Table 2.
Estimated Birth Weightsa (Bayesian g-Computation) for 27,103 Live Births Under a Hypothetical Intervention to Decommission 3 Coal-Fired Power Plants and Mean Difference Between the Natural Course of Events and the Intervention, Milwaukee, Wisconsin, 2011–2013
| Model b , c , d | No Intervention | Decommissioning of Power Plants | Mean Difference | |||
|---|---|---|---|---|---|---|
| Mean BW, g | 95% CrI e | Mean BW, g | 95% CrI e | BW Difference, g | 95% CrI e | |
| Primary analysis | ||||||
| A. All terms, hierarchical, selection | 3,191 | 3,184, 3,198 | 3,259 | 3,215, 3,326 | 68 | 25, 135 |
| Sensitivity analyses | ||||||
| B. Main terms only, hierarchical, selection | 3,191 | 3,184, 3,198 | 3,260 | 3,217, 3,327 | 69 | 27, 136 |
| C. All terms, hierarchical, relaxed selection | 3,191 | 3,184, 3,198 | 3,259 | 3,214, 3,330 | 68 | 24, 139 |
| D. All terms, hierarchical, aggressive selection | 3,191 | 3,184, 3,198 | 3,257 | 3,209, 3,326 | 66 | 19, 134 |
| E. All terms, hierarchical, smoothing spline on maternal age | 3,191 | 3,184, 3,198 | 3,257 | 3,214, 3,320 | 66 | 24, 129 |
| F. All terms, hierarchical, selection with t-distribution slab prior | 3,191 | 3,184, 3,198 | 3,254 | 3,210, 3,313 | 63 | 20, 122 |
| G. All terms, hierarchical, no selection on confounder main terms | 3,191 | 3,184, 3,198 | 3,231 | 3,188, 3,300 | 40 | 0, 109 |
| H. All terms, hierarchical, no selection on any main term | 3,191 | 3,184, 3,198 | 3,319 | 3,219, 3,419 | 128 | 29, 228 |
| I. No selection, nonhierarchical, main terms only | 3,191 | 3,184, 3,198 | 3,320 | 3,221, 3,419 | 129 | 31, 228 |
| J. No selection, hierarchical | 3,191 | 3,184, 3,198 | 3,432 | 2,966, 3,897 | 241 | −224, 706 |
| K. No selection, hierarchical with uniform priors | 3,191 | 3,184, 3,198 | 3,432 | 2,967, 3,896 | 241 | −223, 705 |
| L. No selection, nonhierarchicalf | 3,191 | 3,184, 3,198 | 3,772 | 2,675, 4,872 | 581 | −516, 1,681 |
| M. Maximum likelihood | 3,191 | 3,184, 3,199 | 3,768 | 2,627, 4,901 | 577 | −561, 1,707 |
Abbreviations: BW, birth weight; CrI, credible interval.
a Estimates are given as the posterior mean value and its 95% CrI over 36,000 Markov chain Monte Carlo iterations across 8 independent chains, except for the maximum likelihood model (model M), in which 95% confidence intervals were estimated using quantiles of the nonparametric bootstrap distribution across 10,000 iterations. Variables included in each model included standardized (to have a mean of 0 and a standard deviation of 1) variables for each metal, standardized maternal age at birth (years; continuous), maternal race/ethnicity (4 categories: non-Hispanic White, Hispanic White, non-Hispanic Black, and non-Hispanic any other race), maternal smoking during pregnancy (yes/no), maternal married status (yes/no), and female child sex (yes/no). Prior distributions for models A–L are given in Web Table 1.
b As described in the text. Models included main terms for all variables and all first-order interaction terms unless otherwise noted.
c Main terms and interaction terms given separate, hierarchical normal priors unless otherwise noted (see Table 1 for prior distributions).
d Bayesian model averaging or “selection” using a “spike-and-slab” prior, where the spike is a point mass at 0 and the slab has a normal, hierarchical prior unless otherwise noted (see Table 1 for prior distributions).
e Ninety-five percent CrIs given by the 2.5th and 97.5th percentiles of the estimated posterior distribution, except in model M (95% confidence intervals), where percentiles are from the nonparametric bootstrap distribution.
f Model coefficients given independent standard normal priors.