Bayesian approach to diagnosis

Bayesian approach to diagnosis

Bayesian approach to diagnosis

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Bayes' Theorem - Odds On Favourite

  • An intuitive way to update diagnostic probability. It uses odds, not direct probabilities.
  • Core Formula: $Pre-test Odds × Likelihood Ratio (LR) = Post-test Odds$
  • From Probability to Odds:

    • Odds = Probability / (1 - Probability)
  • From Odds to Probability:

    • Probability = Odds / (1 + Odds)
  • Likelihood Ratios (LR): The factor by which the odds of disease change.

    • LR+ for a positive test: $Sensitivity / (1 - Specificity)$
    • LR- for a negative test: $(1 - Sensitivity) / Specificity$

⭐ A powerful diagnostic test has an LR+ > 10 or an LR- < 0.1, causing large shifts in post-test probability.

Fagan Nomogram for Pre-test, Likelihood Ratio, Post-test

Pre & Post-Test Probability - Before & After Story

  • Pre-test Probability (PTP): The probability of a patient having a disease before a diagnostic test is performed. It's often based on prevalence, clinical history, and physical exam findings.

  • Likelihood Ratios (LRs): Quantify the diagnostic power of a test. They modify the pre-test odds to give you post-test odds.

    • Positive LR (LR+): For a positive test result. $LR+ = Sensitivity / (1 - Specificity)$
    • Negative LR (LR-): For a negative test result. $LR- = (1 - Sensitivity) / Specificity$
  • Post-test Probability (Post-TP): The revised probability of disease after considering the test result.

Fagan Nomogram for Post-Test Probability Calculation

⭐ A test with an LR+ > 10 or an LR- < 0.1 is considered very strong evidence to rule in or rule out a disease, respectively.

Likelihood Ratios - Test Power-Up

  • Likelihood Ratios (LRs) quantify the diagnostic power of a test, indicating how much a test result will shift the pre-test probability to the post-test probability. They are independent of disease prevalence.

  • Positive Likelihood Ratio (LR+): How much to increase the probability of disease with a positive test.

    • $LR+ = \frac{Sensitivity}{1 - Specificity}$
  • Negative Likelihood Ratio (LR-): How much to decrease the probability of disease with a negative test.

    • $LR- = \frac{1 - Sensitivity}{Specificity}$
  • Interpreting LRs:

LR ValueDiagnostic Power
> 10Strong evidence to rule IN
5 - 10Moderate evidence to rule IN
2 - 5Weak evidence to rule IN
1No diagnostic value
0.2 - 0.5Weak evidence to rule OUT
0.1 - 0.2Moderate evidence to rule OUT
< 0.1Strong evidence to rule OUT

Fagan Nomogram for Bayesian Clinical Reasoning

  • Bayes' Theorem formally updates the probability of a disease based on new test results.
  • Start with pre-test probability, which is often the disease prevalence in the relevant population.
  • Use Likelihood Ratios (LRs) to quantify a test's power to change probability.
  • Post-test odds are calculated by multiplying pre-test odds by the appropriate LR.
  • A high LR+ (>10) significantly rules in disease; a low LR- (<0.1) strongly rules it out.
  • This avoids common cognitive biases by systematically integrating new data.

Practice Questions: Bayesian approach to diagnosis

Test your understanding with these related questions

A scientist in Chicago is studying a new blood test to detect Ab to EBV with increased sensitivity and specificity. So far, her best attempt at creating such an exam reached 82% sensitivity and 88% specificity. She is hoping to increase these numbers by at least 2 percent for each value. After several years of work, she believes that she has actually managed to reach a sensitivity and specificity much greater than what she had originally hoped for. She travels to China to begin testing her newest blood test. She finds 2,000 patients who are willing to participate in her study. Of the 2,000 patients, 1,200 of them are known to be infected with EBV. The scientist tests these 1,200 patients' blood and finds that only 120 of them tested negative with her new exam. Of the patients who are known to be EBV-free, only 20 of them tested positive. Given these results, which of the following correlates with the exam's specificity?

1 of 5

Flashcards: Bayesian approach to diagnosis

1/10

A _____ is typically used to diagnose spinal stenosis or other vertebral pathology (ex. osteomyelitis) in patients who cannot undergo MRI

TAP TO REVEAL ANSWER

A _____ is typically used to diagnose spinal stenosis or other vertebral pathology (ex. osteomyelitis) in patients who cannot undergo MRI

CT Myelogram

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