Diagnostic accuracy and screening statistics — formative SAQs

SAQ 1 (10 marks)

A newborn bloodspot screen for a rare metabolic condition comes back positive in an otherwise well baby. The test has a sensitivity of 99 percent and a specificity of 99 percent, and the condition affects 1 in 10,000 babies. [4]

1. Build the 2×2 table for a population of 10,000 babies and calculate the sensitivity, specificity, and positive predictive value. (5) [4] [1]
2. Explain why the positive predictive value is so low despite the excellent specificity, and name the principle that governs it. (3) [4]
3. Describe how you would counsel the family and what the next step is. (2) [4] [13]

Model answer

Of 10,000 babies, one is truly affected (prevalence 1 in 10,000) and 9,999 are well. With a sensitivity of 99 percent, the test catches the single true case as one true positive. With a specificity of 99 percent, one percent of the 9,999 well babies test falsely positive, giving about 100 false positives. Sensitivity is one true positive divided by one affected, or 99 percent; specificity is about 9,899 true negatives divided by 9,999 well, or 99 percent; the positive predictive value is one true positive divided by about 101 positives, or roughly 1 percent. [4] [1]

The positive predictive value is low because it is a function of prevalence, not of the test's intrinsic quality. In a low-prevalence population the many false positives thrown up by the large healthy majority overwhelm the single true case, so even a 99 percent specific test yields mostly false positives. Sensitivity and specificity are fixed properties of the test at its threshold, but the predictive value inherits the ratio of diseased to well, which is what prevalence sets. [4]

I would counsel the family that most babies with a positive screen are well, that the screen is a reason to confirm rather than a diagnosis, and that the next step is the reference-standard confirmatory test. I would avoid conveying a diagnosis before confirmation and would acknowledge the anxiety the screen has caused. [4] [13]