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Domain constraints improve risk prediction when outcome data is missing
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Proposes a Bayesian selective-labels model with prevalence and expertise domain constraints, shows theoretically and on synthetic data that they improve parameter precision and accuracy, and applies it to UK Biobank breast cancer testing.
Problem
Predicting outcomes (e.g., disease risk) when outcomes are observed only for historically tested individuals (selective labels), so untested populations differ along observed and unobserved dimensions and parameter inference is weakly identified.
Approach
A Bayesian model class for selective labels with latent unobservables affecting both testing and outcome, plus two health-domain constraints: a known prevalence constraint fixing the mean outcome, and an expertise constraint setting some testing-deviation coefficients to zero (decision-makers act risk-based except on constrained features). Theory shows constraints do not increase posterior varianc
Key results
- Both prevalence and expertise constraints produce more precise and accurate parameter inferences than the unconstrained model across 200 synthetic datasets.
- On UK Biobank, the highest inferred risk quintile has 3.3x higher observed cancer rate than the lowest (6.0% vs 1.8%) among tested people.
- Without the prevalence constraint, the model infers implausible cancer risk decreasing with age; the prevalence constraint yields the expected increasing age trend.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add a prevalence constraint using known disease prevalence (ablation) | Proposed Bayesian selective-labels model · Synthetic data, Bernoulli-sigmoid models | parameter inference precision and accuracy | Helped |
| Add an expertise constraint that fixes selected testing-policy coefficients to zero (ablation) | Proposed Bayesian selective-labels model · Synthetic data, Bernoulli-sigmoid models | parameter inference precision and accuracy | Mixed |
| Remove the prevalence constraint (ablation) | Proposed Bayesian selective-labels model · UK Biobank breast cancer risk prediction | plausibility of inferred age-related risk trend | Hurt |
| Use inferred risk to rank patients | Proposed Bayesian selective-labels model · UK Biobank breast cancer, tested population | cancer risk ratio, highest vs lowest inferred-risk quintile: 3.3× (6.0% vs 1.8%) | Helped |
| Use inferred risk to rank patients | Proposed Bayesian selective-labels model · UK Biobank breast cancer, untested population with follow-up | cancer risk ratio, highest vs lowest inferred-risk quintile: 2.5× (4.1% vs 1.6%) | Helped |
Surprising findings
- Without the prevalence constraint, the fitted model infers cancer risk first rising then falling with age, contradicting epidemiological evidence.
Limitations
- Real-world validation is limited because outcomes are unobserved for the untested population.
- Uses a linear risk model with few (7) features in the case study.
- Prevalence and expertise constraints rely on domain knowledge that may be inaccurate.
Experimental setup
Datasets: UK Biobank synthetic data
Benchmarks: UK Biobank breast cancer testing synthetic parameter recovery
Metrics: 95% CI width (precision) posterior mean error (accuracy) AUC outcome rate by risk quintile
Baselines: unconstrained Bayesian model model without prevalence constraint tested-population-only baselines untested-as-negative baselines selective labels baselines
Builds on: Heckman correction model generalized linear mixed models selective labels literature
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