Considerthemammogramdiagnosticexamplein Section 2.1.4. (a) Showthatthejointprobabilitydistributionofdiagnosisanddiseasestatusisasshownin Table2.6. Giventhatadiagnostictestresultispositive,explainhowthisjointdistribution showsthatthe12%ofincorrectdiagnosesforthe99%ofwomennothavingbreastcancer swampthe86%ofcorrectdiagnosesforthe1%ofwomenactuallyhavingbreastcancer. (b) ThefirsttestfordetectingHIV-positivestatushadasensitivityof0.999andspecificity of 0.9999.Explainwhatthesemean.Ifatthattime1in10,000menweretrulyHIV- positive,findthepositivepredictivevalue.Basedonthisexample,explainthepotential disadvantageofroutinediagnosticscreeningofapopulationforararedisease. TABLE 2.6

Considerthemammogramdiagnosticexamplein Section 2.1.4.

(a) Showthatthejointprobabilitydistributionofdiagnosisanddiseasestatusisasshownin Table2.6. Giventhatadiagnostictestresultispositive,explainhowthisjointdistribution showsthatthe12%ofincorrectdiagnosesforthe99%ofwomennothavingbreastcancer swampthe86%ofcorrectdiagnosesforthe1%ofwomenactuallyhavingbreastcancer.

(b) ThefirsttestfordetectingHIV-positivestatushadasensitivityof0.999andspecificity of 0.9999.Explainwhatthesemean.Ifatthattime1in10,000menweretrulyHIV-

positive,findthepositivepredictivevalue.Basedonthisexample,explainthepotential disadvantageofroutinediagnosticscreeningofapopulationforararedisease.

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TABLE 2.6 Joint probability distribution for disease status and diagnosis of breast cancer mammogram, based on conditional probabilities in Table 2.1 Disease Diagnosis from Mammogram Positive (+) Status Yes (D) 0.0086 No (D) 0.1188 Negative (-) 0.0014 Total 0.01 0.8712 0.99