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Zorluk: ZorDiagnostic Testing Performance

A 64-year-old woman is admitted to the intensive care unit with acute hypoxemic respiratory failure requiring mechanical ventilation. On hospital day 6, her platelet count drops from a baseline of 220,000/μL220,000/\mu L to 90,000/μL90,000/\mu L. She has been receiving prophylactic subcutaneous unfractionated heparin since admission. The clinical team evaluates her using the 4Ts scoring system and determines she has a low-to-intermediate clinical probability of heparin-induced thrombocytopenia (HIT), estimating her pretest probability to be exactly 20%.

A platelet factor 4 (PF4)-polyanion enzyme-linked immunosorbent assay (ELISA) is ordered. The institutional laboratory specifies that this particular ELISA has a sensitivity of 92% and a specificity of 77% for diagnosing HIT in this population. Two hours later, the test returns a positive result.

Based on these parameters, which of the following is the approximate probability that this patient actually has heparin-induced thrombocytopenia?

  1. A
    20%
  2. 50%Cevap
  3. C
    77%
  4. D
    80%
  5. E
    92%

Cevap

The correct post-test probability (positive predictive value) is 50%.
The correct answer is derived using the likelihood ratio approach. First, the positive likelihood ratio (LR+LR+) is calculated as Sensitivity/(1−Specificity)Sensitivity / (1 - Specificity), which is 0.92/0.23=40.92 / 0.23 = 4. Next, the pretest probability of 20% is converted to pretest odds (0.20/0.80=0.250.20 / 0.80 = 0.25). The post-test odds are then found by multiplying the pretest odds by the LR+LR+ (0.25×4=10.25 \times 4 = 1). Finally, converting the post-test odds of 1 back to a probability yields 1/(1+1)=0.501 / (1 + 1) = 0.50, or 50%. Alternatively, using the full Bayes' theorem formula for Positive Predictive Value (PPV) yields the same result: (0.92×0.20)/[(0.92×0.20)+(1−0.77)×0.80]=0.184/(0.184+0.184)=50%(0.92 \times 0.20) / [(0.92 \times 0.20) + (1 - 0.77) \times 0.80] = 0.184 / (0.184 + 0.184) = 50\%.

Adım Adım Çözüm

1
Convert the pretest probability to pretest odds.
Pretest Odds=0.201−0.20=0.200.80=0.25Pretest\ Odds = \frac{0.20}{1 - 0.20} = \frac{0.20}{0.80} = 0.25
Odds must be used to apply likelihood ratios mathematically.
2
Calculate the Positive Likelihood Ratio (LR+).
LR+=Sensitivity1−Specificity=0.921−0.77=0.920.23=4.0LR+ = \frac{Sensitivity}{1 - Specificity} = \frac{0.92}{1 - 0.77} = \frac{0.92}{0.23} = 4.0
The LR+ quantifies how much more likely a positive test is to occur in a patient with the disease compared to one without the disease.
3
Calculate the post-test odds.
Post−test Odds=Pretest Odds×LR+=0.25×4.0=1.0Post-test\ Odds = Pretest\ Odds \times LR+ = 0.25 \times 4.0 = 1.0
Multiplying the pretest odds by the LR+ yields the updated odds of having the disease.
4
Convert the post-test odds back to post-test probability.
Post−test Probability=Post−test Odds1+Post−test Odds=1.01+1.0=0.50Post-test\ Probability = \frac{Post-test\ Odds}{1 + Post-test\ Odds} = \frac{1.0}{1 + 1.0} = 0.50 (or 50%)
Clinical decisions are made based on probability rather than odds.

Anahtar Kavram

Calculating Post-test Probability using Likelihood Ratios
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Konular

Diagnostic Testing Performance

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