I would like to test the difference of two odds ratios given the following R-output:

`f=with(data=imp, glm(Y~X1+X2, family=binomial(link="logit"))) s01=summary(pool(f1)) s01 `

`est se t df Pr(>|t|) (Intercept) -1.7805826 0.1857663 -9.585070 391.0135 0.00000000 X1 0.2662796 0.1308970 2.034268 390.4602 0.04259997 X2 0.6757952 0.3869652 1.746398 395.6098 0.08151794`

`cbind(exp(s01[, c("est", "lo 95", "hi 95")]), pval=s01[, "Pr(>|t|)"]) `

`est lo 95 hi 95 pval (Intercept) 0.1685399 0.1169734 0.2428389 0.00000000 X1 1.3051000 1.0089684 1.6881459 0.04259997 X2 1.9655955 0.9185398 4.2062035 0.08151794`

To do so, I would need to take the difference of the log odds and obtain the standard error (outlined here: Statistical test for difference between two odds ratios?).

One of the predictor variables is continuous and I am not sure how I could compute the values required for $SE(logOR)$.

Could someone please explain whether the output I have is conducive to this method?

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#### Best Answer

If you want to test whether `exp(X1)`

is statistically different from `exp(X2)`

then you do not need to perform any statistical tests *in this case*.

**Just observe the confidence intervals.** In general, we cannot infer that point estimates are statistically different when the confidence intervals overlap, but this is a special case…..

The confidence interval for `exp(X1)`

is (1.01, 1.68) while for `exp(X2)`

it is (0.92, 4.21)

The confidence interval for `exp(X1)`

is **completely contained** within the confidence interval for `exp(X2)`

Therefore they are not statistically different.

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