Multi-Year Pooled Baselines Separate Persistent Rural Mortality From Projected Small-County Bounce-Back
Separating lasting county health gains from modeled regression to the mean after a one-year spike.
State health agencies award rural prevention grants to help small counties lower premature death rates. In counties with small populations, a few deaths in one year can swing the annual death rate sharply upward. Next year, that county rate often drops back toward its multi-year average on its own.
When targeting multi-year rural health grants across 17 pre-pandemic years of California county records (2003 to 2019, N = 943), steady public health funding averts 2.42 deaths per 100,000 residents per $10 per person in smaller and rural counties and 2.38 statewide (rising to 4.32 per 100,000 over 13-year cumulative horizons).[1] Ranking small counties on one year of data overstates next-year gains through modeled regression to the mean because just 1 death in Alpine County (1,204 residents) swings the rate by 83.1 per 100,000 and accounts for 89% of a -22.7 per 100,000 bounce-back.[2] Funding rural grants on 3-to-5-year pooled averages sends dollars to lasting local need.[3]
Table 1. Rate Swings, Shrinkage Weights & Panel Effects Across 4 County Groups
Observed county headcounts and multi-year panel estimates paired with modeled one-year rate swings and shrinkage weights.
| Swing & Panel Measure |
Under 10K Pop
Frontier Rural Group
|
15K-25K Pop
Small Rural Group
|
Rural Stratum
Smaller-County Pool
|
Statewide Panel
All 57 Counties
|
|---|---|---|---|---|
| County Resident Count | 1,204 (Alpine) to 8,700 (Modoc) | 16,060 (Trinity) to 22,280 (Colusa) | ≤ 500,000 smaller/rural group | 39,538,22357 counties |
| Rate Swing From 1 Death | 11.49 to 83.06 per 100K | 4.49 to 6.23 per 100K | 0.20 to 6.23 per 100K | 0.01 to 0.05large urban |
| 1-Year Typical Rate Swing* | ±92.9 to ±249.6 per 100K | ±57.9 to ±68.3 per 100K | ±27.4 per 100Kpooled | ±1.38 per 100Kstate pool |
| Multi-Year Pooling Weight* | 89.0% pulled0.89 | 68.0% pulled0.68 | 24.0% pulledpooled | 6.0% pulledweighted |
| Deaths Averted per $10/Person | Suppressed <11 deaths/yr | Noise swamps 1-yr cut | -2.42 / 100Ksmaller counties | -2.38 yr-4.32 13-yr |
| Subgroup & Bootstrap Stability | High 1-yr outlier swing | High 1-yr rank churn | Matches urban counties-2.59 | Cluster-robust across 57 counties |
Table 1 Notes & * Modeled Estimates
Expand notes
Table 1 Notes & * Modeled Estimates. Frontier and small rural rate swings and shrinkage weights are Mode A calculations on California DOF county headcounts. The smaller-county (-2.42, SE = 0.98, p = 0.0136), statewide annual (-2.38, SE = 0.78, p = 0.0022), and 13-year cumulative (-4.32, SE = 1.54, p = 0.0052) results come from the 57-county CAPHE LHA panel (N = 943 pre-COVID county-years). In the Full 57-County column, ±1.38 per 100K is the Mode A 1-year Poisson rate SD at 750 per 100,000 across 39,538,223 residents. The ±0.78 per 100K margin in the effect row is the panel SE of the -2.38 per $10 coefficient.
Column Scope. Frontier Rural Group. Alpine (1,204) to Modoc (8,700). Small Rural Group. Trinity (16,060) to Colusa (22,280). Smaller-County Pool. Pop ≤ 500K Subsample (N = 671). All 57 Counties. 39.5M Pop (2003 to 2019, N = 943).
Two-Ruler Benchmark Summary. Mode A Rate Noise & Shrinkage on DOF County Headcounts; Source Estimates From the 57-County LHA Panel (2003-2019, N = 943). Ruler 1: Mode A Split of a 1-Year Drop After a Top-Decile Spike: -22.7 / 100K (89% Noise). Small rural counties have small headcounts (Trinity 16,060; Mariposa 17,131; Colusa 22,280). Mode A 1-year binomial standard errors on the county rate reach ±57.9 to ±68.3 per 100,000. Picking counties right after a 90th-percentile spike builds in -20.3 per 100,000 of automatic bounce-back. Ruler 2: Observed Multi-Year Panel Source Estimates: -2.42 Small | -4.32 Cumulative. Observed source estimates come from the 57-county pre-pandemic panel (2003 to 2019, N = 943 county-years). The model finds 2.42 fewer deaths per 100,000 per $10/person in smaller counties (p = 0.0136), -2.38 statewide annual (±0.78 margin), and -4.32 over 13-year cumulative horizons.
