Dear All,
I hope my message finds you well.
I'm doing a diagnostic study to find out the most accurate method to diagnose fever in febrile infants. I'm using axillary temperature mesuramtent as an index test and rectal temperature as a reference test. The total population size is 201. The number of infants diagnosed using axillary method were 159, whereas rectal temperature was positive for every subject. The number of infants who had normal temperature using axillary method and had fever using rectal method were 36. How can I calculate the sensitivity and specificity? I find it confusion a bit because I don't seem to understand how to allocate the numbers in the cross-tab.
Thank you for your cooperation!
Hello Yazeed,
Can you clarify the results a bit? N = 201, Axillary positives which were also Rectal positives = 159, Number of Axillary negatives when Rectal was positive = 36. Were all 201 classed as Rectal positives? (If so, you will not be able to estimate specificity, as there were no true negative cases.)
The 159 represents the number of true positive cases (TP). The 36 represents the number of false negative cases (FN). You haven't as yet accounted for the false positive cases (FP: instances where axiallary was positive, but rectal was negative) or the number of true negative cases (TN: where axillary and rectal were both negative). These last two would have to sum to 201 - 159 - 36 = 6 cases.
Sensitivity = TP / (TP + FN) = 159 / (159 + 36) = 159 / 195 = .815 or 81.5%
Specificity = TN / (TN + FP) = unknown, due to incomplete description
Good luck with your work.
Thank you for your clarification! Yes, all 201 cases are positive in the gold standard test (rectal temperature). The study is prospective nested cohort. All cases included are positive for fever. I want to compare the accuracy of axillary temperature to rectal. Does this mean I cannot generate a valid conclusion when specificity is not determined? How would you suggest to solve this issue? Thank you again for your answer! David Morse
Just to add a little bit to Prof Morse suggestions. You might take a look at the attached screenshot information. It's a good way to summarize your results. Best wishes David Booth
Hello again Yazeed,
If you're only sampling cases for which the referent condition/method (here, rectal temperature) shows positive, you'll never be able to estimate specificity for the trial condition/method (here, axillary). The only way to estimate specificity is to amass a number of cases in which the referent condition shows negative results, and record the trial condition results for those cases.
Since all 201 of the cases were positive for the referent condition, then did you test only 159+36 = 195 of these cases using the axillary method? Was there some reason for not testing the other 6 cases (or were these records somehow unusable)?
Good luck with your work.
Thank you for your response!
Apparently all 201 cases are positive for the reference test. 42 cases were false negative after double-checking. What would you recommend to establish a valid conclusion when determining specificity is not possible? I presume that specificity is not important here because we're only looking at fever without any other different cause.
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