Lecture: Do Operation in Causal Networks  


Assigned Reading

  • Read chapter 3 in the "Causal Inferences in Statistics book: A primer" book. Read►
  • Do operation Slides►
  • Backdoor Blocking Read►


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."  In one sentence, indicate if your peer-teacher has approved your submission.

Question 1: This problem is based on example 1.2.1 in the "Causal Inferences in Statistics: A Premier" book. The following Table gives the recovery rates of 700 patients who were prescribed a drug, half of whom took the medication.  

  1. What is the probability of taking medications given that the person is female
  2. What is the probability of the remission of symptoms given that the person has taken their medications and the patient is female?
  3. Which variable is leading to a selection bias, if we had observational data on these three variables and wanted to measure impact of taking the medication?
  4. What is the impact of taking the medication?

Med gender and remission network

Number Recovering (Number Taking Medication)
  Med No Med
Men 81 (n=87) 234 (n=270)
Women 192 (n=263) 55 (n=80)
Total  273 (n=350) 289 (350)

Resources available for Question 1:

  • Answer to part d is on page 57 of the "Causal Inferences in Statistics: A premier" book. Read►

Question 2: Organize the data from the previous question into a Netica model, with tables completed. Show how a do operation can be calculated using the Netica software.

Resources for Question 2:

Question 3: Calculate the causal impact of fever on diagnosis of COVID, using do operation:

Resources for Question 3:

  • Removing selection bias in impact of fever Excel►

Question 4:  The following data show the joint distribution of gender, medication taken, and response to the medication (similar to question 1).  Keep mind that the conditional probability of taking the medication given the patient's gender is also called propensity score.  Conditional probability of x given z is calculated as the joint probability of x and z divided by probability of z.

  1. Calculate the propensity of clinician prescribing the medication for each recommendation of AI system.
  2. Calculate the un-confounded impact of clinician's prescription patterns, using inverse propensity scores
  3. Calculate the impact of the AI system on remission of patients' symptoms. To do this, sum the product of probability of remission given AI advice times probability of AI's advice. 

Joint Probability
X, Clinician's Prescription Y, Patient's Remission Z, Artificial Intelligence Advice Probability
Med A Yes Med A 0.116
Med A Yes Other Med 0.274
Med A No Med A 0.010
Med A No Other Med 0.101
Other Med Yes Med A 0.334
Other Med Yes Other Med 0.079
Other Med No Med A 0.051
Other Med No Other Med 0.036

Resources for Question 4:

  • Answer to part b is on page 72-75 in the book "Causal Inferences in Statistics: A premier" book. Read►

Question 5: An adjustment set is a set that allows you to calculate causal impact of exposure/treatment.  There are several different ways of identifying an adjustment set.  If all parents in the Markov Blanket of exposure are stratified, then the causal effect of exposure on outcome can be measured.  This, however, may not be the minimal set.  In this problem, you are asked to use a tool available online to identify the minimal adjustment set for the following graph:

Exposure mediator outcome and 2 covariate model

Resources available for answering Question 5

  •  Tool for determining minimum adjustment set  Web►


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

  1. Graphical models and measurement of counterfactuals Read►

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