Assessing balance in measured baseline covariates when using many‐to‐one matching on the propensity‐score
Bibliographic record
Abstract
The propensity score is defined to be a subject's probability of treatment selection, conditional on observed baseline covariates. Conditional on the propensity score, treated and untreated subjects have similar distributions of observed baseline covariates. Propensity-score matching is a commonly used propensity score method for estimating the effects of treatment on outcomes. Balance diagnostics have been previously described for use when 1:1 matching on the propensity score is employed. We illustrate that these methods can be misleading when many-to-one matching on the propensity score is employed. We then propose modifications of these methods that involve weighting each untreated subject by the inverse of the number of untreated subjects in the matched set. We describe both quantitative and qualitative methods to assess the balance in baseline covariates between treated and untreated subjects in a sample obtained by many-to-one matching on the propensity score. The quantitative method uses the weighted standardized difference. The qualitative methods employ graphical methods to compare the distribution of continuous baseline covariates between treated and untreated subjects in the weighted sample. We illustrate our methods using a large sample of patients discharged from hospital with a diagnosis of a heart attack (acute myocardial infarction). The exposure was receipt of a prescription for a statin at hospital discharge.
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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 | 0.052 | 0.202 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
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".