Homework 5

Due Sunday, October 4 at midnight CST on Moodle

Please turn in two PDF documents from class exercises.

(If you have LaTeX installed, you can knit directly to PDF (preferred method). Otherwise, you can knit to HTML and “Print” the page to save it as a PDF.)


Deliverables

Please turn in exercises from the following class days:

  • Topic 14: Sensitivity Analyses for Unmeasured Variables
  • Topic 15: Causal Discovery

This should be a total of two PDF documents.


Primary objectives

The following learning objectives are the primary focus of this assignment:

  • SENS1: Evaluate the sensitivity of findings to data quality and propose appropriate sensitivity analyses for a research investigation
  • SENS2: Conduct and communicate the results of a sensitivity analysis for unmeasured confounding.
  • DISC1: Demonstrate conceptual understanding of causal discovery by reasoning about outputs of the process and by manually conducting it using regression models.
  • DISC2: Use output from causal discovery to enhance a causal analysis as part of a sensitivity analysis.


Revisiting previous objectives

You can revisit any of the following objectives (excludes REGR1, IPTW1, TVTR1, and TVTR2).

  • EXCH1: Apply the concepts of marginal and conditional exchangeability to answer questions about (hypothetical) data on potential outcomes.
  • EXCH2: Give examples of when marginal and conditional exchangeability would and would not hold in various data contexts.
  • EXCH3: Explain why a direct comparison of the outcomes in the treated and untreated is misleading as an estimate of a causal effect.
  • DESI1: Explain how randomized experiments relate to exchangeability.
  • DESI2: Explain how quasi-experimental and general observational studies relate to exchangeability.
  • DESI3: Compare the strengths and weaknesses of different study designs for answering a research question.
  • PGRA1: Apply the Causal Markov assumption to express the joint distribution of data.
  • CNCP1: Explain how causal and noncausal paths relate to exchangeability and causal effects.
  • DSEP1: Apply d-separation to block noncausal paths in causal DAGs with and without unobserved variables.
  • DSEP2: Apply strategies to deal with exchangeability problems caused by unobserved variables.
  • DSEP3: Simulate data from a causal DAG under linear and logistic regression SEMs to check d-separation properties through regression modeling and visualization.
  • DSEP4: Explain how d-separation relates to conditional exchangeability.
  • TVTR1: Formulate research questions that can be answered in a time-varying treatment setting.
  • TVTR2: Explain why regression does not generally work in time-varying settings with treatment-confounder feedback using d-separation ideas.


If you revisit any of these objectives, you must do so using the graph below. If revisiting an objective requires context for exactly what these variables represent, feel free to pick a context that is suitable for you.

library(dagitty)
dag <- dagitty("dag {
bb=\"0,0,1,1\"
A [exposure,pos=\"0.400,0.350\"]
L [pos=\"0.200,0.350\"]
U1 [latent,pos=\"0.100,0.200\"]
U2 [latent,pos=\"0.100,0.500\"]
Y [outcome,pos=\"0.600,0.350\"]
A -> Y
L -> A
U1 -> L
U1 -> Y
U2 -> A
U2 -> L
}
")

plot(dag)