# How do I find out specificity/sensitivity/predictive value with only prevalence and # of positives

I understand that

specificity = True Positive / (True Positive + False negative)
sensitivity = True negative / (False positive + True negative)

positive pv = True positive / (True positive + False positive)
negative pv = True negative / (true negative + False negative)


However, assume I know only which percent of population is resulted as positive in a certain test. also, I do know the prevalence. How can I calculate specificity/sensitivity/predictive values in this case?

the question can be reduced into:

fill blanks given x, y, z, w
test    diagnosis    sum
positive    ?         ?         x
negative    ?         ?         y
sum         z         w

• 'test' and 'diagnosis' aren't the best labels here, I think. Maybe "Ill" and "Well" or some such? Commented Sep 29, 2013 at 15:47
• I don't think you can - that is really the point of specificity/sensitivity etc. to tell you how good a test it. The margins, by definition really, don't tell you the joint relationship. Commented Sep 29, 2013 at 15:57

This is because (in your notations) x+y=z+w.