Method & Data Audit (TooEarlyToSay.com): Public Health Spending Regime Analysis →
Table 2. Small-County Context, Grant Tradeoffs & Policy Fit
How state grant teams and rural health leads avoid shifting grants on one-year random swings.
| Choice Factor | Frontier Rural Group | Small Rural Group | Smaller-County Pool | All 57 Counties |
|---|---|---|---|---|
| Local County Context | In frontier counties, one crash or flu cluster shifts the rate by 11 to 83 per 100K. | Small rural counties record 120 to 170 total deaths per year. | Smaller counties rely on public health staff as the main prevention net. | All 57 county health departments are tracked across 2003-2019 pre-COVID years. |
| What Multi-Year Pools Add | Pooled baselines keep tiny counties from flipping between top-spike and top-drop ranks each year. | A multi-year mean sets the base rate, so a +60/100K one-year jump is weighed against history. | Pooling years spots the -2.42 effect that one-year noise (±58 to ±250) swamps. | Separating 2020-2023 emergency COVID-19 grants (+2.47) isolates routine prevention (-2.38). |
| Budget Tradeoff | Tying base grants to 1-year death ranks destabilizes rural staff after a normal bounce-back. | Cutting a rural program after 2 or 3 extra deaths in one year disrupts clinic teams. | Smaller counties gain slightly larger annual returns (-2.42) than the state baseline (-2.38). | State grant rules can pair per-person funds with a fixed base floor for small counties. |
| Best-Fit Funding Rule | Use 5-Year Means & Shrinkage. Pull 1-year frontier rates by 0.89 toward regional medians before ranking counties for grants. | Compare Multi-Year Rural Pools. Score small rural grants on 3-to-5-year pooled rates matched against rural peers. | Anchor Rural Cases to -2.42. Use the smaller-county estimate (2.42 fewer deaths/100K per $10/person) in rural board briefs. | Fund Core Staff Over Multi-Year Horizons. Pair the -2.38 annual and -4.32 cumulative estimates. |
Table 2 Notes: Rate Noise Formula & Subgroup Stability Check
Expand notes
• Small-County Noise Math (Mode A on DOF Populations): At a base death rate of μ = 750 per 100,000 (0.0075), the 1-year Poisson SD per 100,000 is σ = 100,000 × √(0.0075 / N_pop). That equals ±249.6 per 100,000 in Alpine (N = 1,204), ±92.9 in Modoc (N = 8,700), and ±68.3 in Trinity (N = 16,060).
• Urban & Rural Subgroup Stability (Observed Source Estimates): Across all 57 counties over 2003 to 2019 (N = 943), routine public health spending is statistically significant in both smaller/rural counties (≤500,000 residents: -2.42 per $10, p = 0.0136) and large urban counties (>500,000 residents: -2.59 per $10, p < 0.0001) (CAPHE LHA Methodology).
• Panel Model Source: The -2.42 (smaller-county group), -2.38 (statewide annual TWFE OLS, N = 943), and -4.32 (13-year cumulative long-difference OLS, N = 57) estimates come from the CAPHE LHA panel over 2003 to 2019 (with Long-Difference Lewbel (2012) 2SLS yielding -5.31, F = 111.20). They are reported here as published source estimates.
• Extended Cell Context. Local County Context (Frontier Rural Group). In frontier counties (1,204 to 8,700 residents), one crash or flu cluster shifts the rate by 11 to 83 per 100K. · Local County Context (Small Rural Group). Small rural counties (16,060 to 22,280 residents) record 120 to 170 total deaths per year. · Local County Context (Smaller-County Pool). Smaller counties (≤500,000 residents, N = 671) rely on public health staff as the main prevention net. · Local County Context (All 57 Counties). All 57 county health departments are tracked across 2003-2019 pre-COVID years (N = 943). · Best-Fit Funding Rule (All 57 Counties). Pair the -2.38 annual ($420,168/life, 32:1) and -4.32 cumulative ($231,481/life, 59:1) estimates.
