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2	Sensitivity and Specificity We most often characterize the sensitivity and specificity of a diagnostic test Sensitivity of test: Probability of positive in diseased Sample a cohort of subjects with the disease Estimate the proportion who have a positive test result: Pr ( + \| D ) Specificity of test: Probability of negative in healthy Sample a cohort of healthy subjects Estimate the proportion who have a negative test result: Pr( - \| H )
3	Predictive Values of Positive and Negative We are actually interested in the diagnostic utility of the test: Predictive value of positive and negative Predictive value of a positive test: Probability of disease when test is positive Pr ( D \| + ) Predictive value of a negative test: Probability of health when test is negative Pr ( H \| - )
4	Bayes Rule for Binary Random Variables We usually compute the predictive value of positive and negative tests using Bayes rule
5	Role of Prevalence Key property: Computation of predictive value of positive uses sensitivity, specificity, AND prevalence of disease
6	Role of Prevalence Key property: Computation of predictive value of negative uses sensitivity, specificity, AND prevalence of disease
7	Diagnostic Testing: Example VDRL in diagnosing syphilis: High sensitivity and high specificity Sensitivity of test: Probability of positive in diseased 90% of subjects with syphilis test positive (Actually depends on duration of infection) Specificity of test: Probability of negative in healthy 98% of subjects without syphilis test negative (Actually depends on age and prevalence of certain other diseases)
8	Diagnostic Testing: Example Predictive values when prevalence is high Ex: STD clinic Prevalence of syphilis 30% PV+: 95% with positive VDRL have syphilis VDRL Pos Neg \| Tot Syphilis Yes 270 30 \| 300 No 14 686 \| 700 Total 284 716 \| 1000
9	Diagnostic Testing: Example Predictive values when prevalence is low Ex: Screening for marriage exam Prevalence of syphilis 2% PV+: 48% with positive VDRL have syphilis VDRL Pos Neg \| Tot Syphilis Yes 18 2 \| 20 No 20 960 \| 980 Total 38 962 \| 1000
10	Role of Prevalence Bottom line: Predictive value of a diagnostic test depends heavily on the prevalence of the disease More generally: When using Bayes rule, to calculate probabilities, the computed values are specific to the assumed “prior” information