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Conditional Independence

Conditional Independence. Farrokh Alemi Ph.D. Professor of Health Administration and Policy College of Health and Human Services, George Mason University 4400 University Drive, Fairfax, Virginia 22030 703 993 1929 falemi@gmu.edu. Lecture Outline. What is probability?

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Conditional Independence

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  1. Conditional Independence Farrokh Alemi Ph.D.Professor of Health Administration and PolicyCollege of Health and Human Services, George Mason University4400 University Drive, Fairfax, Virginia 22030703 993 1929 falemi@gmu.edu

  2. Lecture Outline • What is probability? • Assessment of rare probabilities • Calculus of probability • Conditional independence • Definition • Use • Methods of verification • Causal modeling • Case based learning • Validation of risk models • Examples

  3. Joint Distributions • Shows probability of co-occurrence

  4. Joint Distributions

  5. Example

  6. Example

  7. Reducing Universe of Possibilities

  8. Mathematical Definition of Independence P(A | B) = P(A)

  9. Joint & Marginal Distributions P(A&B) = P(A) * P(B)

  10. CHITEST function

  11. Comparison of Conditioned & Un-conditioned Probabilities P( Medication error ) ≠ P( Medication error| understaffing) 0.29 ≠ 0.68

  12. Mathematical Definition of Conditional Independence P(A | B, C) = P(A | C)

  13. Mathematical Definition of Conditional Independence P(A&B | C) = P(A | C) * P(B | C) 

  14. Dependent Events Can Be Conditionally Independent P( Medication error ) ≠ P( Medication error| Long shift)

  15. Dependent Events Can Be Conditionally Independent P( Medication error ) ≠ P( Medication error| Long shift) P( Medication error | Long shift, Not fatigued) = P( Medication error| Not fatigued)

  16. Use of Conditional Independence • Analyze chain of dependent events • Simplify calculations

  17. Use of Conditional Independence • Analyze chain of dependent events • Simplify calculations

  18. Use of Conditional Independence • Analyze chain of dependent events • Simplify calculations P(C1,C2,C3, ...,Cn|H1) = P(C1|H1) * P(C2|H1,C1) * P(C3|H1,C1,C2) * P(C4|H1,C1,C2,C3) * ... * P(Cn|H1,C1,C2,C3,...,Cn-1)    

  19. Use of Conditional Independence • Analyze chain of dependent events • Simplify calculations P(C1,C2,C3, ...,Cn|H1) = P(C1|H1) * P(C2|H1,C1) * P(C3|H1,C2) * P(C4|H1,C3) * ... * P(Cn|H1,Cn)    

  20. Verifying Independence • Reducing sample size • Correlations • Direct query from experts • Separation in causal maps   

  21. Verifying Independence by Reducing Sample Size • P(Error | Not fatigued) = 0.50 • P(Error | Not fatigue & Long shift) = 2/4 = 0.50

  22. Verifying through Correlations • Rab is the correlation between A and B • Rac is the correlation between events A and C • Rcb is the correlation between event C and B • If Rab= Rac Rcb then A is independent of B given the condition C

  23. Example 0.91 ~ 0.82 * 0.95 

  24. Verifying by Asking Experts • Write each event on a 3 x 5 card •  Ask experts to assume a population where condition has been met  •  Ask the expert to pair the cards if knowing the value of one event will make it considerably easier to estimate the value of the other •  Repeat these steps for other populations • Ask experts to share their clustering • Have experts discuss any areas of disagreement •  Use majority rule to choose the final clusters

  25. Verifying Independence by Causal Maps • Ask expert to draw a causal map • Conditional independence: A node that if removed would sever the flow from cause to consequence • Any two nodes connected by an arrow are dependent.  • Multiple cause of same effect are dependent • The consequence is independent of the cause for a given level of the intermediary event. • Multiple consequences of a cause are independent of each other given the cause

  26. Example Blood pressure does not depend on age given weight

  27. Take Home Lesson Conditional Independence Can Be Verified in Numerous Ways

  28. What Do You Know? • What is the probability of hospitalization given that you are male? 

  29. What Do You Know? • Is insurance independent of age?

  30. What Do You Know? • What is the likelihood associated of being more than 65 years old among hospitalized patients?   Please note that this is not the same as the probability of being hospitalized given you are 65 years old.

  31. What Do You Know? • In predicting hospitalization, what is the likelihood ratio associated with being 65 years old?

  32. What Do You Know? • What is the prior odds for hospitalization before any other information is available?

  33. What Do You Know? • Draw what causes medication errors on a piece of paper, with each cause in a separate node and arrows showing the direction of causality.  List all causes, their immediate effects until it leads to a medication error.       • Analyze the graph you have produced and list all conditional dependencies inherent in the graph. 

  34. Minute Evaluations • Please use the course web site to ask a question and rate this lecture

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