{"doi":"10.1093/aje/kwad077","title":"INTRODUCING PROXIMAL CAUSAL INFERENCE FOR EPIDEMIOLOGISTS","abstract":"Causal inference with observational data has generally proceeded under the assumption of conditional exchangeability. That is, the action (e.g., treatment, exposure, intervention) is independent of the potential outcomes, conditional on a set of covariates (1). However, exchangeability is often questionable. Miao et al. (3) have proposed an alternative approach to identification, a generalization of previous work by Kuroki and Pearl (2), which allows for unmeasured confounding with particular causal structures. Specifically, if there exists a measured variable that is a potential cause of the action and unrelated to the outcome except through measured confounders and a known but unmeasured confounder (i.e., treatment proxy), and another measured variable that is a potential cause of the same outcome and unrelated to the action except through measured confounders and the same unmeasured confounder (i.e., outcome proxy), then the average causal effect (ACE) can be identified nonparametrically under a set of sufficient conditions. Here, we briefly introduce proximal causal inference, where “proximal” denotes that the pair of measured variables is a consequence of the unmeasured confounder, to the epidemiology community and demonstrate its application using a simulation study. To motivate our simulation, we draw from the work of Lu et al. (4). We wish to estimate the ACE of a new treatment (⁠|$A=1$|⁠), versus standard treatment (⁠|$A=0$|⁠), on 12-month human immunodeficiency virus viral load (⁠|$Y$|⁠). The population ACE can be expressed as |$E\\!\\left[{Y}^1-{Y}^0\\right]$|⁠, where |${Y}^a$| is the potential outcome under treatment |$a$|⁠. We consider the confounders age (⁠|$X$|⁠) and CD4 cell count (⁠|$U$|⁠), where age was observed and the true CD4 count was unobserved. The other observed variables, self-rated health (⁠|$W$|⁠) and measured CD4 cell count (⁠|$Z$|⁠), are potential proxies, where measured CD4 count is a treatment proxy (i.e., a measure of the true CD4 count that features in treatment guidelines) and self-rated health is an outcome proxy (i.e., it is affected by true CD4 count and subsequently affects viral load). Several possible variations on the causal structure are depicted in Figure 1. Directed acyclic graphs for the 3 data-generating scenarios considered. |$A$|⁠, action of interest; |$Y$|⁠, outcome of interest; |$Z$|⁠, action or treatment proxy; |$W$|⁠, outcome proxy; |$X$|⁠, traditional observed confounder; |$U$|⁠, unobserved confounder. A) In scenario 1, both standard and proximal g-computation are expected to be unbiased, since |$\\left\\{X,W\\right\\}$| and |$\\left\\{X,W,Z\\right\\}$| block all backdoor paths. B) In scenario 2, standard g-computation is expected to be biased but proximal g-computation is expected to be unbiased. C) In scenario 3, both standard and proximal g-computation are expected to be biased. Notice that this model does not include the treatment proxy. Since the outcome model is a linear regression without interaction terms between |$A$| and any covariate, the ACE is estimated by |${\\hat{\\mathrm{\\alpha}}}_1$|⁠, the least-squares estimate of |${\\mathrm{\\alpha}}_1$|⁠. In this simple case where linear regression is used to model the conditional mean values of both |${W}_i$| and |${Y}_i$|⁠, existing software for 2-stage least-squares estimation can be used for point and variance estimation while allowing for the outcome proxy model to be misspecified (5). The described proximal g-computation procedure can be generalized. If the outcome model above had included interaction terms, the following modification could have been used to estimate the ACE (5). The predicted values of the outcome, |${\\hat{Y}}_i^a$|⁠, are generated from |$\\hat{\\boldsymbol{\\mathrm{\\alpha}}}$| by setting |${A}_i=a$| for all records, where |$a$| is in |$\\left\\{0,1\\right\\}$|⁠; then the ACE is estimated as the mean difference between the predictions, |$\\frac{1}{n}{\\sum}_{i=1}^n\\left({\\hat{Y}}_i^1-{\\hat{Y}}_i^0\\right)$|⁠. Proximal g-","journal":"American Journal of Epidemiology","year":2023,"id":340907,"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":15,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9439,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2023-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":329432,"name":"Stephen R. Cole","orcid":"0000-0003-2117-1311","position":1,"is_corresponding":false},{"id":352751,"name":"Jessie K. Edwards","orcid":"0000-0002-1741-335X","position":2,"is_corresponding":false},{"id":746082,"name":"Grace E. Mulholland","orcid":"0000-0003-0046-2144","position":3,"is_corresponding":false},{"id":334760,"name":"Bonnie E. Shook‐Sa","orcid":"0000-0001-9506-4047","position":4,"is_corresponding":false},{"id":280665,"name":"Eric J. Tchetgen Tchetgen","orcid":"0000-0002-8369-3900","position":5,"is_corresponding":false},{"id":289327,"name":"Paul N. Zivich","orcid":"0000-0002-9932-1095","position":0,"is_corresponding":true}],"reference_count":43,"raw_metadata":null,"created_at":"2026-07-19T01:10:58.548803Z","pmid":"37005072","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":[]}