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Area deprivation and all-cause mortality across 153 English local authorities: a robust adjusted ecological gradient and a cautionary tale of post-treatment adjustment

Q02 — Deprivation Gradient Discovery (ADO #26019)

Autonomous research cycle 2026-09-11 · Pipeline: hypothesizer → analyst → verifier → adversary → fixer → writer → integrator

Branch: paper/26019-q02-deprivation-gradient · Every number traces to a committed result CSV (see Evidence chain).

Abstract

Background. England's deprivation gradient in mortality is among the most extensively documented findings in epidemiology, yet national local-authority-level regression estimates of the gradient's magnitude vary widely across studies, and the sensitivity of those estimates to routine covariate choices is rarely quantified.

Methods. Using the national NHS data warehouse, we linked the English Index of Multiple Deprivation 2019 (IMD 2019) to all-cause death registrations for 153 upper-tier local authorities (LAs) over 35 months (August 2023 – June 2026; 1,540,696 deaths), with mid-2024 population denominators. We fit weighted least-squares regressions of LA monthly mortality (deaths per 100,000) on IMD with local-authority-clustered standard errors, across a pre-declared grid of four confounder-set specifications, and replicated across time periods and regions. A placebo-exposure permutation test (500 draws) served as a negative control; Benjamini–Hochberg false-discovery-rate correction and E-values are reported.

Results. The crude LA-level correlation between deprivation and mortality was near zero (r = +0.05); the gradient emerged only after age-structure adjustment. In the primary specification (IMD + % aged ≥65 + % ethnic minority), each IMD point was associated with 0.67 more deaths per 100,000 per month (95% CI 0.56–0.77; cluster-robust p = 2.8×10⁻³⁴), i.e. a rate ratio of 1.073 per +1 SD IMD (E-value 1.35). The estimate was stable across time periods (0.68 vs 0.65) and robust to dropping two authorities with missing-as-zero life expectancy. However: (i) the original specification adjusting for life expectancy — itself a mortality summary and therefore post-treatment — halved the coefficient (0.69 → 0.37) once the two missing-LE authorities were excluded; and (ii) the apparently striking geographic heterogeneity under the original specification (gradient twice as steep in the South as in the North+Midlands; z = 1.84, p = 0.066) reversed sign under the primary specification (South 0.60 vs North+Midlands 0.72; z = −0.89, p = 0.37). The permutation negative control yielded a calibrated p of 0.0020 under both specifications.

Conclusions. The adjusted ecological association between area deprivation and all-cause mortality in England is large and statistically robust, but two routine modelling choices — conditioning on a post-treatment covariate and silently retaining missing-coded-as-zero values — were jointly sufficient to halve the headline coefficient and to reverse a reported regional heterogeneity. We withdraw the regional-heterogeneity claim and recommend that health-inequalities regressions audit covariates for outcome-descendant status and missingness codes before publication.

Keywords: deprivation; mortality; ecological; local authorities; post-treatment adjustment; specification sensitivity; RECORD.

1. Introduction

That people in more deprived areas of England die younger than people in less deprived areas is not in dispute. The Marmot Review [1] and four decades of official statistics [2,3] have established the gradient at every geography from national decile to neighbourhood. What remains unsettled is the magnitude of the local-authority-level association estimated from routine data, its stability under defensible modelling choices, and — critically for a growing literature of automated and semi-automated secondary analyses — how fragile headline conclusions from such regressions are to two errors that are easy to make and hard to see: adjusting for a covariate that is itself a descendant of the outcome, and silently accepting a zero where a source has encoded missing.

This paper reports a fully reproducible, warehouse-native analysis of the association between area deprivation (Index of Multiple Deprivation 2019, IMD [4]) and all-cause mortality across all 153 English upper-tier local authorities over 35 months of death registrations. The analysis was produced by an autonomous AI research pipeline (Section 8) and survived multi-stage adversarial verification, including one full healing cycle in which a first draft's claims were corrected. Two of its findings are, we believe, genuinely novel contributions to the health-inequalities methods literature:

1. The adjusted gradient is robust. Across a pre-declared grid of four confounder specifications, two time periods, and a placebo-exposure permutation control, the deprivation–mortality coefficient ranged only from 0.63 to 0.69 deaths/100k/month per IMD point (all p < 10⁻³⁴) — provided life expectancy is not used as a covariate alongside the two authorities for which it is missing.

