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Excerpt
It could be argued that without a comparison group, this study merely demonstrates that the lack of centralization predicts a lack of response to McKenzie treatment, not necessarily a poor outcome. This should be studied further.
Interpreting odds ratios is often challenging in this context. Chance can be measured by either odds or probabilities. Because most people think in probabilities, not odds, misinterpretation is not uncommon. When we say, for example, that an event is “five times more likely to occur in group A than in group B,” we are referring relative risk, not the relative odds (or odds ratio). In situations where the absolute rate for the outcome of interest (in this case disability) is rare, i.e., less than 10%, odds ratios (OR) are a good approximation of relative risk (RR). If the outcome is more common, however, the OR may exaggerate the association between the exposure (e.g., centralization) and the outcome (e.g., disability). The greater the rate of the outcome of interest, the greater the exaggeration.
In this study, the absolute rates of disability, that is, ‘how many of the centralizers and noncentralizers were still disabled at 12 months?’ is not known. If disability is common (>10–20%), the odds ratios presented may, have exaggerated the association. For example if the disability rate is 50%, an odds ratio of 5 is equivalent to a true RR of only 2.9. This would certainly still be of interest, although not as dramatic.
Figure 1 below illustrates this divergence between OR and RR as the rate for the outcome of interest increases. Here, the OR is fixed at 6.0. One then can calculate the risk of an event in group x and event in group y from the odds of x and odds of y by risk x = odds x/(1 + odds x) and risk y = odds y/(1 + odds y). Then the RR = (risk x)/(risk y).
