Administrative censoring in ecological analyses of autism and a Bayesian solution

Abstract

Widely cited ecological analyses of autism have reported associations with mercury emissions, with precipitation, and race at the level of counties or school districts. However, state educational agencies often suppress any low numerical autism counts before releasing data--a phenomenon known as "administrative censoring." Previous analyses did not describe appropriate methods for censored data analysis; common substitution or exclusion methods are known to introduce bias and produce artificially narrow confidence intervals. We apply a Bayesian censored random effects Poisson model to reanalyze associations between 2001 Toxic Release Inventory reported mercury emissions and 2000-2001 autism counts in Texas. Relative risk estimates for autism decreased from 4.44 (95% CI: 4.16, 4.74) per thousand lbs. of air mercury emissions using a naive zero-substitution approach to 1.42 (95% CI: 1.09, 1.78) using the Bayesian approach. Inadequate attention to censoring poses a serious threat to the validity of ecological analyses of autism and other health outcomes.

Figure 1

Autism prevalence versus Toxic Release Inventory reported air mercury emissions, with threes substituted for censored values (c = 3) for all data points. Lines show the covariate-adjusted random effects Poisson model predictions using five different fixed value substitution approaches (substituting different values of c for the censored counts).

Algorithm 1

WinBUGS code.