# Sensitivity & Specificity calculation

I have a medical diagnostic test $A$ and test $B$. Test $B$ is the current gold standard. Test $A$ has an excellent negative predictive value and if it is negative, test $B$ is not performed as it is invasive.

However if test $A$ result is positive above certain cut off, test $B$ is performed to confirm the results. I have about $600$ patients who had test $A$, and about $200$ patients who tested positive with test $A$ were then tested with $B$ to confirm the findings.

I want to test the accuracy of test $A$ against test $B$, for the $200$ hundred positive results on test $A$:

1. How can I get the sensitivity/specificity analysis ? as I have positives & negatives for test $B$ but only positives for test (A).
2. What statistical methods will be suitable to compare the accuracy of test (A) against test $B$, the gold standard. Sensitivity requires that you have the true positives (A) as well as the column total (A+C). Specificity requires that you have the true negatives (D) as well as the column total (B+D).

In your case, you have 200 patients who tested positive for diagnostic test A, which would be the row total (A+B). As it is, I don't think you can calculate anything other than the positive predictive value, which is the number of true positives (A) divided by the number of positive calls (A+B). You would need all 600 patients with both test results to assess the sensitivity and specificity of diagnostic test A.

• Thank you very much for your reply, What you have said was my real apprehension that I wont be able do the desired sensitivity & specificity calculations as only the positives for test ( A) had test (B), and not the negatives. You have clarified my confusion about this point. is there any other statiscal analysis I can perform on the available data to compare the accuracy for test A against test B.
– IUHK
Aug 15, 2018 at 23:03
• Let me clarify a bit more, I am comparing the accuracy of Cardiac CT angiography(test A) against invasive coronary angiography (Test-B)in quantification of degree of stenosis. It is believed that cardiac CT over estimated the degree of stenosis . if the patients have >50% stenosis, they undergo invasive angiography. Thats why only 200 out of the 600 patient were included as they had stenosis greater than the cut off 50%, and needed invasive test (B), we want to see if the estimation by CT (test-A) was , confirmed by Test (B),i.e Accuracy of test (A) . what statistical option are available?
– IUHK
Aug 15, 2018 at 23:14
• You could examine how much test B is a good predictor of test A, using linear regression, the continuous value of test A as a dependant variable and the continuous value of test B as an independant variable. The coefficient would give you an estimate as to how much, in average, test A over or underestimates test B. If you don't have those continuous values, and only have dichotomous variables (i.e. variables coded 0 and 1, for under or over the cutoff values), I don't think you can do anything, as every participant has undergone test A, and therefore there is no variability. Aug 16, 2018 at 20:39
• Thank you again for your reply; actually you have clarified a lot to me; i am not good at statistics. I spent a good bit of time collecting the data without taking an advice and pre planning the peject. It looks like i will be left with a garbage at the end but at least you clarified my confusion añd i wont be wasting any more time on this. I am indebted to you for that. My data is collected in categoties normal =0; minimal 1; mild 2; moderate 3; severe 4; the data colected as per patient; per artery and per artery segment ( 16 segments ) .
– IUHK
Aug 16, 2018 at 21:17