Causal Inference (Fall 2024)
Instructor
- Bryan Shepherd, PhD, Professor of Biostatistics
- bryan.shepherd@vanderbilt.edu; 2525 West End, 11119; 615-343-3496
Schedule
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Lectures: Monday, Wednesday, 2:30-4:00, Large Biostat Classroom (11105; 11th floor, 2525 West End)
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Office hours:
- 3:00-4:00pm Fridays, 2525 West End #11119, or via Zoom. Please contact before.
Other information
- No textbook; we will primarily be reading journal articles. However, we will refer to the following textbooks fairly often:
- Imbens GW, Rubin DB (2015). Causal Inference for Statistics, Social, and Biomedical Sciences. Cambridge University Press.
- Pearl J (2009). Causality: Models, Reasoning, and Inference, Second Edition. Cambridge University Press.
- VanderWeele TJ (2015). Explanation in Causal Inference: Methods for Mediation and Interaction.
- The tentative lecture schedule is shown in the table below.
- Students are expected to read the noted section in the text prior to each class.
Grading (tentative)
- Class Participation
- Homework
- Exams
Lectures (tentative)
| Date | Lecture | Topic | Reading | Slides | Homework | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Aug 21 | Potential Outcomes; Rubin Causal Model | Imbens GW, Rubin DB (2015). Causal Inference for Statistics, Social, and Biomedical Sciences. Cambridge University Press. Chapters 1, 3. | Lecture1 | ||||||||
| Aug 26 | Rubin Causal Model | Holland PW (1986). Statistics and causal inference. JASA 81: 945-960. Imbens GW, Rubin DB (2015). Causal Inference for Statistics, Social, and Biomedical Sciences. Cambridge University Press. Chapters 1, 3. Pearl J (2009). Causality: Models, Reasoning, and Inference, Second Edition. Cambridge University Press. Section 11.4.5. (Causation without Manipulation!!!) Bonus: Cole S, Frangakis CE. The Consistency Statement in Causal Inference: A Definition or an Assumption?. Epidemiology 20(1):p 3-5, January 2009. |
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| Aug 28 | Causal Diagrams / Directed Acyclic Graphs | Greenland S, Pearl J, Robins JM (1999). Causal diagrams for epidemiologic research. Epidemiology 10: 37-48. Bonus: Hernan MA, Hernandez-Diaz S, Robins JM (2004). A structural approach to selection bias. Epidemiology 15: 615-625. |
Lecture3a, Lecture3b | Homework 1: Several DAGS (due Sep 4) | |||||||
| Sep 2 | NO CLASS | Labor Day | |||||||||
| Sep 4 | Causal Diagrams and Identification of Causal Effects | Pearl J (2009). Causality: Models, Reasoning, and Inference, Second Edition. Cambridge University Press. Chapter 3. Or you can read this (basically same material): Pearl J (1995). Causal diagrams for empirical research. Biometrika 82: 669-710. |
Lecture4 | Go over Homework 1 Homework 2: DAG and identifying assumptions (due Sep 11) |
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| Sep 9 | Causal Diagrams and Identification of Causal Effects (continued) | Pearl J (2009). Causality: Models, Reasoning, and Inference, Second Edition. Cambridge University Press. Chapter 3. Or you can read this (basically same material): Pearl J (1995). Causal diagrams for empirical research. Biometrika 82: 669-710. Bonus: Chapter 6 of Brady Neal book (Introduction to Causal Inference from a Machine Learning Perspective) |
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| Sep 11 | Causal Diagrams | Go over homework and finish discussion of Pearl's book and SWIGs Richardson TS, Robins JM. Single World Intervention Graphs: a Primer |
Go over Homework 2 |
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| Sep 16 | Propensity Scores | Joffe MM, Rosenbaum PR (1999). Invited commentary: propensity scores. American Journal of Epidemiology 150: 327-333. Rosenbaum PR, Rubin DB (1983). The central role of the propensity score in observational studies for causal effects. Biometrika 70: 41-55. Pearl J (2009). Causality: Models, Reasoning, and Inference, Second Edition. Cambridge University Press. Section 11.3.5. (Understanding Propensity Scores) |
