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Zorluk: OrtaDiagnostic Testing Performance

A 4545-year-old woman visits her primary care physician for a routine wellness examination. She is generally healthy but reports a strong family history of a specific autoimmune thyroid disorder. The physician explains that based on her demographic profile and family history, her pretest probability of having the subclinical form of this disorder is 20%20\%. They discuss a newly approved serum biomarker assay that detects this condition. Clinical validation studies demonstrate that this assay has a sensitivity of 75%75\% and a specificity of 90%90\%. The patient opts to proceed with the screening, and the laboratory reports a positive result. Which of the following is the approximate probability that this patient truly has the subclinical autoimmune disorder?

  1. A
    20%20\%
  2. 65%65\%Cevap
  3. C
    75%75\%
  4. D
    87%87\%
  5. E
    94%94\%

Cevap

65%65\%
The correct answer is 65%65\%. The question requires determining the post-test probability of disease given a positive test result, which is the Positive Predictive Value (PPV). The PPV depends on the test's sensitivity, specificity, and the pretest probability (prevalence) of the condition in the patient's demographic. This can be calculated easily using a hypothetical 100100-person population model:

1. Disease distribution: Based on a 20%20\% pretest probability, 2020 people truly have the disease and 8080 do not.
2. True Positives (TP): Sensitivity is 75%75\%. Out of 2020 people with the disease, 1515 will correctly test positive (20×0.75=1520 \times 0.75 = 15).
3. False Positives (FP): Specificity is 90%90\%, meaning the false positive rate is 10%10\%. Out of 8080 people without the disease, 88 will falsely test positive (80×0.10=880 \times 0.10 = 8).
4. PPV Calculation: The total number of positive results is 2323 (15 TP+8 FP15 \text{ TP} + 8 \text{ FP}). The probability that a positive result is a true positive is 15/23≈0.652115 / 23 \approx 0.6521, or approximately 65%65\%.

Adım Adım Çözüm

1
Set up a hypothetical population (e.g., 100100 patients) to determine the distribution of true disease based on the pretest probability.
With a 20%20\% pretest probability, 2020 patients have the disease and 8080 patients do not have the disease.
Creating a standard population model makes it easier to visualize and calculate true positives and false positives without complex algebraic formulas.
2
Calculate the number of true positive results using the test's sensitivity.
Sensitivity is 75%75\%. Therefore, 75%75\% of the 2020 patients with the disease will test positive (20×0.75=1520 \times 0.75 = 15 true positives).
Sensitivity measures the proportion of actual positives that are correctly identified as such.
3
Calculate the number of false positive results using the test's specificity.
Specificity is 90%90\%, meaning the false positive rate is 10%10\%. Therefore, 10%10\% of the 8080 patients without the disease will incorrectly test positive (80×0.10=880 \times 0.10 = 8 false positives).
Specificity measures the proportion of actual negatives that are correctly identified. The remainder (1−Specificity1 - \text{Specificity}) represents the false positive rate.
4
Calculate the Positive Predictive Value (PPV), which is the probability of having the disease given a positive test.
PPV=True PositivesTotal Positives=1515+8=1523≈0.652\text{PPV} = \frac{\text{True Positives}}{\text{Total Positives}} = \frac{15}{15 + 8} = \frac{15}{23} \approx 0.652, or 65%65\%.
PPV directly answers the clinical question: 'Given a positive test result, what is the actual probability that my patient has the disease?'

Anahtar Kavram

Positive Predictive Value (PPV) calculation and the effect of pretest probability on post-test outcomes.
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Konular

Diagnostic Testing Performance

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