Bayes' theorem

出自KMU Wiki

• T (theory: disease or diagnosis)
• E (evidence): symptom, sign or finding
• P(T): prevalence (prior or pre-test probability) of the disease
• P(¬T): probability of no disease
• P(E): probability of the evidence
• Conditional probabilities
  • P(E|T): sensitivity of the evidence
  • P(E|¬T): "1-specificity" of the evidence
  • P(T|E): posterior or post-test probability of T given E
• P(E|T) x P(T)=P(E and T), probability that both E and T are true
• P(E|T) x P(T)+P(E|¬T) x P(¬T)]=P(E), probability of the evidence
• Likelihood ratio (LR)
• LR for a positive result = true-positive rate / false-positive rate
• LR for a negative result = false-negative rate / true-negative rate
  • True-positive rate = sensitivity
  • False-positive rate = 1-specificity
  • False-negative rate = 1-sensitivity
  • True-negative rate = specificity
• Odds=P(T)/P((¬T)
• Thus, Bayes' theorem tells us that post-test odds = pre-test odds x likelihood ratio