Advances in Health Care Predictive Analytics

Advances in Health Care Predictive Analytics Graphical Models Part I: Intelligent Reasoning with Bayesian Networks Jarrod E. Dalton

COLD OR FLU? How do we tell?

A Simple Bayesian Network

P() Prob. No 70% Yes 30% P() Prob. No 90% Yes 10% P(, ) Prob. No No No 95% No No Yes 5% No Yes No 80% No Yes Yes 20% Yes No No 60% Yes No Yes 40% Yes Yes No 50% Yes Yes Yes 50% P( ) Prob. No No 99% No Yes 1% Yes No 60% Yes Yes 40% A Simple Bayesian Network

P() Prob. No 70% Yes 30% =Yes P(, ) Prob. No No No 95% No No Yes 5% No Yes No 80% No Yes Yes 20% Yes No No 60% Yes No Yes 40% Yes Yes No 50% Yes Yes Yes 50% P( ) Prob. No No 99% No Yes 1% Yes No 60% Yes Yes 40% Causal Reasoning Step 1: Eliminate states inconsistent with observed evidence

P() Prob. No 70% Yes 30% =Yes P(Snz., =Yes) Prob. No No 80% No Yes 20% Yes No 50% Yes Yes 50% P( =Yes) Prob. No 60% Yes 40% Causal Reasoning Step 2: Update beliefs of other nodes

P() Prob. No 70% Yes 30% =Yes P(Snz., =Yes) Prob. No No 80% No Yes 20% Yes No 50% Yes Yes 50% P( =Yes) Prob. No 60% Yes 40% Factor Marginalization What is the marginal probability of sneezing?

P() Prob. No 70% Yes 30% 70% of population does not have a cold among these, 20% sneeze. Among the other 30%, 50% sneeze. P(Snz., =Yes) Prob. No No 80% No Yes 20% Yes No 50% Yes Yes 50% The marginal probability of sneezing is obtained by combining these incidences: P sneezing = Yes = 0.7 0.2 + 0.3 0.5 = 0.29 Factor Marginalization What is the marginal probability of sneezing?

P() Prob. No 70% Yes 30% P() Prob. No 90% Yes 10% P(, ) Prob. No No No 95% No No Yes 5% No Yes No 80% No Yes Yes 20% Yes No No 60% Yes No Yes 40% Yes Yes No 50% Yes Yes Yes 50% A similar calculation of the marginal probability of sneezing before observing that the person had the flu indicated P(sneezing)=17%. P( ) Prob. No No 99% No Yes 1% Yes No 60% Yes Yes 40%

P() Prob. No 70% Yes 30% P() Prob. No 90% Yes 10% P(, ) Prob. No No No 95% No No Yes 5% No Yes No 80% No Yes Yes 20% Yes No No 60% Yes No Yes 40% Yes Yes No 50% Yes Yes Yes 50% Evidential Reasoning P( ) Prob. No No 99% No Yes 1% Yes No 60% Yes Yes 40%

Bayes Rule P() Prob. No 90% P ) = P P( ) P() Yes 10% P( ) Prob. No No 99% No Yes 1% Yes No 60% Yes Yes 40% Evidential Reasoning

Bayes Rule P() Prob. No 90% P ) = P P( ) P() Yes 10% P = No = Yes) = 0.90 0.01 P()??? P( ) Prob. No No 99% No Yes 1% Yes No 60% Yes Yes 40% Evidential Reasoning

Bayes Rule P() Prob. No 90% P ) = P P( ) P() Yes 10% P = No = Yes) = 0.90 0.01 P()??? P( ) P() Prob. No 0.99 0.90 + 0.60 0.10 = 0.951 Yes 0.01 0.90 + 0.40 0.10 = 0.049 90%{ 10%{ Prob. No No 99% No Yes 1% Yes No 60% Yes Yes 40% Evidential Reasoning

Bayes Rule P() Prob. No 90% P ) = P P( ) P() Yes 10% P = No = Yes) = 0.90 0.01 0.049 = 0.184 P( ) Prob. P() Prob. No 95.1% Yes 4.9% No No 99% No Yes 1% Yes No 60% Yes Yes 40% Evidential Reasoning

Bayes Rule P() Prob. No 90% P ) = P P( ) P() Yes 10% P = No = Yes) = 0.90 0.01 0.049 = 0.184 P = Yes = No) = 0.10 0.60 0.951 = 0.063 P( ) Prob. P() Prob. No 95.1% Yes 4.9% No No 99% No Yes 1% Yes No 60% Yes Yes 40% Evidential Reasoning