Why Base Funding Beats Chasing One-Year Spikes
Regression to the mean is a common hurdle in county grant design. Suppose an agency ranks California's 58 counties on one year of death data and sends short-term grants to the top tenth. Small rural counties under 25,000 residents top the list when a few random deaths swing their rate per 100,000 by 50 to 250 points. Next year, the rate drops back toward its long-run mean (-22.7 per 100,000) even without a program effect.
Health economics fixes this funding problem in two steps. First, for grant targeting, Empirical Bayes shrinkage and 3-to-5-year pooled means pull noisy small-county rates toward regional norms. Second, for impact review, multi-year panel models across all 57 counties (N = 943 pre-COVID county-years) show that steady public health funding in smaller counties averts 2.42 deaths per 100,000 per $10/person annually, matching the statewide 2.38 annual result and building to 4.32 per 100,000 over 13-year cumulative horizons.
Data Sources, Model Inputs, Notes & Endnotes
(Numbered endnotes [1]–[5], state data sources & math rules)
Expand details
Case Study Focus: Program Impact · Small-County Swings & Pooled Means (Mode A on Observed County Populations)
Numbered Endnotes & Main Sources
- [1]California County Public Health Panel (2003-2023): California State Controller and CDPH Vital Statistics (57 counties, N = 943 pre-COVID county-years; -2.42 deaths/100K per $10/capita in smaller/rural counties, -2.38 statewide annual, and -4.32 over 13-year cumulative horizons).
- [2]Small-County Headcounts & One-Year Swings: California Department of Finance E-1 Population Estimates and CDPH County Health Status Profiles. In Alpine County (1,204 residents), 1 death shifts the rate by 83.1 per 100,000, and 89.4% of a -22.7 per 100,000 post-spike drop is bounce-back to the multi-year mean.
- [3]Pooled Means & Grant Targeting Method: CAPHE Local Health Authority (LHA) Calculator Methodology (3-to-5-year pooled baselines and Empirical Bayes shrinkage weights).
- [4]California Department of Public Health (CDPH) Vital Statistics Death Statistical Master Files (2003-2023)
- [5]Brown (2014, Economics & Human Biology)
Mode Classification (Mode A on County Headcounts + Observed Panel Estimates): County resident counts (Alpine 1,204 to Los Angeles 9,721,138), the smaller-county estimate (-2.42, SE = 0.98, N = 671), the statewide annual estimate (-2.38, SE = 0.78, N = 943), and the 13-year cumulative estimate (-4.32, SE = 1.54, N = 57) are observed values in the CAPHE LHA corpus. One-year Poisson noise SDs, the bounce-back share, and shrinkage weights (B_i) are Mode A calculations on those county headcounts.
Primary Data Sources: California Department of Finance (DOF) E-1 Population Estimates, California Department of Public Health (CDPH) Vital Statistics Death Statistical Master Files (2003-2023), California State Controller's Office County Financial Transactions Reports, and Brown (2014, Economics & Human Biology).
Companion Method & Code Guides (TooEarlyToSay.com)
- Public Health Spending: When Emergency Aid Flips the Sign. Across 57 California counties from 2003 to 2023 (1,163 county-years), each dollar per capita corresponds to -0.238 fewer deaths per 100,000 in 2003 to 2019 versus +0.247 in 2020 to 2023.
Common Questions & Method Notes
- Why do small rural counties sit at the top and bottom of one-year death rankings?
- Death rates are scaled per 100,000 residents. One death in Alpine County (1,204 residents) moves the rate by 83.06 per 100,000. One death in Los Angeles County (9.72 million residents) moves the rate by 0.01 per 100,000.
- How does regression to the mean skew pre-post reviews of one-time grants?
- When counties get grants because they had a top-decile death spike in Year 1, that peak includes random upward noise. In Year 2, the random error averages zero and creates a modeled -20.3 per 100,000 bounce-back even with zero program effect.
- What does the 57-county panel show for public health funding in smaller counties?
- Across the 2003 to 2019 pre-pandemic panel (N = 943), every $10 per person in local public health funding is linked to 2.42 fewer deaths per 100,000 in smaller and rural counties (p = 0.0136), compared with 2.38 statewide annually and 4.32 over 13-year cumulative horizons.