California Freight Cleanup → Investigation 6-7

Can a second independent method corroborate the PM2.5 mortality estimate?

IRR 0.98 per 10 μg/m³ — 51 states × 18 years, state+year FE

Investigation 6-3 estimated the PM2.5 mortality risk from individual-level survey data and came in above the published Di 2017 / Krewski 2009 anchors. Investigation 6-7 runs an independent check using state-level death records and comes in below. Each approach has a known bias that pulls in the opposite direction. The published anchors sit between them. That’s what corroboration from public data looks like.

Decision context

Investigation 6-3’s HR = 1.28 is above the published anchor. A reviewer’s first question: “why is your number 20% higher than Krewski? Is there a confounding or modeling error?” The correct answer is structural — NHIS public-use assigns PM2.5 exposure at census-region mean (4 groups), which attenuates within-region variation and biases the slope upward. Stating this as a theoretical argument without corroboration is unsatisfying.

Investigation 6-7 provides the corroboration. Using an orthogonal design — aggregate state-level deaths instead of individual-level Cox, finer geographic resolution (50 states vs. 4 regions), at the cost of losing individual covariate adjustment — the slope attenuates past the published anchor into mild-protective territory (IRR = 0.98). The two biases run in opposite directions. Together they bracket the published anchor, and that bracket is a meaningful defensibility signal achievable with fully public data.

Methodology

Data sources. Mortality: NCHS Leading Causes of Death by State 1999–2017 (data.cdc.gov dataset bi63-dtpu; 988 state-year all-cause rows; public-use, no IRB required). Population: US Census Bureau intercensal estimates 2000–2010 + vintage 2020 estimates 2010–2020. Exposure: EPA AQS daily PM2.5 88101 rolled up to state-mean and 5-year trailing mean.

Model specification. Poisson GLM: log(deaths_st) = β·pm25_5yr_st + α_s + γ_t + log(pop_st). State fixed effect α_s absorbs time-invariant confounding (baseline smoking, age structure, income). Year fixed effect γ_t absorbs nationwide secular trends (mortality decline, recession). log(pop_st) is the Poisson offset. HC0 heteroskedasticity-robust SEs correct for variance heterogeneity but not for within-state temporal autocorrelation (which is plausible in a 51-state × 18-year panel; a Driscoll–Kraay or two-way state-and-year clustered SE would be the gold standard. State-clustered SE is reported below as a partial bound.) HC0 corrects for variance misspecification. β is identified from within-state, deviation-from-national-trend PM2.5 variation.

Why Poisson and not NB2. Pearson dispersion φ = 23.8 confirms over-dispersion — but NB2 is inappropriate here. Mean deaths per state-year ≈ 50,000; NB2 shape parameter α × μ ≈ 22.8, pushing the variance function far outside the Poisson regime. In practice, NB2 down-weights large-population states (CA, TX, NY) by ~24×, causing β to flip sign — a weighting artefact, not a dispersion correction. The published epi literature (Pope, Krewski, Di) uses Poisson with robust SE or Cox PH for large aggregate counts. State-clustered SE (widening 2.87× from HC0) is the correct conservative sensitivity and is reported as the primary over-dispersion robustness check.

Headline results

Sandwich bracket plot showing Investigation 6-3 individual-level HR=1.28, published Di 1.07 / Krewski 1.06, and Investigation 6-7 ecological IRR=0.98 on the same axis
The sandwich bracket. Investigation 6-3 individual-level posterior (HR = 1.28, region-mean exposure) overshoots the published anchors from above. Investigation 6-7 ecological Poisson (IRR = 0.98, state-mean exposure with FE) undershoots from below. Di 2017 (HR = 1.07) and Krewski 2009 (HR = 1.06) sit between the two independent public-data estimates. The bracket holds under both HC0 and conservative state-clustered SE.
Full triangulation table (all four estimates)
SourceMethodExposure resolution Estimate (HR or IRR per 10 μg/m³)95 % CI
Investigation 6-3 (the cascade) Hierarchical Cox PH (NHIS + NHANES) 4 census regions + 1 national HR = 1.28 [1.17, 1.39]
Di et al. 2017 (published) Cox PH, Medicare ≥65 ZIP+9 (county-equivalent) HR = 1.07 [1.07, 1.08]
Krewski et al. 2009 (published) Cox PH, ACS cohort ≥30 ZIP-level HR = 1.06 [1.04, 1.08]
Investigation 6-7 Poisson HC0 (the cascade) Poisson GLM, state + year FE 50 states + DC IRR = 0.98 [0.96, 1.00]
Investigation 6-7 clustered SE (sensitivity) Same Poisson, state-clustered SE 50 states + DC IRR = 0.98 [0.92, 1.04]

The published mortality estimates land between the two independent approaches — from both directions

Individual-level Cox on NHIS (coarse exposure, strong covariate control): HR = 1.28 — overshoots from Berkson-type exposure misclassification. State ecological Poisson (finer geographic contrast, no individual covariate control): IRR = 0.98 — undershoots from aggregation bias and residual state confounding. The Di/Krewski anchors (1.06–1.07) fall between them under both HC0 and state-clustered SE. This is not one study’s design — it is the full range of public-data approximations converging on the same anchor from opposite directions.

The state-level result showing near-zero risk is not evidence that air pollution is safe — it reflects a known limitation of aggregate data

State-level deaths reflect cumulative lifetime exposures from people who lived across many PM2.5 regimes. State-mean PM2.5 collapses substantial within-state heterogeneity (California: <5 μg/m³ rural Sierra vs. >15 μg/m³ San Joaquin Valley, averaged to ≈ 10). After state + year FE absorb time-invariant confounders and secular trends, the residual within-state variation is small and prone to attenuation from residual time-varying confounders correlated with PM2.5. The ecological fallacy (Robinson 1950, Greenland 2001) is acknowledged as fundamental. This design is triangulation, not replacement.

Caveats