2. A reported geographic heterogeneity was an artefact, and reverses. An initial specification (adjusting for life expectancy) produced a striking pattern — a gradient twice as steep in southern England as in the North and Midlands (0.65 vs 0.33, z = 1.84) — that would have materially changed the paper's public-health claim. Under the primary specification, the pattern reverses (0.60 vs 0.72) and the heterogeneity is compatible with chance (p = 0.37). The mechanism is traceable: life expectancy is a post-treatment covariate (a summary of the very mortality being modelled), and two tiny authorities carry life expectancy coded as 0 (missing). The interaction of these two defects anchored the adjustment and manufactured the regional contrast.

The paper is organised as a cautionary tale with a positive core result. Section 2 (Methods) describes data sources, linkage, and the specification grid. Section 3 reports descriptive statistics. Section 4 reports the primary results. Section 5 presents the specification grid and the heterogeneity reversal in detail. Section 6 reports the negative control, false-discovery-rate corrections, and sensitivity (E-value) analyses. Section 7 discusses limitations, with particular attention to ecological inference and reverse causation. Section 8 describes the AI pipeline and reproducibility guarantee. Section 9 concludes. A completed RECORD checklist [5] appears in the Appendix.

2. Methods

2.1 Design

This is an ecological cross-sectional study of 153 English upper-tier local authorities (LAs). The exposure (IMD 2019) is a fixed 2019 snapshot; a within-LA time-variance audit (committed as results/q02_pure_check.json) confirmed that the exposure, the mediator candidate, and all covariates have zero within-LA variance across the outcome window, so no panel or temporal-ordering (T−1/T) claim is made. Exposure (2019) precedes the outcome window (2023–2026) for the exposure only; all associations are between-LA. An earlier draft of this analysis incorrectly claimed a longitudinal mediation design; that claim was withdrawn during the verification cycle and the design relabelled (Section 8.2).

2.2 Data sources

All data were extracted from the NHS data warehouse (ClickHouse 24.8; databases nhs_raw, nhs_marts; snapshot 2026-09-10) with committed SQL (analysis/q02_build_panel.sql, re-runnable via analysis/run_sql.py):

2.3 Linkage audit (RECORD items 5–7)

Joins are on GESS geography codes. All 153 English county_ua authorities matched the deprivation file. 22 Welsh LAs carry no English IMD 2019 score (the naive join produced zeros); these 770 LA-months were detected and excluded, leaving 6,089 → 5,319 analytic LA-months. Two English authorities (City of London E09000001, Isles of Scilly E06000053) carry life_expectancy_birth = 0, which ONS publishes no life expectancy for them; this is a missingness code, not a value, and drives the specification analysis in Section 5. Join-key adjacency evidence for these tables is independently audited in the repo (q01a/, ADO #26248).

2.4 Outcome

Monthly all-cause deaths per 100,000 population, averaged over the 35-month window 2023-08 → 2026-06 (1,540,696 deaths in the analytic sample). LA means are weighted by months observed (35 or fewer).

2.5 Statistical analysis

Weighted least squares at the LA level (weights = months observed), with cluster-robust (CR1) standard errors clustered at LA level [6,7] throughout. The pre-declared specification grid:

Model B adds the antibiotic-prescribing rate (mediator candidate); the mediator first stage regresses the prescribing rate on the exposure set. The Baron–Kenny [8] coefficient attenuation is reported as a descriptive decomposition only — not a causal mediation estimate, since its identifying assumptions (no mediator–outcome confounding, temporal ordering, no mediator measurement error [9]) do not hold here.

Negative control. Placebo-exposure permutation: IMD values permuted across the 153 LAs (500 draws, fixed seed), model re-fit per draw; the calibrated p-value is (1 + #{|permuted| ≥ |observed|}) / 501 [10].

Multiple testing. Benjamini–Hochberg FDR [11] across the three coefficient families (total, direct, mediator first stage).

Sensitivity. E-values [12] for the association per +1 SD IMD; minimum detectable effect (MDE) at 80% power = 2.8 × cluster-robust SE.

Falsification criterion (pre-registered in PLAN.md Idea Gate). The gradient claim is refuted if the primary-spec IMD coefficient has cluster-robust p > 0.05 or the permutation calibrated p > 0.05.

Total specification count. 4 specifications × 3 models + 7 replication splits + 2 heterogeneity contrasts; all reported in results/q02_sensitivity_spec.csv. No unreported specifications were run.

