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Zorluk: OrtaDiagnostic Testing Performance

An investigational noninvasive urine biomarker is being evaluated for the detection of urothelial carcinoma in patients with asymptomatic microscopic hematuria. Epidemiological data indicates that the prevalence of urothelial carcinoma in the target demographic (adults aged 50-70 with isolated microscopic hematuria) is 4%4\%.

Validation studies of the new biomarker demonstrate a sensitivity of 80%80\% and a specificity of 90%90\% for detecting urothelial carcinoma.

A 62-year-old man with asymptomatic microscopic hematuria undergoes testing with this new urine biomarker, and the result is positive.

Based on these test characteristics, what is the probability (in percentage) that this patient actually has urothelial carcinoma?

Cevap: 25 %

Cevap

The probability that the patient actually has urothelial carcinoma is 25%.
The positive predictive value (PPV) is heavily influenced by the prevalence of the disease in the population being tested. Despite a seemingly high sensitivity (80%) and specificity (90%), the low prevalence (4%) means that the absolute number of healthy individuals is vastly larger than the number of diseased individuals. Consequently, the 10% false positive rate generates a large number of false positive results (960) that outnumber the true positive results (320). Therefore, the probability that a positive test indicates true disease is only 320 / 1280, or 25%.

Adım Adım Çözüm

1
Assume a hypothetical population of 10,000 patients from the target demographic.
Total population = 10,000.
Using a hypothetical population size makes calculating the exact number of true and false positives simpler than using probabilities directly.
2
Calculate the number of patients with and without the disease based on the 4% prevalence.
Patients with disease = 400. Patients without disease = 9,600.
Prevalence dictates the baseline risk (pretest probability) in the specific demographic being tested.
3
Calculate True Positives (TP) using the 80% test sensitivity.
TP = 400 × 0.80 = 320.
Sensitivity is the proportion of patients with the disease who correctly test positive.
4
Calculate False Positives (FP) using the 90% test specificity.
FP = 9,600 × (1 - 0.90) = 9,600 × 0.10 = 960.
Specificity is the proportion of healthy patients who correctly test negative. The remainder (10%) represents healthy patients who incorrectly test positive.
5
Calculate the Positive Predictive Value (PPV).
PPV = 320 / (320 + 960) = 320 / 1,280 = 0.25 (or 25%).
PPV represents the probability that a positive test result is a true positive.

Anahtar Kavram

Positive Predictive Value (PPV) dependence on disease prevalence

Alternatif Yöntem

This can also be solved using Likelihood Ratios (LR). Pretest Probability = 0.04, so Pretest Odds = 0.04 / 0.96 = 1/24. The Positive Likelihood Ratio (LR+) = Sensitivity / (1 - Specificity) = 0.80 / 0.10 = 8. Post-test Odds = Pretest Odds × LR+ = (1/24) × 8 = 1/3. Converting back to probability: Post-test Probability = Odds / (1 + Odds) = (1/3) / (4/3) = 1/4 = 25%.
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