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. 3rd Edition, Lippincott Williams & Wilkins, 2008). 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) and Recommendations for presenting analyses of effect modification and interaction (Int J Epidemiol 2012;41(2):514-20) are useful resources. They recommend to 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.