Bayes Rule P() Prob. No 90% P ) = P P( ) P() Yes 10% P = No = Yes) = 0.90 0.01 0.049 = 0.184 P = Yes = No) = 0.10 0.60 0.951 = 0.063 P( ) Prob. P( ) Prob. No No 93.7% No Yes 6.3% Yes No 18.4% Yes Yes 81.6% P() Prob. No 95.1% Yes 4.9% Evidential Reasoning No No 99% No Yes 1% Yes No 60% Yes Yes 40%

P() Prob. No 70% Yes 30% P() Prob. No 90% Yes 10% P( ) Prob. No No 93.7% No Yes 6.3% Yes No 18.4% Yes Yes 81.6% P(, ) Prob. No No No 95% No No Yes 5% No Yes No 80% No Yes Yes 20% Yes No No 60% Yes No Yes 40% Yes Yes No 50% Yes Yes Yes 50% Evidential Reasoning P( ) Prob. No No 99% No Yes 1% Yes No 60% Yes Yes 40%

P() Prob. No 70% Yes 30% P( =Yes) Prob. No No 93.7% No Yes 6.3% Yes No 18.4% Yes Yes 81.6% P(, ) Prob. No No No 95% No No Yes 5% No Yes No 80% No Yes Yes 20% Yes No No 60% Yes No Yes 40% Yes Yes No 50% Yes Yes Yes 50% =Yes Evidential Reasoning

P() Prob. No 70% Yes 30% P( =Yes) Prob. No 18.4% Yes 81.6% P(, ) Prob. No No No 95% No No Yes 5% No Yes No 80% No Yes Yes 20% Yes No No 60% Yes No Yes 40% Yes Yes No 50% Yes Yes Yes 50% =Yes Marginal P( =Yes) Prob. No.7(.184)(.95)+.7(.816)(.8)+.3(.184)(.6)+.3(.816)(.5) Yes.7(.184)(.05)+.7(.816)(.2)+.3(.184)(.4)+.3(.816)(.5) Belief Propagation

P() Prob. No 70% Yes 30% P( =Yes) Prob. No 18.4% Yes 81.6% P(, ) Prob. No No No 95% No No Yes 5% No Yes No 80% No Yes Yes 20% Yes No No 60% Yes No Yes 40% Yes Yes No 50% Yes Yes Yes 50% =Yes Marginal P( =Yes) Prob. No 73.5% Yes 26.5% Belief Propagation

Intercostal When does information flow? When does it not flow?

A B C (B unobserved) Intercostal When does information flow? When does it not flow?

A B C (B unobserved) Intercostal When does information flow? When does it not flow?

A B C (B unobserved) Intercostal When does information flow? When does it not flow?

A B C (B unobserved) Intercostal When does information flow? When does it not flow?

A B C (B unobserved) NO Intercostal When does information flow? When does it not flow?

A B C (B observed) Intercostal When does information flow? When does it not flow?

A B C (B observed) NO Intercostal When does information flow? When does it not flow?

A B C (B observed) Intercostal When does information flow? When does it not flow?

A B C (B observed) NO NO Intercostal When does information flow? When does it not flow?

A B C (B observed) Intercostal When does information flow? When does it not flow?

A B C (B observed) NO Intercostal When does information flow? When does it not flow?

A B C (B observed) Intercostal When does information flow? When does it not flow?

A B C (descendent of B observed) Intercostal When does information flow? When does it not flow?

EXAMPLE BIRTH OUTCOMES

OTHER APPLICATIONS OF BAYESIAN NETWORKS

Dynamic Bayes Nets Vaccinated Susceptibile t Susceptibile t+1 Susceptible 0 Direct Contact t Gene Infected t Infected t+1 Recovered t Recovered t+1 Dead t Dead t+1

Decision Nets T Chemotherapy Remission 100 N Radiotherapy Recurrence 20 M Surgery Cancer Death 0 Staging Decisions Outcomes Utilities

Daphne Koller Co-founder of coursera.org Stanford Artificial Intelligence Laboratory (SAIL) Sebastian Thrun (Google X lab, Udacity) Andrew Ng (director of SAIL, co-founder of coursera) Gill Bejerano (Bejerano Lab) Genotype-phenotype linkage in humans Genotype-phenotype linkage between mammals Genome evolution Probabilistic Graphical Models