Covariate Selection Strategy for the Extended Propensity Score to Adjust for Missing Not at Random Data
Bibliographic record
Abstract
Missing data can introduce biases in the estimation of the indicator of interest if appropriate adjustments are not made. The case of Missing Not at Random (MNAR), a missing mechanism in which the missingness also depends on the missing values themselves, has been under-explored. When an outcome has MNAR data, one method to estimate the population mean of the outcome is using the extended propensity score. This method first estimates the extended propensity score, which is the missing probability conditional on the outcome and covariates. Then, the population mean of the outcome is estimated using these estimates. In this paper, we discuss which variables should be included in or excluded from the extended propensity score model to obtain an unbiased estimate of the population mean with small standard errors. First, we show which covariates, at a minimum, should be included in the model of missing probability so that the population mean estimator of the outcome is consistent. Next, we show that the inclusion of some covariates in the missing probability model results in a large variance of the population mean estimates even if they explain the missing probability well. Then, we verify these arguments using simulation experiments and argue that to obtain unbiased, small-variance estimates of the population mean, it is desirable to include only those covariates necessary for consistency. This study allows us to obtain such estimates when the outcome is MNAR and adjusted by the extended propensity score.
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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 | 0.012 | 0.029 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 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".