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Recently there has been much interest in estimating the prevalence (risk, proportion or probability) ratio instead of the odds ratio, especially in occupational health studies involving common outcomes (for example, with prevalence rates above 10%). For example, if 80 out of 100 exposed subjects have a particular disease and 50 out of 100 non-exposed subjects have the disease, then the odds ratio (OR) is (80/20)/(50/50) = 4. However, the prevalence ratio (PR) is (80/100)/(50/100) = 1.6. The latter indicates that the exposed subjects are only 1.6 times as likely to have the disease as the non-exposed subjects, and this is the number in which most people would be interested. There is considerable literature on the advantages and disadvantages of OR versus PR (see Greenland,1 Stromberg,2 Axelson et al3 and others). In this article we will review the existing methods and give examples and recommendations on how to estimate the PR.
The most common method of modelling binomial (no/yes or 0/1) health outcomes today is logistic regression. In logistic regression one models the probability of the binomial outcome (Y = 1) of interest as:
P(Y = 1| X1, X2, …, Xk) = eXβ/(1+eXβ)
where Xβ = β0+β1X1+β2X2+…+βkXk. Then exp(β1) = OR for a 1 unit increase in X1 adjusted for all other variables in the model. Logistic regression yields maximum likelihood estimates (MLEs) of the OR (adjusted for other covariates). If the adjusted OR is the parameter of interest, then these MLEs are generally considered the best estimators available. The adjusted OR can also be used to estimate the adjusted PR, but this should only be done for a rare disease (eg, one with a prevalence of 10% or less). This, together with the fact that …
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