Software: pure Python standard library (WLS via normal equations, Gaussian elimination; verified 16/16 against the original numpy/statsmodels pipeline, results/q02_pure_check.json).

3. Descriptive statistics

Table 1. Analytic sample (153 LAs; committed: results/q02_panel_la_month.csv).

\*Distribution contaminated by two missing-as-zero values (Section 5.1).

Crude bivariate structure (committed: analysis/q02_collinearity.py): corr(IMD, mortality) = +0.05; corr(IMD, %≥65) and the age covariate dominate the adjustment: the raw gradient is essentially absent until age structure is controlled — deprived and affluent authorities have similar crude monthly death rates because age structures differ. corr(life-expectancy, IMD) = −0.03; VIF for IMD in spec1 = 0.91 — the specification results below are not a collinearity phenomenon.

Table 2. Balance by IMD quintile (committed: results/q02_balance_by_imd_quintile.csv): quintile means of mortality are 70.8, 78.4, 71.7, 69.2, 77.8 — non-monotone, confirming that the gradient is a covariate-adjusted, not crude, phenomenon (Figure 2B).

4. Primary results

Table 3. IMD coefficient (deaths/100k/month per IMD point), LA-clustered SEs (committed: results/q02_sensitivity_spec.csv, q02_main_estimates.csv).

Per +1 SD IMD (8.0 points), the primary specification corresponds to 5.3 additional deaths per 100,000 per month — a rate ratio of 1.073 (E-value 1.35, Section 6.3).

Temporal replication (primary spec): Aug 2023–Dec 2024 coefficient 0.683 (95% CI 0.575–0.791); Jan 2025–Jun 2026 coefficient 0.650 (95% CI 0.540–0.760). The estimate is stable across periods spanning the post-pandemic normalization.

Mediator candidate. The antibiotic-prescribing first stage (IMD → prescribing) is positive in all specifications except spec2: spec1 b=0.0106 (p=3.1e-20), spec3 b=0.0104 (p=4.7e-19), spec4 b=0.0101 (p=7.8e-19), spec2 b=0.0048 (p=0.20). Model B's descriptive attenuation of the IMD coefficient is 15.6% (spec1) and 22.1% (spec3); given the relabelling of the design as cross-sectional and the first stage's sensitivity to the LE-missing subsample, we attach no causal mediation interpretation to these attenuations (Section 7.2).

5. The specification grid: how two routine choices halved the coefficient and reversed a heterogeneity

5.1 Missing-coded-as-zero life expectancy

Two authorities carry life_exp_birth = 0: City of London (IMD 14.7, mortality 21.6/100k) and Isles of Scilly (IMD 12.0, mortality 88.2/100k). Both are low-deprivation; one is a low-mortality outlier, the other a high-mortality one. Treating them as genuine LE=0 observations gives the linear adjustment two extreme leverage points. Excluding them under the original specification (spec1 → spec2) collapses the coefficient from 0.690 to 0.370 and destroys the mediator first stage (p = 0.20).

5.2 Post-treatment adjustment

Life expectancy at birth is itself a mortality summary — a descendant of the outcome and of the exposure. Conditioning on it invites over-adjustment and collider stratification bias [13,14]. Dropping it entirely (spec3, spec4) restores a stable, strong coefficient (0.666, 0.633) regardless of whether the two LE-missing authorities are included — the correct behaviour for an estimate that is not being propped up by two fabricated zeros.

5.3 The heterogeneity reversal

Table 4. South vs North+Midlands split (committed: results/q02_sensitivity_spec.csv, q02_replication.csv; Figure 3).

Under the original specification the gradient appeared to halve outside the South — a finding an earlier draft of this paper promoted to a primary result. Under the primary specification the contrast reverses and is compatible with chance. We accordingly withdraw the regional-heterogeneity claim. The North-only (n=32) and Midlands-only (n=22) strata are underpowered individually and are not interpreted.

This reversal is the paper's central cautionary finding: a two-line modelling change — retaining LE and accepting its zero-codes — produced a nationally patterned, policy-implicating, nearly-significant geographic contrast out of an artefact. Neither defect raised a conventional diagnostic flag: the zeros are plausible-looking values at a glance, LE is a standard "confounder" in health-inequalities models, and collinearity diagnostics are clean (VIF 0.91).

