Bayesian propensity score analysis for observational data
Bibliographic record
Abstract
In the analysis of observational data, stratifying patients on the estimated propensity scores reduces confounding from measured variables. Confidence intervals for the treatment effect are typically calculated without acknowledging uncertainty in the estimated propensity scores, and intuitively this may yield inferences, which are falsely precise. In this paper, we describe a Bayesian method that models the propensity score as a latent variable. We consider observational studies with a dichotomous treatment, dichotomous outcome, and measured confounders where the log odds ratio is the measure of effect. Markov chain Monte Carlo is used for posterior simulation. We study the impact of modelling uncertainty in the propensity scores in a case study investigating the effect of statin therapy on mortality in Ontario patients discharged from hospital following acute myocardial infarction. Our analysis reveals that the Bayesian credible interval for the treatment effect is 10 per cent wider compared with a conventional propensity score analysis. Using simulations, we show that when the association between treatment and confounders is weak, then this increases uncertainty in the estimated propensity scores. Bayesian interval estimates for the treatment effect are longer on average, though there is little improvement in coverage probability. A novel feature of the proposed method is that it fits models for the treatment and outcome simultaneously rather than one at a time. The method uses the outcome variable to inform the fit of the propensity model. We explore the performance of the estimated propensity scores using cross-validation.
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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 | 0.063 | 0.227 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.006 | 0.006 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.005 | 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".