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Zorluk: Çok zorDiagnostic and Screening Test Performance

A tropical medicine clinic is evaluating symptomatic patients for a localized outbreak of a novel parasitic infection. The prevalence of the infection among symptomatic patients presenting to this clinic is 20%20\%.

Two independent rapid diagnostic point-of-care tests have been developed to detect the pathogen. They utilize entirely different biological mechanisms: Test A detects a surface glycoprotein antigen, while Test B detects a unique metabolic byproduct. Because they do not cross-react, their performance characteristics are statistically independent for both infected and uninfected individuals.

The performance characteristics of the two tests are as follows:
* Test A: Sensitivity = 80%80\%, Specificity = 90%90\%
* Test B: Sensitivity = 90%90\%, Specificity = 80%80\%

A patient presents with symptoms and is tested using BOTH assays simultaneously. Both Test A and Test B return a POSITIVE result.

Based on these results, what is the probability (expressed as a percentage) that the patient actually has the infection?

Cevap: 90 %

Cevap

90
The positive predictive value (PPV) of a combined independent testing strategy requires finding the joint probability of two true positive results and comparing it against the total probability of two positive results (true positives plus false positives). Using the given prevalence of 20%20\%, a hypothetical cohort of 1,0001,000 patients yields 200200 diseased and 800800 healthy individuals. The joint sensitivity (probability of both tests catching the disease) is 0.80×0.90=0.720.80 \times 0.90 = 0.72, resulting in 144144 true positives. The joint false positive rate (probability of both tests failing on a healthy person) is (1−0.90)×(1−0.80)=0.02(1 - 0.90) \times (1 - 0.80) = 0.02, resulting in 1616 false positives. The resulting PPV is 144/(144+16)=90%144 / (144 + 16) = 90\%. Alternatively, this can be calculated by multiplying the pre-test odds (0.20/0.80=0.250.20 / 0.80 = 0.25) by the combined positive likelihood ratio (0.72/0.02=360.72 / 0.02 = 36) to yield post-test odds of 9.09.0, which converts to a 90%90\% probability.

Adım Adım Çözüm

1
Calculate the joint sensitivity for the combined testing strategy.
0.80×0.90=0.720.80 \times 0.90 = 0.72 (or 72%72\%)
Because the tests are biologically and statistically independent, the probability of a diseased patient testing positive on BOTH tests is the product of their individual sensitivities.
2
Calculate the joint false positive rate (FPR) for the combined testing strategy.
Test A FPR = 1−0.90=0.101 - 0.90 = 0.10. Test B FPR = 1−0.80=0.201 - 0.80 = 0.20. Joint FPR = 0.10×0.20=0.020.10 \times 0.20 = 0.02 (or 2%2\%).
To find the probability of a healthy patient falsely testing positive on BOTH independent tests, you must multiply their individual false positive rates (which is 1−Specificity1 - \text{Specificity}).
3
Determine the number of true positives and false positives in a hypothetical population of 1,000 patients.
Disease Present (20%20\%): 200200 patients. Disease Absent (80%80\%): 800800 patients. True Positives: 200×0.72=144200 \times 0.72 = 144. False Positives: 800×0.02=16800 \times 0.02 = 16.
Mapping the probabilities to a theoretical population makes the Positive Predictive Value (PPV) calculation straightforward using a standard 2×22 \times 2 contingency framework.
4
Calculate the Positive Predictive Value (PPV).
PPV=144144+16=144160=0.90PPV = \frac{144}{144 + 16} = \frac{144}{160} = 0.90.
PPV represents the probability that the patient has the disease given the specific positive test results. It is the ratio of true positives to total positives.

Anahtar Kavram

Calculating the Positive Predictive Value (PPV) of a dual independent testing strategy using joint probabilities.
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Konular

Diagnostic and Screening Test Performance

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