Owen Yang
I am more comfortable with the term ‘effect modification’ in clinical medicine, but even so this is really not always what it means. Or in fact it is what it means, but we over-interpret what it is and get over-excited.
My guess is the term ‘interaction’ is from a molecular studies (proper scientists?), where we find two molecules physically and chemically ‘interact’ with each other to make an effect, for example cyclosporin interacts with ?calcineurin (a protein I think) to suppress T cell function. If there is a lab study then you will find the effect of cyclosporin on T cell suppression is modified by the existence (or the amount) of calcineurin that can be interacted with cyclosporin. If some study like this is actually feasible, there is strong effect in the presence of calcineurin, and no effect in the absence of calcineurin.
We will spare the simple knowledge for the moment. In this prototype of research, when we do stats we will have a ‘main effect’ of cyclosporin and a ‘main effect’ of calcineurin, and a ‘multiplicative term’ (cyclosporin X calcineurin) to describe the ‘interaction’ between cyclosporin and calcineurin. If we find the multiplicative term to be large, then there is possibly a large interaction between cyclosporin and calcineurin. This seems to be so niche at the time, I guess, and this multiplicative term has been called interaction term. The jargon is so catchy that we can just say any two things have interactions without thinking what we mean.
We could have a strong suspicion that the two molecules are interacted in a way, but we would want to see visual evidence that they actually ‘interact.’ Enlighten me if you know what the methods might be (something to do with phosphorylation and precipitation?). I am sure the methods have improved in the 21st century.
The twisted jargon of interaction
In a clinical study, however, the idea of interaction is so twisted. We may say casually throwing a line saying there is an interaction between alcohol and smoking on risk of oesophageal cancer, but we say it without actually thinking what we mean.
What most likely to happen is the relative risk associated with one factor (such as alcohol) is different between two groups according to the other factor (such as smoking). For example, if the relative risk of oesophageal cancer in heavy drinkers is 4.0 compared to light drinkers among non-smokers, but only 2.0 in smokers, there is so-called ‘interaction.’ Smoking attenuates the effect of alcohol drinking by 0.5 fold (from 4.0 to 2.0, so to speak).
To recruit our quantitative mind
Let us just open our minds for a second and accept some basic math. Have you thought about what the risks might be in your patients that may cause the difference in associations?
A naive philosopher could picture something like 40 cancer cases in 100,000 heavy drinkers versus 10 cancer cases in 100,000 light drinkers over a year if they do not smoke (hence relative risk of 4.0), and 20 versus 10 cancer cases if they smoke (hence relative risk of 2.0).
Naive philosopher’s mind
| Type of patients | Risk of cancer in 100,000 |
| Non-smokers | |
| Heavy drinkers | 40 |
| Light drinkers | 10 |
| Smokers | |
| Heavy drinkers | 20 |
| Light drinkers | 10 |
If you have actually pictured up to this point, I might say you beat 95% of medical doctors. Most doctors have not thought in this way at all, and just accept an abstract concept of an interaction and cannot wait to propose their exciting hypothesis.
Dancing with numbers
What might likely be happening in this made-up scenario is that smoking is such a strong risk factor of oesophageal cancer, and so the number could be something like 20 versus 5 (heavy versus light drinker) in non-smokers (hence relative risk of 4.0), and 40 versus 20 in non-smokers (hence relative risk of 2.0).
From a math point of view, there is a relative risk from 4.0 to 2.0. But for the patient themselves, the ‘fold of increase’ is just a perception. What matters more is the absolute risk difference. The difference in risk caused by heaving drinking (versus light drinking) was 15 in non-smokers and 20 in smokers. Drinking is actually more harmful in smokers despite the reduction of relative risk from 4.0 to 2.0.
One version of truth
| Risk of cancer in 100,000 | |
| Non-smokers | |
| Heavy drinkers | 20 |
| Light drinkers | 5 |
| Smokers | |
| Heavy drinkers | 40 |
| Light drinkers | 20 |
Does this change your hypothesis about this interaction?
