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Stat Med. 2013 Jun 15;32(13):2308-19. doi: 10.1002/sim.5600. Epub 2012 Sep 7.

Bayesian modeling of time-dependent vulnerability to environmental hazards: an example using autism and pesticide data.

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Public Health Institute, Richmond, CA, USA.



Flexible modeling of time-dependent effects is required when vulnerability to hazards can be expected to vary over time, but the nature of this temporal dependency cannot be specified in advance. We present an analytic approach requiring minimal a priori assumptions about temporal parameters and producing measures of uncertainty for these parameters.


As a demonstration, we employ data describing autism spectrum disorders and applications of organochlorine pesticides in proximity to maternal residence before, during, and after pregnancy. We formulate a Bayesian model specifying temporal vulnerability as a flexible step function and constrain the dose-response relationship to be linear. We separately pooled information regarding hazard frequency and magnitude among cases and controls and used it as inputs for a Metropolis-within-Gibbs algorithm. To assess statistical significance, we conduct Monte Carlo simulations based on parameters calculated in the Gibbs portion of the algorithm.


This method delineated two discrete periods of association between hazard and outcome. The first corresponded to a previously noted period of vulnerability with the added information of wide credible intervals, suggesting a high degree of uncertainty with respect to timing. Parameters for the second, previously unobserved period displayed slightly higher precision. Assessment of model fit favored the simultaneous inclusion of both these periods, and both periods appeared statistically significant on the basis of posterior distributions of specific parameters using Monte Carlo simulations.


This method enabled a fuller accounting of time-dependent associations between hazards and outcomes without specifying temporal structure in advance.

[Indexed for MEDLINE]

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