Example 1: Colonoscopy

203 people undergo colonoscopy to screen for early colon cancer (the gold standard). They also have a stool sample tested for occult blood. Two people have blood in the stool and confirmed cancer on colonoscopy, eighteen people have blood in the stool but have normal colonoscopy, and one person has cancer found on colonoscopy but has a negative test for fecal occult blood. One hundred eighty two people have a negative colonoscopy and a negative test for fecal occult blood. What is the specificity and sensitivity of the test for fecal occult blood? What is the positive predictive value? What is the negative predictive value for the test?

		Condition (as determined by the gold standard endoscopy)
		+ Test	- Test
Test Outcome Fecal Occult Blood	Positive test outcome	TP = 2 a	FP = 18 b	PPV=TP/(TP+FP) PPV = a/(a+b) =2/2+18 =2/20=10%
	Negative	FN =1 c	TN = 182 d	NPV=TN/(TN+FN) NPV = d/(c+d) =182/1+182 =182/183=99.45%
		TP/(TP+FN) =2/(2+1) =2/3=66.666%	=TN/(FP+TN) =182/ (18+182) =182/200= 91%