Examkin

Question

Difficulty: HardDiagnostic Testing Performance

A 45-year-old female computer programmer is evaluated in the primary care clinic for a 3-month history of right wrist pain, accompanied by tingling and numbness that frequently awakens her at night. Based on the patient's history and physical examination, the physician estimates the pretest probability of carpal tunnel syndrome to be 20%20\%. To aid in the clinical diagnosis before considering nerve conduction studies, the physician performs Phalen's maneuver. Medical literature indicates that in this specific clinical setting, Phalen's maneuver has a sensitivity of 60%60\% and a specificity of 85%85\%. The patient reports reproduction of tingling in the median nerve distribution within 30 seconds, indicating a positive test. Based on these findings, which of the following is the most accurate estimate of the patient's post-test probability of having carpal tunnel syndrome?

  1. A
    12%12\%
  2. 50%50\%Answer
  3. C
    60%60\%
  4. D
    80%80\%
  5. E
    85%85\%

Answer

The correct post-test probability is 50%50\%.
The post-test probability of a disease given a positive test result is mathematically equivalent to the Positive Predictive Value (PPV). PPV is dependent on the test's sensitivity, specificity, and the pretest probability (estimated disease prevalence in a specific clinical context). By modeling a hypothetical cohort of 100100 patients based on a 20%20\% pretest probability, 2020 patients truly have carpal tunnel syndrome and 8080 do not. Applying the 60%60\% sensitivity, 1212 of the 2020 diseased patients will have a true positive test. Applying the 85%85\% specificity, 15%15\% of the 8080 non-diseased patients will have a false positive test (80×0.15=1280 \times 0.15 = 12). The total number of positive tests is 2424 (1212 true positives + 1212 false positives). The PPV is the ratio of true positives to total positives: 12/24=50%12 / 24 = 50\%.

Step-by-Step Solution

1
Identify the known diagnostic parameters from the clinical vignette.
Pretest probability (prevalence in this scenario) = 20%20\%, Sensitivity = 60%60\%, Specificity = 85%85\%.
These three variables are required to apply Bayes' theorem to find the post-test probability (Positive Predictive Value).
2
Set up a hypothetical cohort to calculate True Positives (TP) and False Positives (FP).
Assume a cohort of 100100 patients. The number of patients with the disease is 100×0.20=20100 \times 0.20 = 20. The number of patients without the disease is 100×0.80=80100 \times 0.80 = 80.
Using a 100100-patient cohort is a reliable, intuitive method for converting pretest probabilities into post-test predictive values without memorizing complex formulas.
3
Calculate the exact number of TP and FP patients.
TP=20×0.60=12TP = 20 \times 0.60 = 12. FP=80×(1−0.85)=80×0.15=12FP = 80 \times (1 - 0.85) = 80 \times 0.15 = 12.
TP represents diseased individuals who test positive (Sensitivity). FP represents healthy individuals who falsely test positive (1 - Specificity).
4
Calculate the Positive Predictive Value (PPV).
PPV=TPTP+FP=1212+12=1224=0.50PPV = \frac{TP}{TP + FP} = \frac{12}{12 + 12} = \frac{12}{24} = 0.50, or 50%50\%.
PPV directly answers the clinical question: 'Given a positive test result, what is the probability that the patient actually has the disease?'

Key Concept

Calculating post-test probability (Positive Predictive Value) using pretest probability, sensitivity, and specificity (Bayes' Theorem).
Rate this question

Topics

Diagnostic Testing Performance

More questions from this topic