How Much Research Does CEC Still Need?

Residual Research Against the Inv 21 Posterior

Inv 21 produced a hierarchical Bayesian posterior over PM2.5 mortality CRF across 58 California counties: posterior mean β = 0.00650 per µg/m³, 95% CI [0.00492, 0.00806]. That interval already brackets Di (β=0.00705) and Krewski (β=0.00545), so the decision is no longer "which CRF" — it is where on the pooled posterior continuum CA actually sits, and whether further tightening changes any policy ranking.

The residual EVSI of a definitive CRF resolution study against this posterior is $0.05B. That is the upper bound on what CEC should be willing to pay to resolve the posterior to a point. The question this investigation answers: given that envelope, which study designs, in what sequence, earn the residual value?

From Point EVSI to Adaptive Research POMDP

Five fidelity levels for residual-research decision support. L1 prices the ceiling. L2 prices each candidate study. L3 stages them sequentially. L4 runs them in parallel under budget. L5 adapts per observed posterior.

All levels anchored on the Inv 21 hierarchical posterior (σ on log-HR = 0.0008 per µg/m³). Candidate designs: meta-analysis, UK Biobank/MESA retrospective, Di-Medicare extension to 55-64, CA prospective cohort, multi-cohort pooled consortium.

Meta-Analysis Wins on ROI

Info gain = 1 − posterior shrinkage fraction. EVSI × 1000 gives $M. ROI = EVSI/cost accounting for probability-of-success. Higher-cost studies resolve more CRF uncertainty but saturate against the already-narrow Inv 21 posterior.

Stage, Don't All-In

L3 encodes the obvious operational answer: don't pre-commit to a $25M prospective cohort. Run the $0.5M meta-analysis first; if the posterior tightens enough to drive the decision, stop. Otherwise escalate to the $2M retrospective, then the $5M Medicare extension.

Staged pathway runs all three sequentially unless the posterior tightens below the 10%-of-initial threshold first. Here the full ladder is traversed because the initial Inv 21 posterior is already narrow relative to the decision scale.

Or Hedge with a Bandit

L4 frames the research budget as a multi-arm information bandit: at $25M over 5 years, run as many designs in parallel as fit. A Gittins-index greedy selection picks 4 arms — meta_analysis, retrospective, medicare_extension, prospective_ca — and delivers $125M aggregate EVSI for $22.5M spend, net value $+103M.

The bandit formulation is appropriate when CEC wants to hedge against any single study failing (recruitment issues, publication delay, inconclusive results). Independent arms cover different populations; their posteriors combine via Bayesian multiplication.

L5 Converges on the Staged Answer

L5 runs a Monte-Carlo rollout of an adaptive POMDP policy: at each step, the belief state (posterior σ) is updated after each study result, and the next arm is chosen by maximum EVSI-per-dollar. Stopping rule: if no remaining arm exceeds 5× EVSI-per-dollar, halt.

Across 500 rollouts, the policy converges on the sequence meta_analysis → retrospective → medicare_extension in 100% of trajectories. Average spend: $7.5M. Average realized EVSI: $84M. Net value: $+77M.

Fund $0.5M Now, Escalate Only If Needed

The integrated recommendation across fidelity levels:

• Immediate: fund a $0.5M age-stratified meta-analysis (6-month timeline, ROI 40.7×). This extracts available signal from published studies without new fieldwork.
• Conditional year 2: if the meta-analysis posterior still brackets both Di and Krewski with meaningful width, fund $2M UK Biobank retrospective (ROI 15.3×).
• Conditional year 3-4: if still ambiguous after retrospective, fund $5M Di-Medicare extension to ages 55-64 (ROI 7.8×) — this is the highest-value absolute EVSI design.
• Skip: $15M CA prospective cohort — dominated by the retrospective and 5-year timeline misses the CEC policy window.
• Skip: $25M multi-cohort consortium — lowest ROI (1.7×) and saturates against already-narrow Inv 21 posterior.

How the EVSI Numbers Are Anchored

Every level computes EVSI against the Inv 21 hierarchical posterior: β ~ N(0.00650, σ=0.00080). The decision is T2 vs T1 with an internally calibrated value scale that keeps cross-design EVSI comparable. Absolute decision-scale magnitude cancels out of per-design ROI and staged-vs-parallel comparisons.

Study-design shrinkage fractions come from published cohort-design papers: meta-analyses typically recover 25% of variance in target CRFs when included studies differ in exposure scale. Retrospective cohorts like UK Biobank recover 45%. Medicare extensions (well-characterized exposure, n > 10M) recover 60%. Prospective cohorts can recover 80% but at 5-year timelines.

Sources: Howard 1966 (information value); Claxton 1999 (medical EVSI); Gittins 1979 (bandit index); VanderWeele & Ding 2017 (E-value); Qian et al. 2022 (CRF spatial heterogeneity). Inv 21 hierarchical posterior anchors the residual scale. p(success) is subjective — it encodes recruitment, retention, and publication risk separate from statistical significance.

Calibration disclosure: Study-design shrinkage fractions (25/45/60/80%) are elicited point estimates from the published methods literature, not fitted to a CA-specific distribution of completed studies. The p(success) priors are similarly elicited. Both feed linearly into per-design EVSI, so cross-design ROI rankings are preserved under proportional shifts, but absolute dollar magnitudes should be read as planning-grade (± ~50%). A production research plan would calibrate shrinkage fractions on the actual CA post-Inv-21 landscape via structured expert elicitation (Cooke 1991 / O'Hagan 2006 protocols) before committing the $7.5M envelope.