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# PROC LOGISTIC for 2X2-Tables with cltype = exact for OR

Dear SAS-Users,

I am analyzing different types of creating confidence intervals for the Relativ Risk (RR) out 2X2-Tables. As the Odds Ratio(OR) is a good estimator for the RR in a few situations, I decided to include the exact logistic regression.

I do know that this method is recommended for the use with small sample, but I would like to include samples with 2500 datapoints or more. The problem is, that for example in the case with 1000 in one group and 1500 in the other one SAS sometimes produces Warnings I do not really understand. I will give you an example for each and attach an example file.

1. WARNING: An exact median-unbiased confidence interval was not obtained, possibly due to specifying a MIDPFACTOR= value which is too small.

CASE: 842 responses in the smaller group, 1500 responses in the bigger group.

I didn't specify a MIDPFACOTR, so this is not the problem (SAS produces the exact CI and not die mid-p-one). I do not really understand, what is happening here. I do know, that if the observed value of t_1  ist the biggest or the smallest possible, the conditional likelihood is montonically increasing. But here t_1 is 842, not the biggest or smallest one and so I do not understand, why SAS uses the median-unbiased estimator. Nevertheless, if I would know why the median-unbiased estimator ist used, would the warning mean this: The estimated confidence intervall, which can be produced without an estimator, does not contain the median-unbiased estimator so the confidence intervall isn't valid?

2. WARNING: Invalid confidence interval detected and set to missing.

CASE: 1 response in the smaller group, 203 responses in the bigger group.

Here the "usual" estimator is used. It is equal to the on with 202 or 204 responses in the bigger group (estimator: 0.006), but the limits are different. If there are 202 or 204 responses, the lower limit is smaller than 0.001 and the upper is 0.0037 or 0.0036. In the observed case with 203 responses, the lower limit is 0.006 (=estimator) and the upper is set to missing (warning). Here, I can't think of a reasonable explanation.

I would appreciate any kind of help or advice! Thank you in advance!

Best wishes,

Daniela

SAS Employee
Posts: 31

## Re: PROC LOGISTIC for 2X2-Tables with cltype = exact for OR

Hi Daniela,

Exact methods can get computationally infeasible as the sample size increases. This is probably the reason why you are getting Warnings.

For a reference please take a look at the documentation:

http://support.sas.com/documentation/cdl/en/statug/65328/HTML/default/viewer.htm#statug_logistic_det...

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