Analytical Methods

20+ methods from bivariate correlations through Bayesian spatial models and risk-factor gauntlets, ordered by increasing rigor. Each successive method addresses a limitation of the previous.

Study Design Overview

This is a county-level ecological study. The unit of observation is the US county (n=3,248). The exposure is agricultural pesticide application density (kg/mi², 2019 USGS PNSP estimates). The outcomes are age-adjusted cancer incidence rates (per 100,000, 2016–2020 NCI State Cancer Profiles). We control for 9–13 confounders depending on model specification.

Confounders

1. Bivariate Correlations

Spearman Rank Correlations

Non-parametric correlations between pesticide density and each cancer type. Does not control for confounders; establishes whether any crude association exists. Spearman is robust to non-normal distributions common in county-level health data.

Partial Correlations

Spearman correlations controlling for 9 confounders simultaneously. Tests whether the pesticide–cancer association survives basic confounding control.

Volcano plot of bivariate and partial correlations
Figure 1. Volcano plot of Spearman correlations between environmental/demographic predictors and cancer rates. Correlation magnitude on x-axis, −log10(p) on y-axis. Points above the horizontal line are significant after FDR correction.

2. Multivariate Regression

OLS Regression

Standard ordinary least squares with all confounders. Provides interpretable coefficients but assumes independent observations (violated by spatial autocorrelation).

LASSO (L1 Regularization)

LASSO selects the most predictive variables from 29 candidates via cross-validation. Pesticide is retained among the top 10 selected variables, confirming it adds predictive value beyond the other confounders.

LASSO regularization path showing variable selection
Figure 2. LASSO regularization path for all-site cancer. As the penalty parameter increases (left to right), variables drop out. Pesticide survives until moderate penalization, among the last 10 variables selected.

PCA + Regression

Principal Component Analysis on the pesticide variables (total, herbicide, insecticide, fungicide) to address multicollinearity among pesticide subtypes.

PCA scree plot for pesticide variables
Figure 3. PCA scree plot. The first principal component explains >80% of pesticide variance, representing overall pesticide intensity. PC2 separates herbicide-dominant from insecticide-dominant counties.

3. Spatial Regression

Moran’s I & LISA

Global Moran’s I confirms significant spatial autocorrelation in cancer rates (I > 0.3 for most types). LISA (Local Indicators of Spatial Association) identifies hot/cold spot clusters. This motivates the use of spatial regression models.

Spatial Error & Spatial Lag Models

Spatial Error models account for spatially correlated residuals (unobserved spatially varying confounders). Spatial Lag models account for spillover effects between neighboring counties. Spatial Error wins for 43 of 44 cancer-type tests by AIC.

Geographically Weighted Regression (GWR)

GWR allows coefficients to vary locally, revealing spatial heterogeneity in the pesticide effect. Bandwidth = 133 counties; mean R² = 0.495. About 9% of counties show significant positive pesticide effects, 7.5% significant negative, and 83.4% non-significant.

Spatial Durbin Model

Incorporates both spatially lagged dependent variable and spatially lagged covariates. Wins by AIC (21,312) over Spatial Error (29,246) and Spatial Lag (29,309), indicating that both neighbor effects and spillovers matter.

4. Causal Identification

Instrumental Variables (IV/2SLS)

Uses total crop acreage as an instrument for pesticide application. Crop acreage predicts pesticide use (first-stage F=377.8) but should not directly cause cancer except through pesticide exposure. The IV estimate (0.035) exceeds OLS (0.019), suggesting attenuation bias from measurement error rather than confounding bias.

IV first stage scatter plot
Figure 4. First-stage relationship: total crop acreage per square mile strongly predicts total pesticide application per square mile (F=377.8).

Long-Difference Estimator

Computes Δpesticide (2012 minus 1997) and Δcancer rate for each county. By examining within-county changes over 15 years, this eliminates all time-invariant confounders. Controls for 11 baseline covariates. Kidney (β=0.068, p=0.003) and colorectal (β=0.079, p<0.001) are significant; all-site and NHL are null.

5. Bayesian Spatial Models (BYM2)

The BYM2 (Besag-York-Mollié 2) model is the gold standard for disease mapping. It decomposes county-level variation into:

High ρ values (0.93–0.99) indicate most residual variation is spatially structured, meaning the spatial random effects absorb substantial unmeasured spatial confounding. The fact that pesticide effects survive this aggressive spatial smoothing is notable.

Model Specifications

v1 (9 covariates): demographics + health behaviors + SES.
v2A (12 covariates): + binge drinking, food insecurity, food access.
v2B (13 covariates): + nitrate water contamination (key agricultural confounder test).
All models: 3,000 tuning + 1,500 draw iterations, nutpie sampler, Poisson likelihood with expected-count offset.

