Wakefield (2007) Disease Mapping and Spatial Regression with Count Data

Summary

A critical review of Bayesian hierarchical methods for aggregate count data in spatial epidemiology, covering both disease mapping (estimating area-level relative risks) and spatial ecological regression (relating area risk to area-level exposures). Wakefield introduces a new, interpretable way to choose priors for the variance parameters, refines the standard conditionally-autoregressive (CAR/BYM) models, and works through ecological bias, mutual standardization, and the interplay of spatial model and prior. The running example is the canonical Scottish male lip-cancer data (1975–1980), for which he documents problems in earlier analyses.

Key Claims

• Disease mapping vs. ecological regression are very different risks. For mapping, hierarchical (Poisson + spatial random effect) models give robust area-risk estimates — but the covariate model, the choice of spatial model, and the priors on the variance parameters all matter and need sensitivity checks. For ecological regression, the enterprise is "far more hazardous."
• Ecological bias. An area-level exposure–disease association need not reflect the individual-level relationship (the ecological fallacy); this bias can only be alleviated by bringing in individual-level data. For the Scottish data the previously-used mean model has "limited interpretation from an individual perspective."
• Spatial confounding. When residual spatial dependence is modelled and the exposure is itself spatially structured, the random effect and the exposure compete to explain the same variation, so estimates of the exposure association are distorted — a fundamental caution for spatial ecological regression.
• Prior specification on an interpretable scale. Wakefield proposes choosing the variance-component priors by their implications for interpretable quantities (e.g. the marginal standard deviation / range of relative risks a random effect implies), rather than the reflexive $\mathrm{IG}(\epsilon,\epsilon)$ default — a theme he develops further with Fong and Rue.
• Model refinements. Refinements of the Besag-York-Mollié convolution prior (structured CAR + unstructured heterogeneity), attention to identifiability/propriety, and mutual standardization of expected counts.
• Recommendations. Report sensitivity to the spatial model and to variance priors; treat ecological-regression exposure effects with skepticism absent individual data.

Concepts Introduced or Extended

• Conditional Autoregressive Model

Entities Mentioned

• Jon Wakefield

Quotes

"In disease mapping studies, hierarchical models can provide robust estimation of area-level risk parameters, though care is required in the choice of covariate model, and it is important to assess the sensitivity of estimates to the spatial model chosen, and to the prior specifications on the variance parameters."

"Spatial ecological regression is a far more hazardous enterprise ... there is always the possibility of ecological bias, and this can only be alleviated via the inclusion of individual-level data."

My Take

This is the review that tells you what actually goes wrong with the CAR/BYM disease-mapping machinery the wiki catalogues under conditional autoregressive models, and its two warnings are the durable ones. First, prior choice is not innocuous: the improper intrinsic CAR plus a knee-jerk $\mathrm{IG}(\epsilon,\epsilon)$ variance prior can drive the smoothing, so priors should be set on the scale of interpretable relative-risk variation — exactly the discipline later formalized in Fong-Rue-Wakefield (2010). Second, and more fundamental, spatial ecological regression is dangerous: ecological bias means area-level associations may not hold for individuals, and modelling residual spatial dependence confounds a spatially-structured exposure — so a "significant" exposure effect in a smoothed spatial model can be an artifact. For the wiki it is the applied-epidemiology capstone on the spatial-random-effects thread: the CAR and GLMM pages give the machinery, and Wakefield supplies the cautionary judgment about when it estimates something meaningful.