Decision Management Presentation
Transcript of Decision Management Presentation
Group Fuchsia Presents:Bayes’ Rule
Neuropsychiatric DecisionMaking: The Role of
Disorder Prevalence in Diagnostic Testing
Heather Jacobson, Jessica Landin, Will Liu, Brian Wiggs
Thomas Bayes 1702-1761 English Mathematician Presbyterian Minister Deep interest in probability Bayes’ solution to “inverse
probability” was presented after his death, became “Bayes’ Theorem”
Bayes’ Rule Basics Purpose: To revise probabilities as new
information becomes available- i.e., the probability of our prior probability, given the result of our conditional probability• Example: the probability of condition in a patient
given the probability of this condition in the general population
The theorem states that the post-test likelihood of a condition is a function of the test’s accuracy and the pretest likelihood that the condition was present.
Bayes’
Related Vocab P(A|B)=(P(B|A) * P(A)) /P(B/A)P(A) + P(B/Not A)P(Not A)
Where the denominator is an “unconditional probability” Prior probability- known before current state
• P(A) Likelihood probability- depends on prior node
• P(B/A) Posterior Probability-revised probability given new info
• P(A/B) Sensitivity- probability that the test will have a positive
result (has a disease) when the person actually has the disease
Specificity-Probability that the test will be negative when the person actually lacks the disease
Mr. A Example Mr. A Is a 65 year-old male has
dementia. Dr. X administers the Short Test of
Mental Status (STMS) For persons in Mr. A’s age group,
scores<30 are considered diagnostic of dementia
STMS has a sensitivity of 95% and specificity of 88%
Mr. A Example Mr. A scores below 30. Dr. X should conclude that:
• A.) Mr. A. has a 95% chance of having dementia
• B.) Mr. A has an 88% chance of having dementia
• C.)Mr. A has a 92% chance of having dementia
• D.)She needs more information to specify the post-test likelihood of dementia
Mr. A Example Answer: D
To specify the post-test likelihood of having dementia, Dr. X needs to know what the likelihood of his having dementia before he was tested
Dr. X needs to use Bayes’ Rule!!
Mr. A Example Dr. X estimates that before testing Mr. A has a 75% chance of having dementia• Prior probability of dementia:
P(D+)=75%• Prior probability of no dementia:
P(D-)=25%
Mr. A Example• Bayes’ Rule:
• D+: has dementia• D-: does not have dementia• T+: Test results positive for dementia• T-: Test results negative for dementia
Bayes’ Example 1
Bayes’ Example 1
Counts Method 10,000 people in Mr. A’s age group 75% probability of having dementia
=• 7,500 people with dementia• 2,500 people without dementia
Counts Method Administer STMS
• Expect 300 people without dementia to test positive, given false positive rate of 12%
2,500*12%=300• Expect 7,125 with dementia to test
positive , given true positive rate is 95%7,500*95%=7,125
• 7,125+300=7425 positive tests• P(D+/T+)=7,125/7,425=0.96
Same result as Bayes’ Rule calculation!
Bayes’- Example 2
Bayes’- Example 2
Questions?