## Lecture: Mediation Analysis
## Objectives- Create a counterfactual model of the data
- Estimate mediation effect in real and counterfactual models of the universe
## Assigned Reading- Tutorial on using regression for network construction Read► (Use instructor's last name as password)
- Read about "Graphical Representation of Counterfactuals" in "Causal Inference in Statistics" pages 101-107
- Overview of calculation of mediated effect of Fever through Chills on diagnosis of COVID-19 Read►
- Path analysis of mediation coefficient Excel►
- Mediation Analysis in 4 Steps:
- Learn the order of variables, in this case variables
occur in order of
- Covariate C1,
- Covariate C2,
- Exposure X,
- Mediator M, and
- Outcome Y.
- Learn network through chain of regressions Slides►
- Estimate un-confounded impact of variable on outcome Slides►
- Re-estimate the un-confounded impact of variable on outcome. Estimate mediation impact. Slides►
- Learn the order of variables, in this case variables
occur in order of
## Assignment
- What is the order of occurrences of the symptoms, age, gender, and results of COVID-19 laboratory tests?
- What are the direct predictors of COVID-19 Laboratory test results? Assume the following order for the variables: D1: Age, D2: Female, X1: Shivering, X2: Fatigue, X3: Loss of taste, X4: Fever, X5: Headaches, X6: Loss of smell, X7: Chills, X8: Muscle aches X9: Diarrhea, X10: Cough, X11: Shortness of breath, X12: Runny nose, X13: Sore throat, X14: Loss of balance, X15: Vomiting, X16: Joint pain, X17: Loss of appetite, X18: Wheezing, X19: Difficulty breathing, X20: Excessive sweating, Y: COVID-19 Test Results.
- What is the best network that fits the data? Establish the structure of the network ignoring regressions that explain less than 10% of the variation in test results and ignoring variables where absolute value of coefficients are less than or equal to 0.05.
- Estimate the parameters of the network from repeated LASSO regressions. Report the joint probability of COVID-19 positive test results, if we do not know which symptoms were present.
- What are parents in the Markov blanket of Fever?
- Use regressions to identify these parents in Markov Blanket of Fever
- Use the network to read parents in Markov Blanket of Fever
- What is the un-confounded effect of fever on probability of positive COVID-19 diagnosis?
- Use inverse propensity weights to removing confounding
- Switch the distribution of direct predictors of Fever so that patients with and without Fever have the same distribution of direct predictors
- What is the parents in Markov blanket of Chills?
- Use Network to identify the parents in Markov blanket of Chills
- Use regressions to identify parents in Markov blanket of Chills
- LASSO regress Chills on its direct predictors, not including Fever. Report intercept, coefficients, and McFadden R-square.
- Revise the network to create a counterfactual network in which Fever is not mediated by Chills (no arc from Fever to Chills)
- What is the mediated impact of fever on COVID-19 through Chills?
Resources for Question 1: - Data Download►
- Rachael King's Teach One YouTube►
- Yatisha Rajanala's Teach One Answers► Real Network► Counterfactual Network► Code► Netica Tables►
- Answers and overview of calculations Read►
- Analysis in the observed, "real," network, which includes a link from Fever to Chills
- This network was drawn from repeated LASSO regressions of the data, ignoring R-square < 0.10 and coefficients < 0.05. Read►
- Netica network with associated tables
Zip►
- Analysis in the Counterfactual network, which excludes the link between Fever and Chills:
- Percent of effect of Fever mediated through Chills Excel►
## MoreFor additional information (not part of the required reading), please see the following links: - Pearl's direct and indirect effects Read► Web Appendix►
- Saeed's lecture Video►
- Mediation analysis allowing for exposure-mediator interactions Read►
- Mediation analysis through stable weights Read►
- Practical guide to mediation analysis through inverse odds ratio Read► Slides►
- Mediation analysis revisited Read►
This page is part of the course on Comparative Effectiveness by Farrokh Alemi, PhD Home► Email► |