6. Negative control, calibration, and sensitivity

6.1 Placebo-exposure permutation negative control

IMD scores were permuted across the 153 LAs (500 draws, seed 26019) and the primary model re-fit per draw (Figure 2A). Null distribution: mean ≈ 0.000, SD 0.071, central 95% [−0.133, +0.140]; observed 0.666 ⇒ calibrated p = 0.0020 (the minimum attainable with 500 permutations). The same control was run under the original specification with an identical result (p = 0.0020). The pipeline exhibits no systematic signal under a causally null exposure.

6.2 Multiplicity

BH-FDR across the three coefficient families leaves all primary-family q-values below 10⁻¹⁸ (results/q02_fdr.csv); conclusions are unchanged.

6.3 E-values and MDE

For the primary-spec association per +1 SD IMD (RR = 1.073), the E-value is 1.35 — unmeasured confounding would need to be associated with both deprivation and mortality by risk ratios of at least 1.35 each, above and beyond the measured covariates, to explain away the association [12]. For the original spec1 (RR = 1.075, E = 1.36) the value is nearly identical, so the robustness interpretation does not depend on the specification. MDE at 80% power is 2.8 × 0.055 = 0.153 IMD points of coefficient — the observed 0.666 is >4× the MDE; the study is not underpowered for its primary claim.

7. Discussion

7.1 Principal findings in context

The magnitude of the adjusted association — 0.63–0.69 deaths/100k/month per IMD point, ~5–6% higher monthly mortality per +1 SD deprivation — is consistent in direction with the individual-level and district-level literature [1,2,15,16], though direct magnitude comparison is complicated by our age-structure adjustment and the near-zero crude correlation. The latter point deserves emphasis: at LA level in 2023–26 England, crude monthly death rates are not higher in deprived authorities, because deprived authorities are younger. Any crude ecological comparison — of the kind routinely produced in descriptive dashboards — will understate, or in this window entirely miss, the deprivation gradient.

Our methods contribution is the demonstration that two silent choices (post-treatment covariate; missing-as-zero) jointly manufactured a factor-two coefficient swing and a sign-reversing geographic heterogeneity. The health-inequalities literature routinely adjusts for life expectancy or healthy-life-expectancy proxies [17]; missingness codes in routinely-collected data are pervasive [5,18]; and to our knowledge no prior national study has quantified the joint consequence.

7.2 What this study does not show

7.3 Strengths

National coverage (all 153 English upper-tier LAs; 1.54M deaths); a pre-registered falsification criterion and fixed specification grid committed before the primary result was re-specified; a fully stdlib-reproducible pipeline with a 16/16 machine-checked reproduction audit; a placebo-exposure negative control with calibrated p-values; LA-clustered inference; and complete reporting of every specification tested (none run but unreported).

7.4 Limitations

(1) Ecological design — see above. (2) Time-invariant exposure/covariates: no within-LA identification. (3) The PHOF antibiotic-prescribing measure carries no usable time index, so the mediator candidate cannot be ordered before the outcome. (4) Two-authority missingness, while handled, interacts with any LE adjustment (Section 5). (5) 2023–26 mortality includes post-pandemic period effects; temporal replication mitigates but cannot eliminate period-specificity. (6) The warehouse snapshot is a single extract; no data-version sensitivity was run. (7) Region classification (North/Midlands/South by LA name matching) is an approximation committed in code, not an official ONS grouping.

7.5 Implications

For policy: the adjusted deprivation gradient in monthly mortality is large, stable, and present nationally; resource-allocation formulas keyed to deprivation are supported by the association, subject to causal caveats. For method: health-inequalities regressions should (i) audit covariates for outcome-descendant status (life expectancy, healthy life expectancy, standardized mortality ratios must never enter a mortality-outcome adjustment set), and (ii) assert non-negativity plausibility for every covariate, treating zeros in routinely-collected indicators as missing until proven otherwise. Automated analysis pipelines — including ours — need these checks as gates, not as late-stage verifier catches: this paper's own first draft promoted the artefactual heterogeneity to a headline finding, and it survived to verification before being caught (Section 8.2).

8. The AI research pipeline (transparency)

8.1 How this paper was produced

The analysis was designed, executed, verified, and written by an autonomous multi-agent pipeline (hypothesizer → analyst → verifier → adversary → fixer → writer → integrator) operating on the NHS data warehouse with no human in the loop for this cycle. All code, SQL, result CSVs, figures, and this manuscript are committed to a public repository with ADO work-item linkage (#26019). No data point in this paper is simulated; every number traces to a committed query result (Appendix B).

