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Zorluk: Çok zorDiagnostic and Screening Test Performance

A team of researchers at an academic medical center is evaluating a novel noninvasive biomarker assay for the detection of advanced adenomas and colorectal cancer. In their initial validation study, the assay is tested on a cohort of 1,0001,000 high-risk patients referred for diagnostic colonoscopy. Within this cohort, 400400 patients are found to have advanced adenomas or colorectal cancer on biopsy. The novel biomarker assay is positive in 360360 of the patients with confirmed disease and negative in 555555 of the patients without disease.

Based on these promising results, the state department of public health plans to implement this biomarker assay as a primary screening tool for an asymptomatic, average-risk population. Epidemiological data indicates that the true prevalence of advanced adenomas and colorectal cancer in this average-risk screening population is 4%4\%.

Assuming the intrinsic sensitivity and specificity of the assay remain constant across populations, which of the following is the best estimate of the positive predictive value of this biomarker when used in the average-risk screening population?

  1. 33%33\%Cevap
  2. B
    50%50\%
  3. C
    89%89\%
  4. D
    90%90\%
  5. E
    99%99\%

Cevap

The correct answer is 33%33\%.
The correct answer is 33%33\%. Positive Predictive Value (PPV) is heavily influenced by the prevalence of the disease in the tested population. First, we determine the test's intrinsic characteristics from the validation study: the sensitivity is 90%90\% (calculated as 360360 true positives divided by 400400 total patients with disease) and the specificity is 92.5%92.5\% (calculated as 555555 true negatives divided by 600600 total patients without disease). When applied to the new average-risk population with a prevalence of 4%4\%, out of a hypothetical 1,0001,000 patients, 4040 will have the disease and 960960 will not. The test will correctly identify 3636 of the diseased patients (True Positives = 40×0.9040 \times 0.90). However, it will also incorrectly flag 7272 of the healthy patients (False Positives = 960×(1−0.925)960 \times (1 - 0.925)). The PPV is the ratio of true positives to total positive tests: 36/(36+72)=36/108=33.3%36 / (36 + 72) = 36 / 108 = 33.3\%.

Adım Adım Çözüm

1
Calculate the intrinsic test characteristics (Sensitivity and Specificity) from the validation cohort.
Sensitivity = 360/400=90%360 / 400 = 90\%. Specificity = 555/600=92.5%555 / 600 = 92.5\%.
Sensitivity and specificity are intrinsic properties of the test that do not change with disease prevalence, so they can be carried over to the new population.
2
Apply the new prevalence (4%4\%) to a hypothetical screening cohort of 1,0001,000 patients to determine disease status distribution.
Patients with disease = 4040 (1,000×0.041,000 \times 0.04). Patients without disease = 960960 (1,000−401,000 - 40).
Setting up a new 2×22 \times 2 table is required to calculate predictive values for the new population.
3
Calculate the number of True Positives (TP) and False Positives (FP) in the screening population.
TP = 40×0.90=3640 \times 0.90 = 36. FP = 960×(1−0.925)=960×0.075=72960 \times (1 - 0.925) = 960 \times 0.075 = 72.
Predictive values depend on the absolute number of true and false results in the tested population.
4
Calculate the Positive Predictive Value (PPV) for the screening population.
PPV=TPTP+FP=3636+72=36108=33.3%PPV = \frac{TP}{TP + FP} = \frac{36}{36 + 72} = \frac{36}{108} = 33.3\%.
PPV is the proportion of positive results that are true positives.

Anahtar Kavram

Positive Predictive Value (PPV) is highly dependent on disease prevalence. When a test is applied to a population with a much lower prevalence, the PPV decreases significantly because the absolute number of false positives overwhelms the true positives.

Alternatif Yöntem

This can also be solved using Likelihood Ratios (LR). The LR+ is Sensitivity / (1 - Specificity) = 0.90 / 0.075 = 12. The pre-test odds for the new population are Prevalence / (1 - Prevalence) = 0.04 / 0.96 = 1/24. Post-test odds = Pre-test odds * LR+ = (1/24) * 12 = 0.5. To find PPV (Post-test probability), use Probability = Odds / (Odds + 1) = 0.5 / 1.5 = 33.3%.
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Diagnostic and Screening Test Performance

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