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I have derived two logistic models. one has just the predictor. Other has the predictor adjusted for few co-variates. The odds ratio of the predictor in the first model is 4.6 (1.39-16.70) and the odds ratio of the same predictor from second model is 8.23(1.56-56.7). Now how should I interpret these odds ratios? Is it better because OR increases or the second OR not reliable due to broad CI?

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  • $\begingroup$ Considering your ranges, the two are not very different. It appears that your sample size is small and hence the confidence intervals are very wide. However, the factor seems to be a significant predictor of events with OR of at least 1.56 (very likely more) after correction for covariates. OR after correction of covariates is generally considered a more precise indicator. $\endgroup$
    – rnso
    Apr 22, 2015 at 5:07

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The one that has been adjusted by including other covariates and confounding variables is the so-called better one. Just the magnitude and width of 95% CI tell very little as the original estimate could have been biased upward or downward.

Also, don't be distracted by the "broader" interval. OR operates on a log scale and the CI will appear much wider just because the point estimate is higher. When the actual mean and its 95% CI are expressed in logit (by taking a natural logarithmic transformation), the widths of the CI actually aren't terribly different:

1.53 (0.33, 2.82), the width is about 2.49

2.10 (0.44, 4.03), the width is about 3.59

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