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Effect measure 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). Effect measure modification occurs when the measure of an effect changes over values of some other variable (which does not necessarily need to be involved in the causal pathway). Interaction occurs when two exposures contribute to the effect of interest, and they are both explanatory factors. Interaction is generally studied in order to clarify aetiology while effect modification is used to identify populations that are particularly susceptible to the exposure of interest.

Assessment of effect modification is to identify whether the effect of a treatment (or exposure) is different in groups of patients with different characteristics. To check the presence of an effect modifier, one can stratify the study population by a certain variable, e.g., by 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 itself.

It is recommended to perform a formal statistical test to assess if there are statistically significant differences for the effects (i.e. 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 while analysing the data (Strengthening the Reporting of Observational Studies in Epidemiology (STROBE): explanation and elaboration. Epidemiology 2007;18(6):805-35).

The presence of effect measure 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 recent drug use is the past use of the same drug. This is shown in Evidence of the depletion of susceptibles effect in non-experimental pharmacoepidemiologic research (J Clin Epidemiol. 1994;47(7):731-7) in the context of a hospital-based case-control study on NSAIDs and the risk of upper gastrointestinal bleeding. 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.

For the evaluation of interaction, 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. 4^{th} Edition, Wolters Kluwer, 2020). Other measures of interaction include the attributable proportion (A) and the synergy index (S). In Estimating measures of interaction on an additive scale for preventive exposures (Eur J Epidemiol 2011;26:433-8), the authors mention that the use of these measures should only be applied on risk factors rather than preventive factors as it might lead to inconsistent results. In addition, most measures, such as the S measure, are limited to binary variables.

According to Exploring interaction effects in small samples increases rates of false-positive and false-negative findings: results from a systematic review and simulation study (J Clin Epidemiol. 2014;67(7):821-9), with sufficient sample size, most interaction tests perform similarly with regard to type 1 error rates and power.

Using 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) are useful resources. They recommend describing any methods used to examine interactions and to present the results as follows:

- 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 gives enough information to the reader to calculate effect modification on an additive and multiplicative scale (see Modeling Ratios or Differences? Let the Data Tell Us, AJPH Methods 2017;107(7):1087-91). Statistical tests are dependent on the measurement scale – ratios or differences – used to assess interaction and modification effect.
- 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, the renin-angiotensin system (and by extension ACEi/ARB use), and COVID-19, may modify the strength of the effect size between ACEi/ARB use and the 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.