I'm aware of the issues regarding the use of relative risk in a case control study. But a colleague recently told me that odds ratios are inappropriate for cross-sectional and cohort studies but can't seem to elaborate further. I think he's just assuming that since relative risk is used in cohort studies rather than case controls, odds ratios must be used for case controls and not cross-sectional studies or cohorts. However, I can't find very much information of the appropriateness of odds ratios in these contexts. Can anyone point me in the right direction? Thanks!
Solved – Odds ratios are inappropriate for a cross-sectional or cohort study
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An answer to all four of your questions, preceeded by a note:
It's not actually all that common for modern epidemiology studies to report an odds ratio from a logistic regression for a cohort study. It remains the regression technique of choice for case-control studies, but more sophisticated techniques are now the de facto standard for analysis in major epidemiology journals like Epidemiology, AJE or IJE. There will be a greater tendency for them to show up in clinical journals reporting the results of observational studies. There's also going to be some problems because Poisson regression can be used in two contexts: What you're referring to, wherein it's a substitute for a binomial regression model, and in a time-to-event context, which is extremely common for cohort studies. More details in the particular question answers:
For a cohort study, not really no. There are some extremely specific cases where say, a piecewise logistic model may have been used, but these are outliers. The whole point of a cohort study is that you can directly measure the relative risk, or many related measures, and don't have to rely on an odds ratio. I will however make two notes: A Poisson regression is estimating often a rate, not a risk, and thus the effect estimate from it will often be noted as a rate ratio (mainly, in my mind, so you can still abbreviate it RR) or an incidence density ratio (IRR or IDR). So make sure in your search you're actually looking for the right terms: there are many cohort studies using survival analysis methods. For these studies, Poisson regression makes some assumptions that are problematic, notably that the hazard is constant. As such it is much more common to analyze a cohort study using Cox proportional hazards models, rather than Poisson models, and report the ensuing hazard ratio (HR). If pressed to name a "default" method with which to analyze a cohort, I'd say epidemiology is actually dominated by the Cox model. This has its own problems, and some very good epidemiologists would like to change it, but there it is.
There are two things I might attribute the infrequency to - an infrequency I don't necessarily think exists to the extent you suggest. One is that yes - "epidemiology" as a field isn't exactly closed, and you get huge numbers of papers from clinicians, social scientists, etc. as well as epidemiologists of varying statistical backgrounds. The logistic model is commonly taught, and in my experience many researchers will turn to the familiar tool over the better tool.
The second is actually a question of what you mean by "cohort" study. Something like the Cox model, or a Poisson model, needs an actual estimate of person-time. It's possible to get a cohort study that follows a somewhat closed population for a particular period - especially in early "Intro to Epi" examples, where survival methods like Poisson or Cox models aren't so useful. The logistic model can be used to estimate an odds ratio that, with sufficiently low disease prevalence, approximates a relative risk. Other regression techniques that directly estimate it, like binomial regression, have convergence issues that can easily derail a new student. Keep in mind the Zou papers you cite are both using a Poisson regression technique to get around the convergence issues of binomial regression. But binomial-appropriate cohort studies are actually a small slice of the "cohort study pie".Yes. Frankly, survival analysis methods should come up earlier than they often do. My pet theory is that the reason this isn't so is that methods like logistic regression are easier to code. Techniques that are easier to code, but come with much larger caveats about the validity of their effect estimates, are taught as the "basic" standard, which is a problem.
You should be encouraging students and colleagues to use the appropriate tool. Generally for the field, I think you'd probably be better off suggesting a consideration of the Cox model over a Poisson regression, as most reviewers would (and should) swiftly bring up concerns about the assumption of a constant hazard. But yes, the sooner you can get them away from "How do I shoehorn my question into a logistic regression model?" the better off we'll all be. But yes, if you're looking at a study without time, students should be introduced to both binomial regression, and alternative approaches, like Poisson regression, which can be used in case of convergence problems.
It is not true in all situations. The odds ratio only gives an estimate of the relative risk if the outcome is a low probability outcome. (Same insight as Poisson approximation to the binomial distribution).
Imagine a case-control study for lung cancer, then we check the number of smokers in both groups. Technically, the only thing we can test is given that an individual has lung cancer, what is the probability that they smoke. We can do the same for the non cancer group, and obtain a ratio of the both probabilities. This would be the relative risk. But we do not really care about this quantity. We actually want, given that an individual smokes, what is the probability that they have lung cancer divided by the same probability for non-smokers.
The nice thing about the odds ratio is that it is bi-directional. So: the odds of smoking given lung cancer divided by the odds of smoking given control is actually equivalent to the odds of lung cancer given smoking divided by the odds of lung cancer without smoking. This bi-directionality of the odds ratio allows us to obtain the comparison we want from case-control studies.
Now, if we know the outcome to have a low rate in both groups $-$ the proportion of individuals with lung cancer is small among smokers and non-smokers $-$ then the odds ratio approximates the relative risk. This is the one time we can use the odds ratio to approximate the relative risk in case-control studies. I'm assuming that in case-control studies, the cases are rare events. So certain persons may skip this caveat and state what the OP stated.
The best resource I've found for questions like the one here is Agresti's book on Categorical Data Analysis.
Best Answer
Quick reference can be made to Bhopal's Concepts of Epidemiology 2nd edition (Ch. 9).
Odds ratios calculations are possible and valid in cohort, case-control and cross-sectional designs, but the OR is often not the estimate that is desired or is less efficient than alternatives.
1) Cross-sectional studies often want to estimate prevalence, so a relative measure such as OR wouldn't make sense if prevalence is your goal. It is certainly possible to estimate the OR though.
2) Cohort studies will have information about person-time at risk, and so the desired outcomes are often incidence rates, population attributable risk, or risk ratios. The odds ratio estimate for rare outcomes will approximately estimate the risk ratio in this design, but it makes more sense to compute the risk ratio directly.