Lecture on Likelihood Ratios in Diagnostic Testing

Introduction

Presenter: Terry Shainefeld, UAB School of Medicine
Topic: Use of likelihood ratios in diagnostic tests and determining post-test probability

Definition: Likelihood ratios indicate how many times more or less likely a test result is in diseased individuals compared to non-diseased.
Components:
- Numerator: Probability of test result in diseased individuals
- Denominator: Probability of test result in non-diseased individuals
Incorporates: Sensitivity and specificity into a single number

Positive Likelihood Ratio (LR+):
- Used for positive test results
- Formula: Sensitivity / (1 - Specificity)
- Higher LR+ increases post-test probability
- Choose test with largest LR+ to rule in disease
Negative Likelihood Ratio (LR-):
- Used for negative test results
- Formula: (1 - Sensitivity) / Specificity
- Lower LR- reduces post-test probability
- Choose test with smallest LR- to rule out disease

Choosing a Diagnostic Test:
- Example: Tests for determining infection in children
  - Tests: C-reactive protein, procalcitonin, white blood cell counts
  - Rule In: Choose test with highest LR+ (e.g., procalcitonin)
  - Rule Out: Choose test with lowest LR- (e.g., C-reactive protein)
- Different tests often have different roles
Determining Post-Test Probability:
- Tool: Fagan's nomogram
  - Components: Pre-test probability, likelihood ratio, post-test probability
  - Process: Draw a line from pre-test probability through LR to post-test probability
- EBM Calculators: Use LR to calculate post-test odds, convert odds to probability

Positive LRs: Increase probability
Negative LRs: Decrease probability
McGee's Estimation:
- Probability change by 15% with each step in LR
- LR of 2, 5, 10 increase probability significantly
- LR of 0.5, 0.2, 0.1 decrease probability significantly
Key Takeaway:
- Choose tests with high LR+ for ruling in disease
- Choose tests with low LR- for ruling out disease