Hello everyone! I've been reading a lot of questions about this recently yet I am just quite confused. I tried running an odds ratio calculation on the following data:
Positive outcome
- Number in exposed group: 2 (a)
- Number in non-exposed group: 3 (c)
Negative outcome
- Number in exposed group: 1 (b)
- Number in non-exposed group: 64 (d)
I calculated an OR of 42.6667 (95% CI=2.9692 to 613.1169) with a P value of 0.0058 most of research article I've read, their OR ranges between 1-5 (5 is the highest) and only one article reported an OR of 32. I have a sample size of 70 (n=70) with a low outcome (5 turned out to be positive with the disease)
Question:
- Is it normal to have an OR value of this high and also a very wide confidence interval? I was thinking that odds ratio is not that reliable to be reported if the sample size is small. What can you recommend on such case?
Thank you in advance!
The odds ratio is bound to be very large (or very small) whenever most of the observations are in one cell of a 2x2 table. You might consider reporting Yule's Y (in addition to the OR) in such cases.
- https://en.wikipedia.org/wiki/Coefficient_of_colligation
HTH.
I am not sure if I understand the question. Are you just worried about a number looking big, and if so the log-odds-ratio might be used (and often it is more useful anyway. As Bruce Weaver says, with 3 cells being very small, any deviation in those will change the value a lot, hence the LB of the interval being 3. A good way to look at it is of the 3 expose, 2/3 had had a positive outcome. 2/3 is a pretty likely outcome if the probability is 50% or even lower, but let's say 50%. This means an equally like outcome would be 1/3. Now the result is
1 2
3 64
and a one on eight chance of
0 3
3 64
The basic conclusion is that when you have very small margins (here the row and column totals) the statistical estimates with be uncertain and even with a high observed OR you should be cautious. At least focus more on the CI than the point estimate. I think it is always worth considering what would happen to your results if you moved just one or two data points around. If this would change your conclusion be very careful!
The attached figure shows the OR vs ln(OR) distinction Daniel Wright described. To make things comparable to your data, I kept N=70 for every 2x2 table, with a=2, b= 1. I let d vary from 1 to 66, with c = 67-d. The figure shows what happens to the OR and ln(OR) as the data pile up in cell d.
HTH.
And just for fun, here's a plot showing Yule's Y as a function of the count in cell d.
A high calculated Odds Ratio (OR) indicates a strong positive association between two categorical variables in an investigation. It suggests that a certain factor increases the odds of a specific outcome. The significance of the OR should be evaluated in context and with consideration of the confidence interval. The interpretation of what is considered “high” depends on the field of study and research question. The following could be of interest.
Andrade, C. (2023). Understanding misunderstandings about the relative risk and odds ratio. The Journal of Clinical Psychiatry, 84(3), 47383. https://doi.org/10.4088/JCP.23f14943
Chen, H., Cohen, P., & Chen, S. (2010). How big is a big odds ratio? Interpreting the magnitudes of odds ratios in epidemiological studies. Communications in Statistics - Simulation and Computation, 39(4), 860–864. https://doi.org/10.1080/03610911003650383
Khan, S. (2020). Meta-analysis of Odds Ratio. In S. Khan (Ed.), Meta-analysis: Methods for health and experimental studies (pp. 87–118). Springer. https://doi.org/10.1007/978-981-15-5032-4_5
Good luck,
A high calculated odds ratio is not necessarily abnormal. The interpretation of the odds ratio depends on the context of the study and the research question being asked. In general, an odds ratio greater than 1 indicates that the exposure is associated with an increased odds of the outcome, while an odds ratio less than 1 indicates that the exposure is associated with a decreased odds of the outcome.
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