proc logistic: discrepancies in estimates/ORs and p-vals/confidence intervals

[reubendon]

proc logistic data = test;
	class predictor (ref = "1");
	model outcome (event = "1") = predictor; 
run;

RESULTS:

Question 1: Why are my odds ratios different from exp(estimate)? For example, when predictor = "0", coefficient = 0.5660, and using OR = exp(estimate), exp(0.5660) = 1.76 but the calculated odds ratio estimate is 2.226.

Question 2: The coefficient for predictor = "2" is significant, but a value of OR = 1 spans the 95% Wald confidence interval. If this coefficient is significant, shouldn't 1 not be in the CI?

[SAS_Rob]

Take a look at this usage note.

23087 - Odds ratio estimate is not equal to the exponentiated parameter estimate - exp(Beta)

Essentially, the default parameterization for the CLASS variables involves effects coding and thus the odds ratios are no longer merely exp(beta) and interpretation of the parameter estimates is no longer simply the log odds comparing the level vs the reference.

[quickbluefish]

If you add the option / param=ref  to the end of your CLASS statement, you will find that the odds ratios equal exp(estimate), i.e., 

class predictor (ref='1') / param=ref;

There's a good explanation of what's going on here:

https://stats.oarc.ucla.edu/sas/faq/in-proc-logistic-why-arent-the-coefficients-consistent-with-the-...

[Ksharp]

For your second question. p-value is highly depended on the size of sample.
if your size of sample is large enough, you would always get <.0001 .
It has nothing to do with CI of OR or estimated coefficient.
And p-value is said for alpha=0.05, if you set alpha=0.0001, you would also get H0 is not significant conclusion.