Understanding Medical Test Errors and Probabilities

Oct 14, 2024

Lecture Notes: Probability and False Negatives/Positives

Introduction

  • Activity 7D: Last section on probability
  • Focus: False negatives and false positives

Medical Tests and Errors

  • False Positive: Test indicates disease is present when it is not.
  • False Negative: Test indicates no disease when it actually is present.
  • Goal: Medical tests aim to minimize these errors.
  • Opinion Question: What's worse? False positive or false negative? Depends on the disease.

Example: Strep Throat

  • False Positive:
    • Unnecessary antibiotic usage
    • Contributes to antibiotic resistance
    • Less harmful individually, but a global concern
  • False Negative:
    • Untreated strep can lead to serious complications
    • Preferable to err on the side of caution

Probability Tables

  • Importance: Simplifies complicated probability concepts
  • Focus on Tables: Construct and use probability tables to solve problems
  • Example Diseases: COVID-19
    • False Positive: Can cause unnecessary isolation, missing work
    • False Negative: Risk of spreading the disease

Example Problem: COVID-19 Testing Reliability

  • Given Data:
    • 80% do not have COVID
    • 2.25% false positive rate
    • 80% true positive rate
  • Objective:
    • Fill in probability table
    • Calculate conditional probabilities

Table Filling Steps

  1. Calculate Total Numbers: Use given percentages to find numbers in each category.
  2. Complete the Table: Fill in each cell using logical deductions from given data.
  3. Conditional Probabilities: Use table to find probabilities of interest, e.g., probability of disease given a positive test.

Example Problem: Pregnancy Tests

  • Accuracy Rates:
    • 90% detection for pregnant
    • 99% accuracy for non-pregnant
  • Study Context: 30% participants are pregnant
  • Process:
    • Construct and fill a probability table
    • Calculate specific probabilities

Exercises

  1. Question: If positive test, what's probability of true pregnancy?
  2. Question: If negative test, what's probability of not being pregnant?

Summary

  • Key Concepts:
    • Importance of understanding false positives/negatives in medical testing
    • Using probability tables to calculate conditional probabilities
  • Applications:
    • Real-world medical testing scenarios, decision-making based on probability

Conclusion

  • Encourage practice with provided data and problems
  • Use probability tables to simplify complex probability and statistical questions

End of Lecture