Discrete Log-Gaussian Cox Processes for Aggregated Disease Counts

Fits a spatially discrete approximation to a log-Gaussian Cox process model for spatially aggregated disease count data, estimated by Monte Carlo Maximum Likelihood as in Christensen (2004) and Johnson, Diggle and Giorgi (2019) . Performance-critical steps (aggregated correlation assembly, Metropolis-adjusted Langevin algorithm (MALA) sampling, the Monte Carlo likelihood, and the Kronecker-structured space-time likelihood) are implemented in C++ via 'RcppArmadillo'. Provides a one-line, 'glm'-like interface and statistical extensions including a nugget term, general 'Matern' smoothness, raster and misaligned covariates, restricted spatial regression, importance-sampling diagnostics and re-anchored Monte Carlo maximum likelihood (MCML).

SDALGCP2

Fast, modern disease mapping. SDALGCP2 fits a spatially discrete approximation to a log-Gaussian Cox process (SDA-LGCP) to spatially aggregated disease counts, with a one-line, glm-like interface and C++ speed. The method is described in Johnson, Diggle & Giorgi (2019, Statistics in Medicine, doi:10.1002/sim.8339).

Installation

# install.packages("remotes")
remotes::install_github("olatunjijohnson/SDALGCP2")

You need a C++ toolchain (Rtools on Windows, Xcode CLT on macOS) because the performance-critical kernels are compiled.

Quick start — one line to fit

data is an sf object whose columns hold the response, covariates and offset. Everything else (candidate-point spacing, the spatial scale, MCMC settings) is chosen automatically.

library(SDALGCP2)

fit <- sdalgcp(cases ~ deprivation + offset(log(population)), data = regions)

summary(fit)              # glm-style coefficient table + spatial parameters
rr  <- predict(fit)       # an sf: relative_risk, relative_risk_se, adjusted_rr, adjusted_rr_se
plot(fit)                 # relative-risk map
plot(fit, "exceedance", threshold = 1.5)   # hotspot probabilities

That is the whole workflow. The same sdalgcp() call also covers:

What you get

Relative risk	Uncertainty (SD)	Exceedance P(RR > 1.5)	Continuous surface

Why SDALGCP2

• Easy: sdalgcp(formula, data) — feels like glm(); sensible defaults so a first fit needs no tuning.
• Fast: aggregated correlation assembly, the MALA sampler and the Monte Carlo likelihood run in C++ (RcppArmadillo + OpenMP) — 8–10× faster end-to-end than the original, returning the same estimates (see Performance).
• Grid-free scale: the spatial scale φ is optimised continuously by default (no grid), with a proper standard error — see the derivation PDF.
• Continuous covariates done right: rasters enter on the intensity scale (log-sum-exp), not by averaging predictors over polygons — see the raster PDF.
• Spatio-temporal without ever forming the (N·T)² covariance.
• Honest uncertainty: re-anchored Monte Carlo likelihood, importance-sampling diagnostics, a nugget term, model checking (residual Moran's I).

Tutorials

See the package website for worked, reproducible articles:

• Spatial disease mapping — the full workflow end to end.
• Raster predictors — intensity-scale covariates vs naive areal averaging.
• Spatio-temporal — space-time relative risk.
• Estimating the scale — grid (scale = "grid") vs continuous (scale = "continuous") φ.

Reference

Johnson, O., Diggle, P. & Giorgi, E. (2019). A spatially discrete approximation to log-Gaussian Cox processes for modelling aggregated disease count data. Statistics in Medicine 38, 4871–4887. \doi{10.1002/sim.8339}