If HbA1c greater than 15% predicts diabetic retinopathy and 88% of patients without retinopathy have HbA1c less than 15%, what is the specificity of the threshold?

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Multiple Choice

If HbA1c greater than 15% predicts diabetic retinopathy and 88% of patients without retinopathy have HbA1c less than 15%, what is the specificity of the threshold?

Explanation:
Specificity measures how well a test identifies people who do not have the condition. Here, treating an HbA1c above 15% as a positive test for retinopathy, the portion of people without retinopathy who test negative is 88% (they have HbA1c below 15%). That is exactly the definition of specificity. So the threshold has a specificity of 88%. (For completeness: sensitivity would be about how many with retinopathy test positive, positive predictive value about the probability of retinopathy given a positive test, and negative predictive value about the probability of no retinopathy given a negative test.)

Specificity measures how well a test identifies people who do not have the condition. Here, treating an HbA1c above 15% as a positive test for retinopathy, the portion of people without retinopathy who test negative is 88% (they have HbA1c below 15%). That is exactly the definition of specificity. So the threshold has a specificity of 88%.

(For completeness: sensitivity would be about how many with retinopathy test positive, positive predictive value about the probability of retinopathy given a positive test, and negative predictive value about the probability of no retinopathy given a negative test.)

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