Someone wrote to ask me about the difference between risk ratio and odds ratio, so how about a mini tweetorial on risk vs. odds?
In the last tweetorial, we used this table of data to calculate the risk for the outcome among the exposed and among the unexposed. We did that by dividing the # of outcome events in each group by the size of the group. 
Do you remember? Or, if you weren't tuned in before, want to give it a whirl? What was the risk among the exposed?
The risk of our outcome of interest among the exposed is the number of exposed cases (200) divided by the total exposed people (1000) = 0.20, so choice 1 was correct. However, the other three choices also calculate meaningful quantities. Let's discuss!
If you picked choice 2, you were calculating the risk for the outcome among the unexposed. Right idea, just the wrong row.
If you picked choice 3 or 4, you were not calculating the risk, but the odds (of outcome among the exposed and unexposed, respectively!) The odds are also an important tool in our epidemiological toolboxes, so they are worth noticing!
If we think of a 6-sided die, the odds of rolling a "3" are 1 to 5. The probability of rolling a "3" is 1/6 (like risk!). Without getting into a lot of detail, calculating the odds doesn't involve using the total column of the 2x2 table, just the inner 4 cells!
Just like we did with the risk, we can compare odds to each other using an effect measure called the "odds ratio" or OR.
12.5! That's pretty big! Remember the risk ratio we calculated using the data in this 2x2 table earlier? Odds tend to be a good estimate of risk when the outcome is not very common.
In our scenario, the outcome is not rare (220 of 2000 in the study population had the outcome). Many of these outcome events were in the exposed group. So it is unsurprising that the odds>risk among exposed and the OR overestimates the RR.
For the epidemiology fans, willing to go on a small tangent: who has heard about the "rare disease assumption"?
The "rare disease assumption" usually first comes up in Epi 101 class because it is needed to interpret OR calculated in case-control studies with survivorship sampling (where we can only compute odds and not risks due to the sampling strategy) as an estimate of the risk ratio.
Take home message: risk (ratios) and odds (ratios) are not the same, but when the outcome is rare among your population/sample, they can be pretty darn close! If not, you should take care to call a risk a risk, an odds and odds, (and a spade a spade!) 😄♠️
Now, for those who requested a deeper dive last time...grab your flippers! The potential overestimation of risk ratios by ORs is not only a challenge in some case-control designs, but also in trials and cohort designs using binary logistic regression to obtain ORs.
ORs for common outcomes are not incorrect; they are just a ratio of two odds. Odds ratios are also generally more convenient to model. However, we have to be careful with the interpretation. If the outcome occurs frequently, the OR can drastically overestimate the risk ratio.
Misinterpretation (e.g. into a clinical guideline) could have negative consequences. If you want to get more into this advanced topic, I can recommend this paper (open access on PMC): ncbi.nlm.nih.gov/pmc/articles/P…
You made it! What are the odds?! Rock on.
