Comparative Effectiveness HAP 823

Lecture: Markov Blanket  

 

Assigned Reading

Assignment

Include in the first page a summary page.  In the summary page write statements comparing your work to answers given or videos.  For example, "I got the same answers as the Teach One video for question 1."  Including a statement in the summary that your work was approved by peer-teachers.

For these assignment you can use any statistical package, including R, SAS, and SPSS, Python. R packages and BNLearn are also used often.  OpenBUGS and Gibbs Sampler, Stan, OpenMarkov, and Direct Graphical Model are also open source software.  Netica is free for networks less than 15 nodes.

Question 1: Using the following graph, answer the following questions:

  1. List the Markov Blanket of Y
  2. List the Markov Blanket of W
  3. List the parents in Markov Blanket of Z
  4. If we regress Z on X, W, Y, and not T, which variables will be statistically significant (parents in Markov Blanket of Z)?
  5. For measuring un-confounded effect of Y on T, which arcs in the graph should be stratified (removed)?

xyzwt graph

Resources for question 1:

  • Learn more about Markov Blankets YouTube►
  • For an intelligent tutor copy this prompt into your choice of AI system Prompt►
  • Get practice grade for this question Prompt►

Question 2: In the following, calculate the probability of negative outcome under different scenarios.

Write an SQL code to calculate the probability of negative outcome in the situation where the patient is severely ill and has not signed a "Do Not Resuscitate" (DNR) order.  Note that probabilities for events that are mutually exclusive and exhaustive should add up to one. In some SQL calculations, this is not the case.



Additional resources for Question 2:

Question 3: Redo problem 2 in Netica or other software and verify the accuracy of your answer.  To accomplish this, organize the 4-node network inside Netica and direct the links between the nodes, as in the graph structure in question 3.  Then for every node, enter the table of probabilities as per tables given in Question 3.  For example, for the DNR node enter the two probabilities of 0.1 and 0.9 into the Table within the node for DNR.  Once the entire network (the graph and the related probabilities) has been entered into Netica, answer following questions:

  1. Evaluate the expected outcome for a patient who is severely ill and has not signed a "Do Not Resuscitate" order.
  2. Evaluate the effect of treatment on outcome for patients who are severely ill.  Repeat for patients who are not severely ill.  What is the expected outcome when we stratify (remove the arc) for severity of illness?

Resources for Question 3:

Question 4: A cause is associated with the effect, precedes it, has a mechanism that leads to the effect, and removal of risk increasing cause reduces the frequency of observing the effect.  A Markov blanket of Y is a set of variables that, when known, makes all remaining variables provide no additional information for predicting Y. A minimal Markov blanket, also called a Markov boundary, contains no unnecessary variables. Suppose we examine four variables: X1, X2, X3, and X4. Assume that X1 and X2 each contribute information about Y after accounting for the other. Once X1 and X2 are known, X3 and X4 provide no additional information about Y, either individually or jointly. Answer the following:

  1. What is the minimal Markov blanket of Y among these four variables? Explain why each variable is included or excluded. How is identifying a Markov blanket related to identifying redundant predictors? Does high correlation between two predictors necessarily mean that one can be excluded? Does identifying a minimal Markov blanket guarantee that its variables are uncorrelated? Explain your reasoning.
  2. Suppose the event represented by X2 occurs after Y, while the event represented by X1 occurs before Y. Among the variables in the predictive Markov blanket, which could potentially cause Y? Could a variable that occurs after Y remain useful for predicting or explaining Y retrospectively? Explain why excluding that variable from the possible causal set does not necessarily remove it from the predictive Markov blanket.

Resources for Question 4:

Optional Question 5: The following network shows the relationship between symptoms of COVID and its diagnosis (shown as positive test result). 

Diagnosis of COVID from its symptoms

  1. Does knowing that a female patient has a positive test result increase the chance that she is over 30 years old? 
  2. Is it correct to say that patients with cough and fever have an elevated chance of positive COVID test? 
  3. List the 5 symptoms of COVID that appear last in progression of the disease. 
  4. Is muscle ache associated with positive COVID test result? 
  5. When is throwing up not associated with positive COVID test results? 
  6. What is the Markov blanket of fever? 
  7. What are the co-parents of fever? 
  8. Is muscle ache a cause of fever or the reverse? 
  9. Is sore throat a common cause or a common effect? 
  10. If a patient does not currently have fever, what factors can be used to establish whether the patient will develop fever later? 
  11. What are two backdoor paths from COVID test results to loss of smell? 
  12. Is a runny nose associated with wheezing? 
  13. What are 3 variables that indirectly predict COVID? 
  14. What symptom most mediates the impact of largest number of indirect variables on COVID test results? 
  15. How many variables are direct predictors of COVID test results? 
  16. Write an equation for calculating probability of fever from patient's age, gender and other symptoms. 
  17. If the patient does not report a symptom, should we assume that the symptom was not present? 

Resources for answering Question 5:

  • See Exhibit 20.1 for definition of various terms in Big Data in Health Care, Chapter 20, page 492

Optional Question 6: In the following directed graph, answer these questions:

  1. Is Z independent of V, if T is not observed?
  2. Is Z independent of V, if T is observed?
  3. Is U independent of V, if W or X are not observed?

D seperation

Resources for Question 6:

  • Professor Abbeel's lecture on directed separation YouTube►

Optional Question 7: In the following network, calculate the average effectiveness of treatment.  First calculate the probability of the outcome for treated patients.  Then calculate the probability of the outcome for patients not treated.  Report the difference of the two probabilities as the average treatment effectiveness. SQL or Netica could help in solving this problem.

Additional resources for Question 7:

More

For additional information (not part of the required reading), please see the following links:

  1. Introduction to Markov process Tim's Lecture►
  2. Explanation of predictions Aloudah's Lecture►

This page is part of the HAP 823 course on Comparative Effectiveness by Farrokh Alemi, Ph.D. Home► Email►