{"doi":"10.1093/aje/kwad034","title":"Interaction in Theory and in Practice: Evaluating Combinations of Exposures in Epidemiologic Research","abstract":"The concept of interaction in etiological epidemiologic research can be described as the circumstance where the causal effect of exposure on outcome depends upon another factor. In this sense, epidemiologic research commonly considers interaction,. For example: How is risk of lung cancer affected by cigarette smoking and asbestos separately and in combination? Is effectiveness of selective serotonin reuptake inhibitors for treatment of unipolar depression dependent upon patient characteristics? Note that we largely use the terms “interaction” and “effect modification” interchangeably. These are sometimes distinguished from one another, as when there is similar interest in 2 exposures vs. 1 exposure of primary interest with effects that may vary across subgroups. More generally, consider a hypothetical study of dichotomous outcome Y and dichotomous factors A and B, aimed at evaluating whether the effect of A on risk of Y among those with B is different among those without B. Similarly, we can consider risk related to the combination of A and B together instead of subgroup-specific effects of A, to evaluate whether risk among those with both A and B is greater or less than expected based on effects of A and B individually—which we could describe qualitatively as “synergism” or “antagonism” (1, 2). The vague descriptions above are adequate to describe the concept of epidemiologic interaction. But progressing from vague descriptions of interaction to formal evaluation requires resolving ambiguity about the meanings of “the effect” in the phrase “the effect of A on risk of Y,” and “expected” in the phrase “greater or less than expected.” Interpretation of Risk Ratios as Joint Effects and Subgroup-Specific Effects Abbreviation: RR, risk ratio When interest is in sufficiently rare outcomes such that odds ratios approximate risk ratios, the RERIRR can be approximated using odds ratios. Approaches for estimating standard errors for RERI and statistical inference are described in VanderWeele and Knol (9), which also provides code for SAS (SAS Institute, Inc., Cary, North Carolina) and STATA (StataCorp LLC, College Station, Texas). Above, we have described how interaction can be assessed as departure from multiplicativity or as departure from additivity. The choice between these approaches is important; conclusions regarding the presence or absence—or even the direction—of interaction can differ depending upon the model scale. Figure 1 demonstrates this, considering the effects of 2 factors, A and B, for each of which presence (vs. absence) causes increased risk. The 2 lines correspond to the expected joint effects when there is no interaction between A and B on the multiplicative scale (i.e., |$R{R}_{AB}=R{R}_A\\times R{R}_B$|⁠; dashed line) and on the additive scale (i.e., |$R{R}_{AB}=R{R}_A+R{R}_B-1$|⁠; solid line). As described previously, interaction can be assessed by first considering risk among those with both A and B present, next defining a model and scale relating exposure to outcome, and finally comparing observed joint effects with expected joint effects. Consider a scenario where risk among those with neither factor is 1%, factor A increases risk by 1% (i.e., |$R{D}_A$| = 0.01, |$R{R}_A$| = 2), and factor B increases risk by 1% (i.e., |$R{D}_B$| = 0.01, |$R{R}_B$| = 2). If observed risk among those jointly exposed to A and B is 4% (i.e., |$R{D}_{AB}$| = 0.03, |$R{R}_{AB}$| = 4), which falls in the dark shaded region between the 2 curves, it is consistent with a superadditive interaction but no interaction on the multiplicative scale. Conversely, an observed risk among those jointly exposed to A and B of 3% corresponds to a submultiplicative interaction but no interaction on the additive scale. If additivity accurately describes the relationship between risk and exposures A and B, then the apparent interaction on the multiplicative scale is strictly a mathematical artifact that results from model misspecification. Table 2 sum","journal":"American Journal of Epidemiology","year":2023,"id":352302,"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":8,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9517,"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":369131,"name":"Ashley I. Naimi","orcid":"0000-0002-1510-8175","position":1,"is_corresponding":false},{"id":320647,"name":"Brian W. Whitcomb","orcid":"0000-0002-8646-5823","position":0,"is_corresponding":true}],"reference_count":10,"raw_metadata":null,"created_at":"2026-07-19T01:12:50.107998Z","pmid":"36757201","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":[]}