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Difficulty: HardDiagnostic and Screening Test Performance

A team of clinical researchers is investigating a novel salivary biomarker for the detection of oral squamous cell carcinoma. They conduct an initial validation study in a high-risk cohort consisting exclusively of patients with chronic heavy tobacco and alcohol use. In this specific cohort, the prevalence of the cancer is 50%50\%. Analysis of the study data reveals that the positive predictive value of the biomarker test is 90%90\%.

Following these promising results, the researchers propose implementing this biomarker as a routine screening tool in a general community dental practice, where the prevalence of oral squamous cell carcinoma is 10%10\%. The sensitivity and specificity of the assay are intrinsic properties of the test and remain constant across both populations.

What is the expected positive predictive value of this biomarker test when used in the general community dental practice?

  1. A
    18%
  2. 50%Answer
  3. C
    81%
  4. D
    90%
  5. E
    99%

Answer

The expected positive predictive value of the biomarker test in the general community dental practice is 50%.
The positive predictive value (PPV) is heavily dependent on the prevalence of the disease in the tested population. When prevalence decreases, PPV decreases. To calculate the exact new PPV, one can use odds and likelihood ratios (LR). In the 50%50\% prevalence cohort, the pre-test probability is 0.50.5, meaning pre-test odds are 1:11:1 (or 11). The PPV (post-test probability) is 90%90\%, so the post-test odds are 0.9/0.1=90.9 / 0.1 = 9. Because Post-test Odds = Pre-test Odds ×\times LR+, the LR+ for this biomarker is 99.

In the new community practice, the prevalence (pre-test probability) is 10%10\%, giving pre-test odds of 0.1/0.9=1/90.1 / 0.9 = 1/9. Using the test's fixed LR+ of 99, the new post-test odds are (1/9)×9=1(1/9) \times 9 = 1. Converting odds back to probability (Odds / (11 + Odds)), the new PPV is 1/(1+1)=0.51 / (1 + 1) = 0.5, or 50%50\%.

Alternatively, this can be proven using hypothetical values that fit the initial constraints. If sensitivity and specificity are both 90%90\%, a population of 10001000 with 50%50\% prevalence has 500500 diseased (450450 True Positives) and 500500 healthy (5050 False Positives), yielding a PPV of 450/(450+50)=90%450/(450+50) = 90\%. Applying these same parameters to a 10%10\% prevalence population yields 100100 diseased (9090 True Positives) and 900900 healthy (9090 False Positives). The new PPV is 90/(90+90)=50%90/(90+90) = 50\%.

Step-by-Step Solution

1
Determine the Positive Likelihood Ratio (LR+) of the test from the initial high-risk cohort data.
In the high-risk cohort (50%50\% prevalence), the pre-test odds are 1:11:1 (or 11). With a PPV of 90%90\%, the post-test odds are 0.9/0.1=90.9 / 0.1 = 9. Since Post-test Odds = Pre-test Odds ×\times LR+, the LR+ must be 9/1=99 / 1 = 9.
Extracting the test's inherent diagnostic performance (LR+) allows us to mathematically apply it to a population with a different prevalence.
2
Calculate the new pre-test odds and post-test odds for the general community dental practice.
The new prevalence is 10%10\%, meaning the pre-test odds are 10%/90%=1/910\% / 90\% = 1/9. Post-test Odds = Pre-test Odds ×\times LR+ = (1/9)×9=1(1/9) \times 9 = 1.
This determines the odds that a patient with a positive test in the new, lower-prevalence population actually has the disease.
3
Convert the post-test odds back to a probability to find the new Positive Predictive Value.
Probability = Odds / (11 + Odds) = 1/(1+1)=0.51 / (1 + 1) = 0.5, or 50%50\%.
The question asks for the expected PPV (a probability, not an odds ratio), which calculates out to 50%50\%.

Key Concept

The relationship between disease prevalence, likelihood ratios, and predictive values (Bayes' Theorem).
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Topics

Diagnostic and Screening Test Performance

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