Why Residual CRF Uncertainty Still Matters
Expected Value of Sample Information (EVSI) measures how much a decision-maker should be willing to pay to resolve uncertainty before committing to a policy. The classical form asks: what is the expected cost of choosing the wrong policy under the current uncertainty?
Under both the Di CRF (Medicare ≥65) and the Krewski CRF (ACS ≥30), the optimal transport scenario is T2_accelerated. The structural choice between the two CRFs does not flip the policy ranking — so the discrete-choice wrong-decision cost is $0. The residual CRF uncertainty lives inside the Inv 21 hierarchical posterior, which integrates over Di, Krewski, Turner, and IHD cohorts across 58 California counties. Resolving that posterior is what a targeted study buys.
The 4× burden difference between the two CRFs (94k contested deaths/yr across ages 30–64) matters for health-burden accounting and intervention sizing — even though the two CRFs rank the five transport scenarios identically. That gap is what the Inv 21 posterior brackets, and what residual research should resolve.
Two CRFs, Same Optimal Scenario
| Policy | Deaths Avoided (Di) | Net Benefit (Di) | Deaths Avoided (Krewski) | Net Benefit (Krewski) |
|---|---|---|---|---|
| T1 Baseline | 453 | $5.62B | 1,450 | $17.77B |
| T2 Accelerated | 630 | $5.81B | 2,001 | $22.52B |
| T3 Delayed | 190 | $2.85B | 609 | $7.96B |
| T4 Equity | 546 | $5.78B | 1,919 | $22.51B |
| T5 Heavy Duty | 488 | $4.58B | 1,486 | $16.73B |
Green highlights = optimal policy under each CRF. Both Di and Krewski rank T2_accelerated first on net benefit ($5.81B / $22.52B). T4_equity is a close second on both CRFs. The CRF scales the magnitude by ~4× but preserves the policy ranking.
Where the Uncertainty Lives
The two CRFs agree on the 65+ population — both are based on strong evidence for elderly PM2.5 mortality. They disagree on the 30–64 age group: 14.7 million Californians whose PM2.5 mortality risk is uncertain.
| Age Group | Population | Burden (Deaths/yr) | Status |
|---|---|---|---|
| 65+ | 4,795,619 | 31,407 | Both CRFs agree |
| 30–64 | 14,666,708 | 94,490 | Contested |
| Total 30+ | 19,462,327 | 125,897 | — |
The contested population is 75% of the total burden. Di et al. studied Medicare enrollees (65+ only) and cannot speak to younger ages. Krewski et al. studied the ACS CPS-II cohort (30+) but with older data and lower spatial resolution. The 30–64 age band sits inside Krewski’s cohort and outside Di’s — a coverage gap, not a methodological one.
The contested burden drives the residual EVSI. Even though Di and Krewski agree on the policy ranking, they disagree on the size of the 30–64 mortality burden. The Inv 21 hierarchical posterior integrates over that disagreement. Tightening it with new age-stratified evidence is what the residual $0.05B EVSI values.
Three Ways to Tighten the Posterior
| Option | Cost | Timeline | ROI vs Inv 21 residual |
|---|---|---|---|
| Meta-analysis of existing studies with age stratification | $0.5M | 6 months | 100:1 |
| Retrospective analysis of existing cohort (UK Biobank, MESA) | $2M | 1 year | 25:1 |
| Prospective cohort (CA-specific, ages 30–64) | $15M | 5 years | 3:1 |
ROI divides residual EVSI ($0.05B against the Inv 21 hierarchical posterior) by study cost. The $0.5M meta-analysis (100:1) and $2M retrospective (25:1) both sit inside the EPA Clean Air Act research literature's 5–30:1 band. The $15M prospective cohort (3:1) falls below it: once pooling is applied, a redundant cohort does not pay back its cost.
Naive vs design-aware ROI. The 100:1 / 25:1 / 3:1 figures above are naive post-pool ratios: residual EVSI divided by study cost, assuming each study fully resolves the residual. Inv 24 refines this with pre-posterior, design-aware EVSI per study (meta-analysis 40.7×, retrospective cohort 15.3×, Medicare extension 7.8×) and sequences a 3-arm adaptive portfolio capturing $84M EVSI at $7.5M staged spend. Both framings are legitimate: the naive ratios here bound what's possible at the cheapest resolution; Inv 24's design-aware numbers are what actually gets captured by a specific study design.
The residual question is quantitative, not structural. Di and Krewski agree on the transport policy ranking; they disagree on the size of the 30–64 mortality burden. An age-stratified meta-analysis of existing PM2.5 mortality cohorts can tighten that burden estimate at minimal cost, improving the accuracy of health-cost accounting across the rest of the portfolio.
EVSI calculation · Di et al. 2017 (NEJM, Medicare 65+), Krewski et al. 2009 (HEI, ACS CPS-II 30+) · Inv 21 hierarchical-Bayes posterior over 58 CA counties · 10,000 Monte Carlo draws · VSL = $11.6M (EPA 2024) · Policy costs from CEC scenario definitions.