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Effect measure modification and interaction are often encountered in epidemiological research and it is important to recognize their occurrence. The difference between these terms is rather subtle and has been described in On the distinction between interaction and effect modification (Epidemiology 2009;20(6):863–71). Effect measure modification occurs when the measure of an effect changes over values of some other variable (which does not necessarily need to be a causal factor). Interaction occurs when two exposures contribute to the causal effect of interest, and they are both causal factors. Interaction is generally studied in order to clarify etiology while effect modification is used to identify populations that are particularly susceptible to the exposure of interest.

To check the presence of an effect measure modifier, one can stratify the study population by a certain variable, e.g. by gender, and compare the effects in these subgroups. It is recommended to perform a formal statistical test to assess if there are statistically significant differences between subgroups for the effects (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 method 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]). From the perspective of public health and clinical decision making, the additive scale is usually considered the most appropriate. 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.

For the evaluation of interaction, the standard measure is the relative excess risk due to interaction (RERI), as explained in the textbook Modern Epidemiology (K. Rothman, S. Greenland, T. Lash. 4rd Edition, Lippincott Williams & Wilkins, 2020). Other measures of interaction include the attributable proportion (A) and the synergy index (S). 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.

Due to confusion about these terms, it is important that effect measure modification and interaction analysis are presented in a way that is easy to interpret and allows readers to reproduce the analysis. For 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) 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 to describe any methods used to examine interactions, and present the results as follows:

- Separate effects (rate ratios, odds ratios or risk differences, with confidence intervals) of the exposure of interest (e.g. drug), 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;
- Effects of the exposure within strata of the potential effect modifier;
- 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 association between exposure and outcome was 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.