You work in a setting in which school teachers refer students to you who they believe may have learning difficulty. One day you give the reading test to a student called Aleksandra, who was referred to you by her school teacher. The test indicates that Aleksandra’s reading score is below expected.

Aleksandra's teacher asks you what the percentage chance is that Aleksandra has learning difficulty. What is the best reply?

Question

You work in a setting in which school teachers refer students to you who they believe may have learning difficulty. One day you give the reading test to a student called Aleksandra, who was referred to you by her school teacher. The test indicates that Aleksandra’s reading score is below expected.

Aleksandra's teacher asks you what the percentage chance is that Aleksandra has learning difficulty. What is the best reply?

BlackTom AI · Accepted Answer

Positive predictive value (PPV) depends on the test’s sensitivity, specificity and the prevalence (base rate) of the condition in the population tested. Use Bayes’ rule to convert a positive test result into the probability the child truly has the condition.

Bayes formula for PPV:
PPV = [sensitivity × prevalence] / [sensitivity × prevalence + (1 − specificity) × (1 − prevalence)]

Step-by-step reasoning and numeric illustration:
1. Suppose the published validation study of the reading test produced a PPV of about 75% for a “below expected” score. That PPV arises from particular sensitivity, specificity and the prevalence in that study. For illustration, if sensitivity = 0.80 and specificity = 0.90, and the study prevalence p ≈ 0.27, then:
   - numerator = sensitivity × prevalence = 0.80 × 0.27 = 0.216
   - false positives term = (1 − specificity) × (1 − prevalence) = 0.10 × 0.73 = 0.073
   - denominator = 0.216 + 0.073 = 0.289
   - PPV = 0.216 / 0.289 ≈ 0.748 ≈ 75%
2. This demonstrates how the 75% figure is a PPV that depends on the original study’s base rate (prevalence). If the local prevalence differs (for example, a clinic that sees many referred children will have a higher prevalence), the PPV will change.

Why the correct answer is correct:
- Saying “75%” with the caveat that it assumes a similar base rate explicitly acknowledges PPV’s dependence on prevalence. That is the appropriate way to communicate the probability after a positive screen.

Why the other options are incorrect:
- Options invoking “90%” are inconsistent with the published PPV (75%) and would be wrong unless different test parameters/prevalence were specified.
- The option that ties the estimate to specificity being higher than sensitivity is misleading: PPV is determined by both sensitivity and specificity plus prevalence, not simply by which is larger.

Conclusion: The best reply is “75%, but this estimate assumes the base rate (prevalence) in your setting is about the same as the base rate (prevalence) was in the original study,” matching the provided answer.

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