# Conditional Exact Logistic Regression

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?