Hello All,
One of our projects was looking at the potential interaction between an environmental factor and socioeconomic factors on a birth defect. As recommended by the tutorial (Vanderweele and Knol 2014), we assessed interaction on both additive and multiplicative scale. However, we found 1 pair of factors had significant interaction on both additive scale and multiplicative scale. This really surprised us since the tutorial mentioned in his tutorial that "interaction is often present on one scale and absent on the other." It seems to be rare from the mathematic stand point and we aren't sure how we should interpret (cause they may be linked to totally different biological mechanisms) this or is it correct?
Can someone think of why it would happen and how the result should be interpreted?
Thank you all.
Reference: VanderWeele, Tyler J., and Mirjam J. Knol. "A tutorial on interaction." Epidemiologic Methods 3.1 (2014): 33-72.
Interaction between two variables means the inconsistency of one variable in performance over the different levels of the variable and vice versa. If existent it should on both the additive and multiplicative scales because both scales are related. A multiplicative scale can be made additive by a logarithmic transformation for instance.
Effect measures in health care research may be expressed more parsimoniously (e.g., no need for an interaction term) on one scale than another. Epidemiologic measures, such as relative risks and odds ratios are multiplicative; whereas public health measures of cost and resource utilization (e.g., differences in effect measures) may be more additive scale. As long as exposures are associated with the effect measure, a statistical model associated with one scale will require an interaction term to capture the effect measures more naturally expressed on the other scale.
That said, I can see a few reasons why an interaction term may be significant on both scales. First, it could be that an interaction term on the multiplicative scale captures a proportion effect between exposures (e.g., above additivity on the multiplicative scale). This, then, would require an exponential effect to be represented on the additive scale. Secondly, since we (unfortunately) evaluate interaction terms using p-values, it is possible that a large sample size may find a significant, but trivial, interaction term on the scale that is more naturally associated with the effect measure. Finally, I suppose it is possible that an association may be greater than additivity, but not quite multiplicative. Thus, you might need an interaction term to capture the effect/exposure association regardless of the model that is selection.
In the end, I think the choice of scale should be selected by the theoretical framework and which scale more completely and naturally addresses the question under study.
Paul
- Badges
- Science topic
- Similar topics
- Medicine
- Physiology
- Biosignals
- Biomedical Signal Processing
- Statistical Analysis