A school nurse examined a population of 1,000 children in an attempt to detect h

Question

A school nurse examined a population of 1,000 children in an attempt to detect hearing impairment. The prevalence of a hearing impairment in this population is known to be 20%. The sensitivity of the examination is 50% and its specificity is 80%. All children labeled as "positive" (i.e., suspected of having a hearing impairment) by the school nurse are sent for further examination by an audiologist. The sensitivity of the audiologist's examination is 98% and its specificity is 90%.

What is the overall sensitivity of the sequential examinations?

Explanation / Answer

P(hearing impairment) = 0.2

P(school nurse tested positive/hearing impairment) = 0.5 =>P(school nurse tested negative/hearing impairment) = 0.5

P(school nurse tested negative/no hearing impairment) = 0.8 =>P(school nurse tested positive/no hearing impairment) = 0.2

P(audiologist's examination positive/hearing impairment) = 0.98

P(audiologist's examination negative/no hearing impairment) = 0.9

overall sensitivity of the sequential examinations = P(both test poisitve/hearing imapairment) = 0.5*0.98 = 0.49 or 49%

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