS March 2020 | hospitalization rate estimate: 0.7337 -> 0.7396 | Mixed |
| Use the Model 2 IPW estimator instead of the MAR estimator | Hospitalization-rate estimation for NYS March 2020 · COVID-19 NYS March 2020 | hospitalization rate estimate: 0.7337 -> 0.7836 | Mixed |
| Use the Model 1 IPW estimator instead of the MCAR estimator | Hospitalization-rate estimation for NYS March 2020 · COVID-19 NYS March 2020 | hospitalization rate estimate: 0.7533 -> 0.7396 | Mixed |
| Use the Model 2 IPW estimator instead of the MCAR estimator | Hospitalization-rate estimation for NYS March 2020 · COVID-19 NYS March 2020 | hospitalization rate estimate: 0.7533 -> 0.7836 | Mixed |
| Use IPW rather than the MAR estimator | Model 1 simulation · Simulation study, Model 1 | bias | Helped |
| Use IPW rather than the MAR estimator | Model 2 simulation · Simulation study, Model 2 | bias | Helped |
Surprising findings
- The MAR estimate on the COVID-19 data (0.7337) differs notably from the Model 1 and Model 2 estimates, with Model 2 exceeding the MCAR estimate.
Limitations
- Semiparametrically efficient estimation is not developed; IPW estimators only under correctly specified working models.
- Identification relies on untestable assumptions (selection at random across domains, completeness, and shadow-variable conditions) that must be justified by domain experts.
- Simulation estimates show finite-sample bias at small sample sizes (e.g., +0.141 bias at n=500 in Model 1).
Experimental setup
Datasets: COVID-19 Case Surveillance Public Use Data with Geography (New York State, March 2020 and March 2023) simulated data
Benchmarks: simulation study (n in 500, 1000, 2000; 1000 replicates) COVID-19 NYS hospitalization data
Metrics: bias bootstrap 95% confidence interval boxplot distribution of estimates
Baselines: MAR estimator MCAR estimator complete case analysis
Builds on: shadow variable approach data fusion directed acyclic graphs
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