Modelling Spatial Risk for Suicides by LSOA in Cornwall County

A Bayesian spatial risk assessment using Intrinsic Conditional Autoregressive (ICAR) modeling to analyze suicide risk patterns across Lower Layer Super Output Areas (LSOAs) in Cornwall, England.

Project Overview

This project investigates the spatial variation in suicide risk across Cornwall County using a Zero-Inflated Negative Binomial (ZINB) model with spatial random effects. Cornwall presents a unique case study as it recorded the second-highest suicide counts in 2022 despite being only the 40th most populous county in England.

Research Objectives

• Analyze spatial patterns of suicide risk at the LSOA level in Cornwall
• Investigate the relationship between area-level deprivation and suicide incidence
• Account for spatial autocorrelation and overdispersion in sparse count data
• Identify areas with elevated suicide risk for potential public health intervention

Data Sources

Outcome Variable

• Suicide Counts (2023): Number of registered suicides per LSOA
  • Source: Office for National Statistics (ONS)
  • Geographic Unit: 336 LSOAs in Cornwall County
  • Average population per LSOA: ~1,500 people

Covariates

• Index of Multiple Deprivation (IMD) 2019: Composite deprivation measure across seven domains

  • Source: Ministry of Housing, Communities and Local Government
  • Domains: Income, employment, health, education, crime, housing, environment

• Small Area Mental Health Index (SAMHI): Composite annual mental health measure

  • Source: SAMHI dataset
  • Components: NHS mental health attendances, antidepressant prescriptions, QOF depression data, DWP mental health benefit claims

Methodology

Model Selection

Two modeling approaches were compared using Leave-One-Out (LOO) cross-validation:

1. Negative Binomial with ICAR spatial effects
2. Zero-Inflated Negative Binomial (ZINB) with ICAR spatial effects (selected model)

Model Specification

The final ZINB-ICAR model addresses:

• Excess zeros: High proportion of LSOAs with zero suicide counts
• Overdispersion: Variance exceeding that expected under Poisson distribution
• Spatial autocorrelation: Dependence between neighboring areas

Model Structure:

ϕ ~ ICAR(N, node1, node2)
Y ~ Negative Binomial(log(E) + α + β_imd*X + β_samhi*L + σ*ϕ)

Priors:
α ~ Normal(0.0, 1.0)
β_imd ~ Normal(0.0, 1.0)
β_samhi ~ Normal(0.0, 1.0)
σ ~ Normal(0.0, 1.0)
Sum(ϕ) ~ Normal(0.0, 0.001*N)

Key Findings

Model Parameters

Parameter	Mean	95% CI	Interpretation
α (Baseline)	-1.38	(-2.83, -0.06)	Generally low suicide counts
β_imd (Deprivation)	0.52	(-0.52, 1.50)	Positive but non-significant association
β_samhi (Mental Health)	-0.30	(-1.40, 0.79)	Negative but non-significant association
σ (Spatial variation)	1.88	(1.20, 2.62)	Significant spatial overdispersion
φ_nb (Zero-inflation)	18.25	(0.63, 53.96)	High proportion of zero counts

Spatial Results

• No LSOAs showed statistically significant deviations in suicide risk
• Substantial variation in point estimates suggests potential spatial heterogeneity
• ICAR spatial smoothing may have attenuated extreme local values

Technical Requirements

Software Dependencies

• Stan: Bayesian modeling framework
• R: Statistical computing environment
• Required R packages:
  • rstan or cmdstanr
  • loo (model comparison)
  • sf (spatial data handling)
  • ggplot2 (visualization)
  • bayesplot (Bayesian diagnostics)

Data Format

• LSOA boundary files (shapefile format)
• Suicide count data (CSV format)
• IMD scores by LSOA
• SAMHI scores by LSOA
• Spatial adjacency matrix for ICAR model

Model Performance

• Successfully handles excess zeros and overdispersion
• ICAR component provides spatial smoothing while preserving local patterns
• Zero-inflation parameter indicates model appropriately captures data structure