Question

A hypothetical study (Study A) looked at the association of opiate use and sleep disorders. Recent opiate use was measured using a questionnaire asking about prescription medication containing opiates and illicit opiate use. The investigators were concerned that self-reported exposures may be inaccurate due to the legal and social implications of this class of drugs, so they also collected urine samples for an immunoassay screening test (gold standard). Some of your colleagues are planning another study (Study B) involving opiate exposures, and you help them decide how best to measure their exposure by evaluating the accuracy of the survey used in Study A against the immunoassay results. Calculate the sensitivity and specificity of exposure for cases and controls. Show all your work.

Cases		Gold Standard Results (Immunoassay)
		Exposed	Not Exposed	Total
Survey Results	Exposed	435	57	492
	Not Exposed	90	418	508
	Total	525	475	1000

Controls		Gold Standard Results (Immunoassay)
		Exposed	Not Exposed	Total
Survey Results	Exposed	270	48	318
	Not Exposed	55	352	407
	Total	325	400	725

Answer 1

for the cases

sensitivity=True positive/(true positve+false negative)=TP/(TP+FN)=435/525=0.8286

specificity= True negative(True negative+false positive)=TN/(TN+FP)=418/475=0.88

for control

sensitivity=270/325=0.8308

specificity=352/400=0.88

Cases		Gold Standard Results (Immunoassay)
		Exposed	Not Exposed	Total
Survey Results	Exposed	435(TP)	57(FP)	492
	Not Exposed	90(FN)	418(TN)	508
	Total	525	475	1000

Controls		Gold Standard Results (Immunoassay)
		Exposed	Not Exposed	Total
Survey Results	Exposed	270(TP)	48(FP)	318
	Not Exposed	55(FN)	352(TN)	407
	Total	325	400	725