Statistical Interaction

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A Statistical Interaction is a Statistical Measure that describes the situation in which the effect of one causal variable on an outcome depends on the state of a second causal variable.



References

2022a

  • (Wikipedia, 2022) ⇒ https://en.wikipedia.org/wiki/Interaction_(statistics) Retrieved:2022-3-20.
    • In statistics, an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the effect of one causal variable on an outcome depends on the state of a second causal variable (that is, when effects of the two causes are not additive).[1] Although commonly thought of in terms of causal relationships, the concept of an interaction can also describe non-causal associations. Interactions are often considered in the context of regression analyses or factorial experiments.

      The presence of interactions can have important implications for the interpretation of statistical models. If two variables of interest interact, the relationship between each of the interacting variables and a third "dependent variable" depends on the value of the other interacting variable. In practice, this makes it more difficult to predict the consequences of changing the value of a variable, particularly if the variables it interacts with are hard to measure or difficult to control.

      The notion of "interaction" is closely related to that of moderation that is common in social and health science research: the interaction between an explanatory variable and an environmental variable suggests that the effect of the explanatory variable has been moderated or modified by the environmental variable.

  1. Dodge, Y. (2003). The Oxford Dictionary of Statistical Terms. Oxford University Press. ISBN 978-0-19-920613-1.

2022b

  • (Wikipedia, 2022) ⇒ https://en.wikipedia.org/wiki/Glossary_of_clinical_research#I Retrieved:2022-3-20.
    • QUOTE: Interaction (Qualitative & Quantitative)
      • The situation in which a treatment contrast (e.g. difference between investigational product and control) is dependent on another factor (e.g. centre). A quantitative interaction refers to the case where the magnitude of the contrast differs at the different levels of the factor, whereas for a qualitative interaction the direction of the contrast differs for at least one level of the factor. (ICH E9)

2022c

  • (Wikipedia, 2022) ⇒ https://en.wikipedia.org/wiki/Interaction Retrieved:2022-3-20.
    • Interaction is a kind of action that occurs as two or more objects have an effect upon one another. The idea of a two-way effect is essential in the concept of interaction, as opposed to a one-way causal effect. Closely related terms are interactivity and interconnectivity, of which the latter deals with the interactions of interactions within systems: combinations of many simple interactions can lead to surprising emergent phenomena. Interaction has different tailored meanings in various sciences.

2021

2019a

2019b

  1. VanderWeele TJ, Knol MJ. A tutorial on interaction. Epidemiol Methods 2014;3:33–72
  2. MacKinnon DP, Fairchild AJ, Fritz MS. Mediation analysis. Annu Rev Psychol 2007;58:593–614.

2017

Type of assessment Aim of the assessment
Effect modification Separate exposure effects according to another variable (...)
Interaction Evaluate individual and joint effects of exposures (...)
Mediation Evaluate direct and indirect effects of exposures (...)
Box 1: Main motivation for the assessment of effect modification, interaction and mediation.
The clinical motivation behind the assessment of effect modification is to identify whether the effect of a treatment (or exposure) is different in groups of patients with different characteristics. If the effects are the same, the treatment (or exposure) effect is called homogeneous; if the effects are different, they are called heterogeneous(...).

Assessing effect modification may also help to identify a subset of patients who would not benefit from an intervention at all(...).

Interaction is of interest when researchers want to obtain the joint effect of two (or more) exposures on a disease or outcome.[1] To be considered a synergistic interaction, the joint effect has to be higher than the effect expected by the sum of their individual effects. Conversely, there is an antagonistic interaction between exposures, when the joint effect is less than the sum of their individual effects. This is in contrast to effect modification, where the effect of an exposure on an outcome is assessed in different strata of a third variable, but a joint effect is not assessed.

From a clinical perspective, to assess interaction is particularly important when a disease can be treated by a combination of two or more treatments.

  1. Rothman KJ. Synergy and antagonism in cause-effect relationships. Am J Epidemiol. 1974;99(6):385–388.

2014

2009a

$E\left(y\right)=\beta_0+\beta_1X_1+\beta_2X_2+\beta_3X_1X_2$

Where $E(y)$ is the estimated effect, $\beta_0$ is the intercept that can be interpreted as the background risk, $\beta_1$ and $\beta_2$ are the regression coefficients of the risk factors $X_1$ and $X_2$. By including the product term $\left(X_1 \times X_2\right)$ the interaction effect is estimated through estimation of the regression coefficient $\beta_3$ (...)

2009b