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Towards the Efficient Inference by Incorporating Automated Computational Phenotypes under Covariate Shift
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Develops doubly robust, semiparametrically efficient estimators that incorporate automated computational phenotypes (ACPs) into semi-supervised covariate-shift inference, showing efficiency gains come from ACPs on unlabeled data.
Problem
Estimating parameters on an unlabeled population when gold-standard phenotypes are available only for a covariate-shifted labeled subset; naively substituting ACPs for gold-standard labels can bias inference.
Approach
Derives the efficient influence function for target parameters under covariate shift with ACPs as an extra variable, yielding a cross-fitted doubly robust estimator that attains the semiparametric efficiency bound and never loses efficiency relative to using labeled data only; gains come specifically from ACPs on unlabeled data.
Key results
- On real datasets, the proposed estimator's CI length is reduced vs PPI by up to ~60% (e.g., Politeness Hedge: 1.2818 vs PPI 1.9696, 65.17% ratio).
- Theory shows incorporating ACPs never reduces efficiency; the efficiency gain equals a PSD term from ACPs on unlabeled data only.
- Synthetic simulations show ARE >1 across settings except when ACP is uninformative (alpha=0) or fully explained by X (zeta=1).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Incorporate ACPs for unlabeled data | Proposed estimator · Semi-supervised estimation under covariate shift | asymptotic variance | Helped |
| Use ACPs that are only a function of X (ablation) | Proposed estimator · Semi-supervised estimation under covariate shift | estimation efficiency | No clear effect |
| Add ACPs for labeled data only (ablation) | Estimator without ACPs · Semi-supervised estimation under covariate shift | estimation efficiency | No clear effect |
| Use ACPs predictive of Y and providing information beyond X | Proposed estimator · Synthetic data | ARE | Helped |
| Set ACP signal strength α to 0 (ablation) | Proposed estimator · Synthetic data | ARE | No clear effect |
| Set ACP-covariate correlation ζ to 1 (ablation) | Proposed estimator · Synthetic data | ARE | No clear effect |
| Decrease correlation ζ between ACP and covariates (ablation) | Proposed estimator · Synthetic data | ARE | Helped |
| Increase ACP signal strength α (ablation) | Proposed estimator · Synthetic data | ARE | Helped |
| Increase unlabeled sample size (ablation) | Proposed estimator · Synthetic data | ARE | Helped |
| Increase labeled sample size (ablation) | Proposed estimator · Synthetic data | ARE | Hurt |
| Use the proposed method instead of RePPI | Income — Age · Income — Age | 95% CI length: 0.0012 -> 0.0008 | Helped |
| Use the proposed method instead of RePPI | Wine — California · Wine — California | 95% CI length: 0.7693 -> 0.7845 | Hurt |
Surprising findings
- ACPs on the labeled data contribute no efficiency gain; all gains come from ACPs on unlabeled data.
- Proposed method is slightly less efficient than PPI++ or RePPI in some wine coefficients (e.g., California, New York).
Limitations
- Assumes covariate shift and p(yhat|x,y)=q(yhat|x,y), with the latter untestable when Y is unavailable in unlabeled data.
- Efficiency gain requires ACPs that carry information beyond X; gains vanish if ACP depends only on X.
Experimental setup
Datasets: UF health system EHR diabetes cohort U.S. Census income data Stack Exchange/Wikipedia politeness data Wine Enthusiast reviews synthetic Gaussian data
Benchmarks: synthetic simulations (MSE/ARE) UF diabetes EHR income politeness wine
Metrics: mean squared error asymptotic relative efficiency 95% confidence interval length coverage
Baselines: PPI PPI++ RePPI estimator without ACPs
Builds on: prediction-powered inference semiparametric efficient estimation double/debiased machine learning
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