# //fpnotebook.com/

## Positive Predictive Value

*Aka: Positive Predictive Value, Test Precision*

- See Also
- Screening Test
- Contingency Grid or Cross Tab (includes Statistics Example)
- Bayes Theorem (Bayesian Statistics)
- Fagan Nomogram
- Experimental Error (Experimental Bias)
- Lead-Time Bias
- Length Bias
- Selection Bias (Screening Bias)
- Likelihood Ratio (Positive Likelihood Ratio, Negative Likelihood Ratio)
- Number Needed to Screen (Number Needed to Treat, Absolute Risk Reduction, Relative Risk Reduction)
- Negative Predictive Value
- Pre-Test Odds or Post-Test Odds
- Receiver Operating Characteristic
- Test Sensitivity (False Negative Rate)
- Test Specificity (False Positive Rate)
- U.S. Preventive Services Task Force Recommendations

- Definitions
- Positive Predictive Value (PPV)
- Percent of patients with positive test having disease
- P(Disease | test positive)
- Assesses reliability of positive test

- Precision
- Identical to the PPV, but Precision term is used more in data science
- Reflects what percentage of positive items are relevant (true positives)
- See Test Recall (Test Sensitivity)

- Positive Predictive Value (PPV)
- Indications
- Puts Test Specificity in context of disease Prevalence
- Lower disease Prevalence results in lower PPV
- Test Specificity effect is magnified
- False Positives increase substantially
- Results in less reliable positive test
- Example: HIV Test in a patient in a low risk, low Prevalence cohort has an increased risk of False Positive testing

- Calculation
- PPV = (True positive) / (True positive + False Positive)

- Example 1: High Prevalence Disease
- Major DepressionPrevalence is 10 per 100 (10%)
- New Screening Test efficacy
- Test Sensitivity: 100%
- Test Specificity: 99% (10 False Positive in 1000)

- Screen 1000 patients
- True positives: 100 per 1000 (10% Prevalence)
- False Positives: 10 per 1000 (99% Test Specificity)
- PPV: 100 true positives / 110 total positives = 91%

- Summary
- Pre-Test Probability: 10% (baseline Prevalence)
- Post-Test Probability: 91% (PPV)
- Contrast with PPV 50% for moderate Prevalence disease (1% Prevalence)
- Contrast with PPV 9% for low Prevalence disease (0.1% Prevalence)

- Statomatic

- Example 2: Moderate Prevalence Disease
- Celiac Disease has a worldwide Prevalence of 1 per 100 (1%)
- New Screening Test Efficacy
- Test Sensitivity: 100%
- Test Specificity: 99% (10 False Positives in 1000)

- Screen 1000 patients
- True positives: 10 per 1000 (1% Prevalence)
- False Positives: 10 per 1000 (99% Test Specificity)
- PPV: 10 true positives / 20 total positives = 50%

- Summary
- Pre-Test Probability: 1% (baseline Prevalence)
- Post-Test Probability: 50% (PPV)
- Contrast with PPV 91% for high Prevalence disease (10% Prevalence)
- Contrast with PPV 9% for low Prevalence disease (0.1% Prevalence)

- Statomatic

- Example 3: Low Prevalence Disease
- SclerodermaPrevalence is 1 per 1000 (0.1%)
- New Screening Test efficacy
- Test Sensitivity: 100%
- Test Specificity: 99% (10 False Positives in 1000)

- Screen 1000 patients
- True positives: 1 per 1000 (0.1% Prevalence)
- False Positives: 10 per 1000 (99% Test Specificity)
- PPV: 1 true positive / 11 total positives = 9%

- Summary
- Pre-Test Probability: 0.1% (baseline Prevalence)
- Post-Test Probability: 9% (PPV)
- Contrast with PPV 91% for high Prevalence disease (10% Prevalence)
- Contrast with PPV 50% for moderate Prevalence disease (1% Prevalence)

- Statomatic