I know that the OR is a kind of 'default' option if you estimate associations in case-control studies. I was told (once upon a time) during my epi traning that the OR must be used, because the prevalence of a given disease is determined by the investigator through the selected sampling ratio of cases and controls (e.g. 1 cases=4 controls --> 20 % disease prevalence).
However, my understanding is that usually the odds of past exposure are compared between patients and controls. So why can't we calculate a prevalence ratio (=prevalence of the exposure compared between cases and controls) to make this comparison? This seem easier to calculate and easier to communicate.
Hi Adrian, in my experience, the OR is a relatively easy way to compare outcomes in two groups, in a manner that's accessible to non-statisticians. The ability to describe which group has more risk (greater odds) of outcome X is very useful.
That said, there's a paper that addresses your question:
Mary Lou Thompson, J E Myers, D Kriebel. "Prevalence odds ratio or prevalence ratio in the analysis of cross sectional data: what is to be done?"
Occup Environ Med 1998;55:272–277
These authors would appear to agree with your preference for the prevalence ratio.
From the parmacoepi point of view, the best risk estimator is the relative risk (RR, event rate in exposed/event rate in non-exposed). This cannot be measured in case-controls studies, because the cases and the controls are independent, and the overall event rates are fixed by the cas/control ratio. All you can have is the exposure in the cases and the exposure in the controls. From these you can measure odds ratios (exposed to non-exposed) and relative exposures ratio (exposure in cases / exposures in controls)
It can easily be demonstrated that when events are rare the OR is a good estimate of the RR. When exposures are rare then the RER is a good estimate of the OR, so either can be used. RER is a good estimate of RR only if both exposure and events are rare, which makes it a little more complicated to use and interpret.
As long as you explain exactly what you are doing and why, it is probably not very important. But if you're trying to look at drug-related risks, most probably reviewers will prefer OR to RER with which they are less familiar.
Dear all,
thanks a lot for your responses.
In fact, I was wondering why OR seems to be the only measure of association specifically in case control studies.
In cross-sectional studies, I know that orevalence ratios (estimated for instance based on binominal or Poisson regression) can be estimated and that PRs can used instead of ORs, as ORs are overestimating associations when disease prevalences are high.
In case control studies, I know that ORs are supposed to be employed, because disease prevalences (determined by our case-/control sampling scheme) are unknown.
However, ORs compare odds of exposure (rather then disease) between cases and controls.
As I learned from Nicholas' reply there is some "relative exposure ratio" -- this is the measure I had in mind as it seems that it contrast the prevalences of exposures between cases and controls!
Thanks a lot for your help
(@ Christina: interesting article o study designs by Pierce - wasn't aware of that)
Adrian
Also, OR is used for retrospective evaluation (following the logic of Moore), and RR is used for prospective evaluation.
Of course you can use the term ratio of cases to controls in exposed and unexposed, which denotes a cohort approach, but then of course the term controls is not the right one (it should be non-cases). In a cohort you determined the numbers of exposed and unexposed (or controls) and count the cases (or events) and non-cases (or those who don't have the event of interest). This will in fact give you the RR which I believe is a more precise measure of association, since OR is just an approximation of RR when events are rare. If you are looking at a cohort, you also get essential information for decision-making, beyond the OR or RR, which the attributable risk / etiologic fraction. In fact without absolute risk measures, OR is not very useful. In the usual 2x2 table, a is the number of exposed cases, b the number or exposed non-cases, c the number of unexposed cases and d the number of unexposed non-cases. The cohort approach is horizontal (a/(a+b)/c/(c+d)) because the number of exposed and unexposed (controls) is fixed, whereas in a case control study you determine the number of cases and controls and the approach is orthogonal (vertical), i.e. you measure the number/rate of exposed among cases and the number/rate of exposed among controls. If you do have the total number of cases in a population, and of controls, then your real measure of association for a rare event would in fact be the population relative exposure rates (CPR) (a/(a+c)/b/(b+d) in fact (a/(a+c))/(a+b)/(a+b+c+d). This can be done in a case-population approach. It will be equivalent to the OR (or vice-versa, rather) when the exposure is rare, just as the OR approximates the RR when the event rate is low. The higher the exposure and the event rates, the less accurate and therefore useful the OR is.
But this reasoning may be specific to pharmacoepi, not to traditional epidemiology.
In any statistical measure we get inference from this measure and generalized the conclusion on reference population. In case -control study, we are not sure that the size of exposed and non -exposed appearing in case or control represent the actual size in the population which cases or control drawn. So we can not calculate risk among exposed or non exposed. In the same way, we are not able to ascertain that size of case and control in the study is the actual size in the reference population, for this reason odds ratio is used and not the proportion.
Masoud your explanation makes sense. Cases and controls are independent groups in case control design thats why we calcuate odds ratio!
You cannot calculate the risk ratio directly because according to design, case-control studies use a biased sample by outcome status. It means that the risk (Probability of diseased given exposure status) estimation will be biased too. Odds ratios have a nice property, they are symmetric, estimating the odds of exposure given cases over the odds of exposure given controls will be equal to odds of disease given cases over the odds of disease given controls.
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