6. Compound & Pathway Analysis

Compound-Specific BYM2

12 individual compounds tested in separate BYM2 models (each with 12 baseline covariates). Six herbicides, three insecticides, three fungicides. Tests whether the signal is driven by specific chemical classes or is a generic agricultural-intensity artifact.

Exposure Pathway Stratification

BYM2 models run separately on urban (RUCC 1–3) and rural (RUCC 4–9) county subsets. If the association were purely occupational, we would expect it only in rural counties. Similar RRs in both strata suggest dietary or ubiquitous environmental exposure.

7. Positive Control Validation

The PM2.5–lung cancer relationship is well-established (meta-analytic RR ≈ 1.10–1.15 per 10 μg/m³). We tested this in our pipeline: the IV/2SLS estimate yields a 17.9% relative increase per 10 μg/m³, consistent with published estimates. This confirms the pipeline can detect known environmental carcinogens.

Methods Comparison

Analysis Pesticide Effect Spatial Control Interpretation
Spearman CorrelationPositive, significantNoneCrude association exists
Partial CorrelationPositive, significantConfounders onlySurvives basic confounding
OLS RegressionPositive, significantNoneMultivariate effect is small but real
LASSO SelectionSelected (10/29 vars)RegularizationAdds predictive value
Spatial Error ModelAttenuatedSpatial autocorrelationWins for 43/44 cancer types
GWR9% sig+, 7.5% sig−Locally varyingSpatially heterogeneous
Spatial DurbinLowest AIC modelSpillovers + lagNeighbor effects matter
IV / 2SLSIV > OLS (0.035 vs 0.019)Endogeneity (F=377.8)OLS biased toward zero
Long-Diff Kidneyβ=0.068, p=0.003Within-county ΔTemporal variation confirms signal
Long-Diff Colorectalβ=0.079, p<0.001Within-county ΔTemporal variation confirms signal
BYM2 v1 All-SiteNull (RR ≈ 1.00)Full BYM2 (ρ=0.997)Spatial RE absorbs all-site signal
BYM2 v1 KidneyRR=1.025, P(>0)=0.997Full BYM2 (ρ=0.986)SURVIVES spatial smoothing
BYM2 v1 ColorectalRR=1.015, P(>0)=0.991Full BYM2 (ρ=0.989)SURVIVES spatial smoothing
BYM2 v2B KidneyRR=1.034, P(>0)=0.997+ nitrate (ρ=0.971)ROBUST to agricultural confounding
BYM2 v2B ColorectalRR=1.018, P(>0)=0.991+ nitrate (ρ=0.939)ROBUST to agricultural confounding
Compound BYM2Herbicides sig, insecticides NSCompound-level BYM2Chemical class specificity
Neg ControlsLivestock/diabetes NSAlternative exposuresNot agricultural intensity
Pathway BYM2Urban RR ≈ Rural RRStratified BYM2Dietary/ubiquitous pathway
Smoking GauntletPest kidney survivesCovariate in BYM2Independent of smoking
Obesity GauntletBoth kidney covariates sigCovariate in BYM2Independent risk pathways
Alcohol GauntletPest CRC survives (alcohol NS)Covariate in BYM2Not alcohol confounding
Inactivity GauntletBoth pest covariates surviveCovariate in BYM2Independent of inactivity
Exploratory ScreenPest top for kidney/CRC26 cancers × all predictorsHypothesis-free confirmation

8. Risk Factor Gauntlets

Each IARC-established carcinogen (smoking, obesity, alcohol, physical inactivity) is tested as a primary exposure across 12 cancer types using three methods: BYM2, long-difference, and IV/2SLS. The pesticide covariate is included in every gauntlet model to test whether it survives as a covariate.

This design tests two things simultaneously: (1) whether each risk factor itself shows expected IARC-linked cancer patterns, and (2) whether pesticide associations are independent of that risk factor. See full results on the Gauntlets page.

9. Exploratory Screening

A hypothesis-free scan of all available predictors against all 26 cancer types. Four analytical layers:

This complements hypothesis-driven analysis by asking: among all possible predictors, does pesticide emerge as a top correlate for the same cancer types identified by BYM2? See Exploratory page.

10. Temporal Cancer Panel

Cancer incidence panel data from CDC EPHT (9 cancer types, 16 rolling 5-year windows from 2001–2020, 2,727 counties). Animated choropleth maps show how geographic patterns evolve over time. Combined with pesticide application trends and health behavior trends from County Health Rankings. See Temporal Trends page.

11. Sensitivity Analyses