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B-CALM: Bias-Limited Bayesian Borrowing for RCT-Anchored Treatment Effects under Covariate Mismatch
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Proposes B-CALM, a Bayesian borrowing framework that jointly models RCT and observational outcome surfaces on a shared latent state, with a comparative-bias prior whose precision caps OS information about the RCT CATE, validated on synthetic, semi-synthetic (STAR), and pediatric-obesity external-control data.
Problem
Estimating RCT-defined conditional average treatment effects (CATEs) when the RCT is small and observational studies are larger but confounded and only partially overlap in measured covariates.
Approach
Decomposes the observational outcome surface into baseline bias and comparative (treatment-contrast) bias on a shared latent state, places a Gaussian-process prior on the comparative bias whose variance acts as an explicit sensitivity knob, and proves that OS information about the trial CATE is capped by that prior precision.
Key results
- Synthetic factorial study: B-CALM average 90% coverage 0.939 with RMSE 0.206 vs 0.318 for RCT-only and negative transfer 0.023; pooled coverage 0.581.
- Comparative-bias sweep: B-CALM coverage stays near nominal while pooled falls to 0.07 and CF to 0.23 at the strongest bias setting; B-CALM's weakest cell is 0.857 at strength 0.5.
- Pediatric obesity: B-CALM ATE -0.184 [-0.336,-0.031] with 9.4% width reduction over RCT-only; CF reduces width 70.6% but has bias-susceptibility ratio 2.91.
Surprising findings
- OSCAR/CALM beats B-CALM under strong comparative bias (RMSE 0.199 vs 0.239 at strength 0.5), and gains nothing when OS is clean.
- Removing the comparative-bias function drops coverage from 0.915 to 0.324 while RMSE moves much less, so b_Delta matters mainly for calibration.
Limitations
- Comparative bias b_Delta is not identifiable without prior restrictions; results depend on sigma_Delta choice.
- With poor covariate overlap, B-CALM reverts toward RCT-only, adding no precision.
- Posterior computation is expensive at EHR scale.
Experimental setup
Datasets: synthetic factorial DGP Tennessee STAR class-size trial covariates (semi-synthetic) pediatric-obesity RCT with EHR external controls
Benchmarks: synthetic factorial study semi-synthetic STAR benchmark pediatric-obesity external-control application
Metrics: RMSE 90% credible interval coverage interval width negative transfer rate ATE credible interval width reduction
Baselines: RCT-only OS-only pooled RCT+OS causal forest OSCAR/CALM BCF MR-OSCAR
Builds on: CALM R-OSCAR MR-OSCAR power priors commensurate priors causal forest
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