In multivariate regression analysis, it seems that people use different definitions of adjusted odds ratios. Could you please clarify for me what an adjusted OR is and how it differs from a non-adjusted OR?
Thanks!
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Unadjusted OR is a simple ratio of probabilities of outcome in two groups $p_1, p_2$ (check here or here):
$$OR = \frac{p_1/(1-p_1)}{p_2/(1-p_2)} $$
and it can be derived from the results of logistic regression (as opposed to counting a simple ratio calculated by hand from a $2 \times 2$ table). However, in logistic regression you can include other, confounding variables so to control their influence on your dependent variable and if you do so, what you can get is OR that is adjusted for the influence of confounders (see also here). So you adjust by controlling additional variables in logistic regression model.
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$\begingroup$ Thanks a lot for your answer. A quick follow-up question: in multivariate regression analysis, in order to evaluate the relative contribution of mulitple factors, you then need to look at adjusted odds ratios and not simply odds ratios? $\endgroup$– davCommented Jan 2, 2015 at 20:32
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$\begingroup$ Yes, the same as with $R^2$ and adjusted $R^2$ etc. $\endgroup$– TimCommented Jan 2, 2015 at 20:36