Positive Predictive Value

Aka: Positive Predictive Value, Test Precision

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II. Definitions

  1. Positive Predictive Value (PPV)
    1. Percent of patients with positive test having disease
    2. P(Disease | test positive)
    3. Assesses reliability of positive test
  2. Precision
    1. Identical to the PPV, but Precision term is used more in data science
    2. Reflects what percentage of positive items are relevant (true positives)
    3. See Test Recall (Test Sensitivity)

III. Indications

  1. Puts Test Specificity in context of disease Prevalence
  2. Lower disease Prevalence results in lower PPV
    1. Test Specificity effect is magnified
    2. False Positives increase substantially
    3. Results in less reliable positive test
    4. Example: HIV Test in a patient in a low risk, low Prevalence cohort has an increased risk of False Positive testing

IV. Calculation

  1. PPV = (True positive) / (True positive + False Positive)

V. Example 1: High Prevalence Disease

  1. Major Depression Prevalence is 10 per 100 (10%)
  2. New Screening Test efficacy
    1. Test Sensitivity: 100%
    2. Test Specificity: 99% (10 False Positive in 1000)
  3. Screen 1000 patients
    1. True positives: 100 per 1000 (10% Prevalence)
    2. False Positives: 10 per 1000 (99% Test Specificity)
    3. PPV: 100 true positives / 110 total positives = 91%
  4. Summary
    1. Pre-Test Probability: 10% (baseline Prevalence)
    2. Post-Test Probability: 91% (PPV)
      1. Contrast with PPV 50% for moderate Prevalence disease (1% Prevalence)
      2. Contrast with PPV 9% for low Prevalence disease (0.1% Prevalence)
  5. Statomatic
    1. https://fpnotebook.com/drbits/fpnstats/#/tests?truePositive=100&falsePositive=10&falseNegative=0&trueNegative=890&pretestProbability=10

VI. Example 2: Moderate Prevalence Disease

  1. Celiac Disease has a worldwide Prevalence of 1 per 100 (1%)
  2. New Screening Test Efficacy
    1. Test Sensitivity: 100%
    2. Test Specificity: 99% (10 False Positives in 1000)
  3. Screen 1000 patients
    1. True positives: 10 per 1000 (1% Prevalence)
    2. False Positives: 10 per 1000 (99% Test Specificity)
    3. PPV: 10 true positives / 20 total positives = 50%
  4. Summary
    1. Pre-Test Probability: 1% (baseline Prevalence)
    2. Post-Test Probability: 50% (PPV)
      1. Contrast with PPV 91% for high Prevalence disease (10% Prevalence)
      2. Contrast with PPV 9% for low Prevalence disease (0.1% Prevalence)
  5. Statomatic
    1. https://fpnotebook.com/drbits/fpnstats/#/tests?truePositive=10&falsePositive=10&falseNegative=0&trueNegative=980&pretestProbability=1

VII. Example 3: Low Prevalence Disease

  1. Scleroderma Prevalence is 1 per 1000 (0.1%)
  2. New Screening Test efficacy
    1. Test Sensitivity: 100%
    2. Test Specificity: 99% (10 False Positives in 1000)
  3. Screen 1000 patients
    1. True positives: 1 per 1000 (0.1% Prevalence)
    2. False Positives: 10 per 1000 (99% Test Specificity)
    3. PPV: 1 true positive / 11 total positives = 9%
  4. Summary
    1. Pre-Test Probability: 0.1% (baseline Prevalence)
    2. Post-Test Probability: 9% (PPV)
      1. Contrast with PPV 91% for high Prevalence disease (10% Prevalence)
      2. Contrast with PPV 50% for moderate Prevalence disease (1% Prevalence)
  5. Statomatic
    1. https://fpnotebook.com/drbits/fpnstats/#/tests?truePositive=1&falsePositive=10&falseNegative=0&trueNegative=989&pretestProbability=0.1

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