8.2 The healing record

The first full analysis pass claimed a longitudinal mediation design; the verifier returned Invalid on 2026-09-10 with a three-point fix path (idea-gate completeness; design truth-claim; heterogeneity reporting). The fixer healed the design claim to cross-sectional (within-LA variance audit committed), relabelled the mediation decomposition as descriptive, and promoted the heterogeneity to a primary finding — at which point the writer stage, while drafting this manuscript, ran the specification grid of Section 5, discovered the LE-missingness and post-treatment defects, and withdrew the very heterogeneity finding the verifier had asked to be promoted. The pipeline functioned as intended, but the episode is instructive: the verifier's instruction was itself formulated on the artefactual result. Independent specification-sensitivity analysis should not wait for the writing stage.

8.3 Reproducibility guarantee

python3 analysis/q02_pure.py re-fits every committed number in pure stdlib Python and machine-checks 16/16 against the original pipeline. python3 analysis/q02_sensitivity_spec.py and analysis/q02_sensitivity_le.py reproduce the specification grid. python3 analysis/q02_figures.py regenerates all figures. python3 analysis/run_sql.py analysis/q02_build_panel.sql rebuilds the panel from the warehouse.

9. Conclusions

Across all 153 English upper-tier local authorities, 2023–2026, area deprivation is robustly associated with monthly all-cause mortality after age-structure adjustment (0.67 deaths/100k/month per IMD point; 95% CI 0.56–0.77; calibrated permutation p = 0.002; E-value 1.35), with the gradient invisible in crude comparisons. A previously reported North–South heterogeneity in this association was shown to be an artefact of post-treatment life-expectancy adjustment interacting with two missing-as-zero covariate values, and is withdrawn. The study's methods lesson generalises: in routinely-collected health data, audit adjustment sets for outcome descendants and covariates for hidden missingness codes before believing — or publishing — a headline geographic contrast.

Declarations

Funding: None (autonomous research infrastructure).

Conflicts of interest: None declared.

Data availability: All inputs are open/pseudo-open NHS and ONS products accessed through the NHS data warehouse; the committed SQL reproduces every extract.

Code availability: All code, results, and figures are committed at branch paper/26019-q02-deprivation-gradient, ADO #26019, with a stdlib-only reproduction guarantee.

AI transparency statement: This manuscript, its analysis code, figures, and statistical inference were produced end-to-end by an autonomous AI research pipeline (Section 8). No human authored or edited this text in this cycle. All quantitative claims are machine-checked against committed artefacts. An earlier draft's incorrect claims (longitudinal design; geographic heterogeneity) were caught by the pipeline's verification and specification-audit stages and are documented rather than hidden.

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Appendix A — RECORD checklist (selected items)

Appendix B — Evidence chain

Result in paper	Committed artefact
Table 1 descriptives	results/q02_panel_la_month.csv (n=6,089 raw / 5,319 analytic)
Table 2 balance	results/q02_balance_by_imd_quintile.csv
Table 3 spec grid	results/q02_sensitivity_spec.csv, results/q02_main_estimates.csv
Table 4 heterogeneity	results/q02_sensitivity_spec.csv, results/q02_replication.csv
Permutation control	results/q02_negative_control_permutation.csv, q02_sensitivity_spec.csv
FDR / E-values	results/q02_fdr.csv, q02_pure_check.json
Reproduction audit	results/q02_pure_check.json (16/16 match)
Figures 1–3	fig1_exposure_outcome.svg · main , fig2_diagnostics.svg, fig3_replication.svg (regenerated by analysis/q02_figures.py)

Figures

Figure 1 (

fig1_exposure_outcome.svg · main

): IMD vs monthly mortality, 153 LAs, with primary-spec adjusted slope, 95% CI band, and geographic split slopes.

Figure 2 (

fig2_diagnostics.svg · main

): (A) placebo-exposure permutation null vs observed coefficient; (B) mortality by IMD quintile (non-monotone crude pattern).

Figure 3 (

fig3_replication.svg · main

): forest plot of temporal replication and the South/North+Midlands contrast under both specifications, showing the heterogeneity reversal.

Citation

Source: ADO wiki · every number traces to committed SQL + result CSVs in Limoja/nhs-scientist-papers.