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I have paired data for two tests. I would like to say that Test A is more sensitive than Best B, but not sure if I'm using the correct methods or if my data support it. I know McNemar's Exact test can be used to determine a statistical difference, but I would like to go further. My data are as follows:

Data Test_compare;
input ID :$2. test :$1. pos :$1.;
datalines;
 1 A 1
 2 A 1 
 3 A 1
 4 A 1 
 5 A 1 
 6 A 1
 7 A 1
 8 A 1
 9 A 1
 10 A 1 
 11 A 1
 12 A 1
 13 A 1
 14 A 1
 15 A 1
 16 A 1
 17 A 1
 18 A 1
 19 A 1
 20 A 1
 21 A 1
 22 A 1
 23 A 1
 24 A 1
 25 A 1
 26 A 1
 27 A 1
 1 B 1
 2 B 1 
 3 B 1
 4 B 1 
 5 B 1 
 6 B 1
 7 B 1
 8 B 1
 9 B 0
 10 B 0 
 11 B 0
 12 B 0
 13 B 0
 14 B 0
 15 B 0
 16 B 0
 17 B 0
 18 B 0
 19 B 0
 20 B 0
 21 B 0
 22 B 0
 23 B 0
 24 B 0
 25 B 0
 26 B 0
 27 B 0
 ;

 proc logistic data=test_compare;
    strata id;
    class test (ref='B') / param=ref;
    model pos(event='1') = test;
    exact test / estimate=both;
 run;

I have used Conditional Exact Logistic Regression which has produced the following Exact Odds Ratio:

                    Exact Odds Ratios
 Parameter      Estimate        95% Confidence Limits   p-Value
 test   A         26.914    *      5.855    Infinity    <.0001

Is this saying the odds of a positive result with test A are 26.9(5.855, +INF) times greater than that of Test B?

Thank you for your help!

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  • 1
    $\begingroup$ No, it is trying to say they are infinite but it has given up at 26.914. Try searching this site for separation for more details. $\endgroup$ – mdewey Feb 21 at 17:10
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No. As @mdewey implied in a comment, you have quasi-complete separation. All of your A's have pos = 1. The model breaks down.

Paul Allison wrote a very good paper at SAS Global Forum 2008: Convergence Problems in Logistic Regression. Some key points from that paper: a) The maximum likelihood estimate does not exist b) the EXACT option in SAS PROC LOGISTIC does not use maximum likelihood and the p value it prints is accurate and based on simulations. c) The parameter estimates are either conditional ML estimates or median unbiased estimates.

See Allison's paper for the details.

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