{"doi":"10.1093/aje/kwab143","title":"Keil et al. Respond to “Causal Inference for Environmental Mixtures”","abstract":"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 extrapolation-based 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).","journal":"American Journal of Epidemiology","year":2021,"id":211111,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":2,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9581,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2021-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":105708,"name":"Jessie P. Buckley","orcid":"0000-0001-7976-0157","position":1,"is_corresponding":false},{"id":363698,"name":"Amy E. Kalkbrenner","orcid":"0000-0002-3888-0539","position":2,"is_corresponding":false},{"id":105707,"name":"Alexander P. Keil","orcid":"0000-0002-0955-6107","position":0,"is_corresponding":true}],"reference_count":8,"raw_metadata":null,"created_at":"2026-07-18T23:52:16.049481Z","pmid":"34079996","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}