Keil et al. Respond to "Causal Inference for Environmental Mixtures".
Keil et al. Respond to "Causal Inference for Environmental Mixtures".
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凯尔等人。
DOI：
10.1093/aje/kwab143
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发表时间：
2021
影响因子：
5
通讯作者：
Kalkbrenner,AmyE
中科院分区：
文献类型：
--
作者：
Keil,AlexanderP;Buckley,JessieP;Kalkbrenner,AmyE
We thank Dr. Zigler for writing an insightful commentary (1) that nicely summarizes appealing aspects of our work and offers helpful criticism. We had raised many of the points ourselves in our article (2) and appreciate the opportunity to more fully address others. We used a Bayesian approach to estimate a joint effect of airborne metals exposure on infant birth weight that reflects a useful public health question: Would decommissioning coal-fired power plants improve birth outcomes? Dr. Zigler’s main concern about our primary estimand relates to the necessity for model extrapolation below our exposure range, where “validity is almost entirely dependent upon the adequacy of the statistical model”(1, p. 2659). This concern is appropriate and reflects broader tradeoffs with exposure mixtures between what is useful and what is answerable. With the sensitivity to model specification in mind, our primary analysis utilized a series of first-order product terms to approximate a nonlinear/nonadditive model while using Bayesian model averaging (BMA). BMA was appealing for allowing uncertainty in model form as well as for the well-studied utility of model averaging in extrapolationbased forecasting (3). We additionally addressed a study question examining hypothetical percentile-based interventions on ambient levels of all 6 metals. Because this question did not necessitate extrapolation for inference, this strategy explicitly addressed Dr. Zigler’s query about how Bayesian g-computation “would fare in settings with fewer data limitations”(1, p. 2660). We also used numerous sensitivity analyses to study sensitivity to priors, and we used simulations to better understand the conditions necessary for our approach to yield favorable bias-variance tradeoffs. Nonetheless, as we stated,“accuracy outside the range of the data is untestable in the data set at hand”(2, p. 2655); hence, we agreed with Dr. Zigler when we wrote that specification “bias is unknown in our coal plant example”(2, p. 2653). Perhaps most importantly, we acknowledge that estimates of human exposure may not be ideal for evaluating potential interventions. Our reliance on existing, deidentified exposure data hindered inference relative to a bespoke modeling analysis, but the extensive undertaking in generating the exposure data on which we relied suggests that this would be not be simple. Thus, we wrote that our general framework could be “greatly improved by better interfaces between causal inference and exposure sciences”(2, p. 2655). We believe this to be a key question for future research—how can exposure modeling be tuned to address causal questions? When considering the criticisms raised about BMA, it is worth revisiting motivations for using g-computation. The underlying statistical model is a nuisance model: The target parameter is not modeled directly but is based on model predictions, which allows considerable model flexibility (4). Except in special cases, Bayesian approaches to causal inference lead to bias, including residual confounding from model selection or shrinkage. This may simply be a reality of Bayesian causal inference (5). Hence, we explored in simulations whether our approach would yield a favorable bias-variance tradeoff in settings with heavy extrapolation and a true model that was included in the set of possible models. It did. Each of the alternative nuisance model approaches suggested by Dr. Zigler in his commentary (1) involve carefully constructed priors for estimating independent or joint effects of exposures directly from model parameters. Such approaches have looked promising in simulations when inference is made on model parameters. However, such …
