Question

1. during a hearing screening programme, 1000 newborns are screened and 40 fail. diagnostic testing later confirms hearing loss in only 5 infants.

the screening programme demonstrates:

a. high specificity, low sensitivity
b. high sensitivity, low positive predictive value
c. high positive predictive value
d. poor sensitivity and poor specificity

Explanation:

Define the given parameters

We identify the key values from the screening scenario:

• Total newborns screened: \(1000\)
• Number of newborns who fail the screening (test positive): \(40\)
• Number of newborns confirmed with hearing loss (true cases): \(5\)

Analyze the positive predictive value

The positive predictive value (PPV) is the probability that a subject has the condition given a positive test result:

$$ \text{PPV} = \frac{\text{True Positives (TP)}}{\text{Total Test Positives}} $$

Assuming all 5 confirmed cases were among the 40 who failed the screening (which is the standard assumption for a screening program where only those who fail are referred for diagnostic testing):

• \(\text{TP} = 5\)
• \(\text{Total Test Positives} = 40\)
• \(\text{PPV} = \frac{5}{40} = 12.5\%\)

A PPV of \(12.5\%\) is considered low because the vast majority of those who fail the screening (\(87.5\%\)) do not actually have the condition.

Analyze the sensitivity

Sensitivity is the probability that the test correctly identifies those with the condition:

$$ \text{Sensitivity} = \frac{\text{True Positives (TP)}}{\text{Total Diseased}} $$

Since diagnostic testing confirmed hearing loss in 5 infants, and assuming the screening successfully detected them:

• \(\text{TP} = 5\)
• \(\text{Total Diseased} = 5\)
• \(\text{Sensitivity} = \frac{5}{5} = 100\%\)

Even if there were undetected cases (false negatives), detecting all 5 confirmed cases indicates a high sensitivity. Screening programs are designed to have high sensitivity to avoid missing any affected individuals.

Match with the options

We evaluate the calculated metrics against the choices:

• High sensitivity: Correct, as it is designed to catch all true cases.
• Low positive predictive value: Correct, as only \(12.5\%\) of those who failed actually had the disease.

This matches option B.

Answer:

• (A) High specificity, low sensitivity
• (B) High sensitivity, low positive predictive value (Correct answer)
• (C) High positive predictive value
• (D) Poor sensitivity and poor specificity