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European Network of Centres for Pharmacoepidemiology and Pharmacovigilance

Chapter 7: Effect modification and interaction

Effect modification and interaction are often encountered in epidemiological research, and it is important to recognise their occurrence. The difference between these terms is rather subtle and has been described in Effect modification, interaction and mediation: an overview of theoretical insights for clinical investigators (Clin Epidemiol 2017;9:331-8) and in Tutorial: A nontechnical explanation of the counterfactual definition of effect modification and interaction (J. Clin. Epidemiol. 2021;134:113-24), which provides a more lay definition of these concepts.

Effect modification occurs when the effect of a single exposure on an outcome depends on the values of another variable, i.e., the effect modifier, which does not necessarily need to be involved in the causal pathway. Interaction occurs when there is interest in the causal effect of two exposures on an outcome and how the effect of either exposure depends upon the value of the other exposure. In Suicide and death by other causes among patients with a severe mental illness: cohort study comparing risks among patients discharged from inpatient care v. those treated in the community (Epidemiol Psychiatr Sci. 2022;31:e32), a test for interaction by age group indicated that younger adults with severe illness had a higher relative risk of all-cause mortality than middle-aged adults. Contrary to effect modification, interaction is a symmetric concept as two independent exposures have an equal status in the definition of interaction.

Interaction is generally studied in order to clarify aetiology, i.e., an interaction between environmental and inhered factors, while effect modification is used to identify subpopulations that are particularly susceptible to the exposure of interest. The key distinction between interaction and effect modification is that with effect modification, interest is in the effect of one single exposure on an outcome and this relationship does not have to be causal, whereas with interaction interest is in the causal effect of two exposures on an outcome. Assessment of effect modification is to identify whether the outcome of a treatment (or exposure) differs across patient population subgroups. To check the presence of an effect modifier, one can stratify the study population by a certain covariate, e.g., gender, and compare the effects in these subgroups. These subgroups can be constructed based on a priori knowledge regarding the effect modifier or derived from analysing the observed data and covariates itself.

It is recommended to perform a formal statistical test to assess if there are statistically significant differences for the effects (i.e., the measures) between subgroups (see CONSORT 2010 Explanation and Elaboration: Updated guidelines for reporting parallel group randomised trials, J Clin Epidemiol. 2010;63(8):e1-37 and Interaction revisited: the difference between two estimates, BMJ. 2003;326(7382):219). The study report should explain which measure was used to examine these differences and specify which subgroup analyses were predefined in the study protocol and which ones were performed at analysis stage (see Strengthening the Reporting of Observational Studies in Epidemiology (STROBE): explanation and elaboration. Epidemiology 2007;18(6):805-35).

The presence of effect modification depends on which measure is used in the study (absolute or relative) and can be measured in two ways: on an additive scale (based on risk differences [RD]), or on a multiplicative scale (based on relative risks [RR]). An example of potential effect modifier in studies assessing the risk of occurrence of events associated with drug use is the presence or severity of the underlying illness. Novel antihyperglycaemic drugs and prevention of chronic obstructive pulmonary disease exacerbations among patients with type 2 diabetes: population based cohort study (BMJ. 2022;379:e071380) observed effect measure modification on a multiplicative scale with history of asthma, but not for age, sex or severity when studying the association between GLP-1 receptor agonists with risk of severe and moderate COPD exacerbations among patients with type 2 diabetes and COPD, compared with sulfonylureas.

Evidence derived from studies considering effect modification provides more information and may lead to stronger conclusions about treatment effects. In the absence of prior knowledge about which covariates to consider as potential effect modifiers, one may test the data to investigate their presence. In False discovery rate control for effect modification in observational studies (Electron J Statist. 2018;12(2):3232-53), several analyses are proposed to test the presence of effect modification using the observed data itself.

Interaction is often considered in regression models whose design have variables with one or more levels; binary, categorical or dichotomised. For the evaluation of the interaction variable, the standard measure is the relative excess risk due to interaction (RERI), as explained in the textbook Modern Epidemiology (T. Lash, T.J. VanderWeele, S. Haneuse, K. Rothman. 4th Edition, Wolters Kluwer, 2020). Other measures of interaction include the attributable proportion (A) and the synergy index (S). Most measures, such as the S measure, are limited to binary variables.

Using statistical measures only, it is often difficult to understand the direction and size of an interaction effect. Therefore, visually inspecting the data using bar graphs (i.e., categorical variables) or line graphs (i.e., continuous variables) is another way of assessing and interpreting the marginal effects of interaction terms.

For further recommendations regarding reporting, Strengthening the Reporting of Observational Studies in Epidemiology (STROBE): explanation and elaboration (Epidemiology 2007;18(6):805-35), Recommendations for presenting analyses of effect modification and interaction (Int J Epidemiol. 2012;41(2):514-20), Confidence interval estimation of interaction (Epidemiology. 1992;3(5):452-6) and The reporting of studies conducted using observational routinely collected health data statement for pharmacoepidemiology (RECORD-PE) (BMJ. 2018;363:k3532) and Causal inference and effect estimation using observational data (J Epidemiol Community Health 2022;76:960–6) are useful resources. They provide recommendations on how to describe methods used to examine interactions and present the results:

  • Separate effects (rate ratios, odds ratios or risk differences, with confidence intervals and p-values) of the exposure of interest (e.g. drug) and of the effect modifier (e.g. gender) and of their joint effect using one single reference category (preferably the stratum with the lowest risk of the outcome), as suggested in Estimating measures of interaction on an additive scale for preventive exposures (Eur J Epidemiol. 2011;26(6):433-8), as this provides enough information to calculate effect modification on an additive or multiplicative scale (see Modeling Ratios or Differences? Let the Data Tell Us, AJPH Methods 2017;107(7):1087-91);
  • Effects of the exposure (e.g., drug) within strata of the potential effect modifier (e.g., gender);
  • Measures of effect modification on both additive (e.g., RERI) and multiplicative (e.g., S) scales including confidence intervals;
  • List of the confounders for which the models assessing the association between exposure and outcome were adjusted for.

The article Evaluating sources of bias in observational studies of angiotensin-converting enzyme inhibitor/angiotensin II receptor blocker use during COVID-19: beyond confounding (J Hypertens. 2021;39(4):795-805) highlights that factors associated with differences in hypertension phenotype, and the renin-angiotensin system (and by extension ACEi/ARB use), may modify the strength of the effect size between ACEi/ARB use and the COVID-19 outcomes. These factors should be assessed as potential effect-modifying factors rather than confounding factors, as treating these factors as confounders can induce bias. It further emphasises the above recommendations that if present, effect size estimates should be presented across strata (including 95% confidence intervals) along with measures of interaction on both the additive and multiplicative scales.

IL-6 inhibition in the treatment of COVID-19: A meta-analysis and meta-regression (J Infect. 2021;82(5):178-85) estimates the relative risk of mortality between arms of RCTs comparing IL-6 inhibitors (tocilizumab and sarilumab) to placebo or standard of care in adults with COVID-19. Meta-regression was used to investigate treatment effect modification and showed no evidence of such effect by patient characteristics.

Nonsteroidal Antiinflammatory Drugs and Susceptibility to COVID-19 (Arthritis Rheumatol. 2021;73(5):731-39) investigated whether active use of NSAIDs increases susceptibility to developing suspected or confirmed COVID-19 compared to the use of other common analgesics. There was no evidence of effect modification by age or sex.