Homework 3: DAG, identifying assumptions, and estimation (due Sep 25) | ||||||||
| Sep 18 | The average treatment effect ... on whom? Cohort pruning, the ATM and the ATO | Li, L., & Greene, T. (2013). A weighting analogue to pair matching in propensity score analysis. The International Journal of Biostatistics, 9(2), 215-234. Fan Li, Kari Lock Morgan & Alan M. Zaslavsky (2018) Balancing Covariates via Propensity Score Weighting, Journal of the American Statistical Association, 113:521, 390-400. |
[LECTURE NOTES NEEDED] |
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| Sep 23 | Propensity Scores in Practice | Kurth T, Walker AM, Glynn RJ, Chan KA, Gaziano JM, Berger K, Robins JM (2005). Results of multivariable logistic regression, propensity matching, propensity adjustment, and propensity-based weighting under conditions of nonuniform effect. American Journal of Epidemiology 163: 262-270. Franklin JM, Eddings W, Austin PC, Stuart EA, Schneeweiss S (2017). Comparing the performance of propensity score methods in healthcare database studies with rare outcomes. Statistics in Medicine. Austin PC, Stuart EA (2015). Moving towards best practice when using inverse probability of treatment weighting (IPTW) using the propensity score to estimate causal treatment effects in observational studies. Statistics in Medicine 34: 3661-3679. |
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| Sep 25 | Double Robustness | Bang H, Robins JM. Doubly robust estimation in missing data and causal inference models. Biometrics. 2005;61:962-972. [sections 1-2,5-6] Bonus: Funk MJ, Westreich D, Wiesen C, Sturmer T, Brookhart MA, Davidian M. Doubly robust estimation of causal effects. Am J Epidemiol. 2011 Apr 1;173(7):761-7. Kang JDY, Schafer JL. Demystifying double robustness: a comparison of alternative strategies for estimating a population mean from incomplete data. Statistical Science 2007; 22:523-539. Bonus: Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo, Christian Hansen, Whitney Newey, James Robins, Double/debiased machine learning for treatment and structural parameters, The Econometrics Journal, Volume 21, Issue 1, 1 February 2018, Pages C1–C68. |
Lecture8 | Go Over Homework 3 Homework 4 (due Oct 2) Homework 4: Apply 4 different propensity score approaches and a regression-based approach (standardization) to estimate the average causal effect of starting an NNRTI-based regimen vs. a boosted PI-based regimen on the risk of death during the first year after ART initiation in the simulated CCASAnet data. Use the hypothetical DAG in the attached zip file to guide the choice of covariates. Also obtain a doubly robust estimator. Perform a sensitivity analysis to investigate the sensitivity of the association on unmeasured confounding. In the zip file below, I have included the data, a data dictionary, and an R file that does a little bit of data management to make the problem simpler (i.e., excludes missing data, only looks at death during the first year, excludes some other types of regimens, and combines some categories for certain variables). It also contains some code that shows a logistic regression model and the bootstrap for the unadjusted analysis. Please use the bootstrap to get confidence intervals and logistic regression for the outcome and propensity score models. This homework should be emailed to me as a 1-page report (main document) describing statistical methods, results, and conclusions. Please state assumptions and interpret your findings. Please send it to me as a pdf document with your name on top. The end of the report should include Supplementary Material which includes the analysis code and any diagnostics that were performed. |
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| Sep 30 | Sensitivity Analyses | VanderWeele TJ, Ding P (2017). Sensitivity analysis in observational research: introducing the E-value. Annals of Internal Medicine. Ding P, VanderWeele TJ (2016). Sensitivity analysis without assumptions. Epidemiology 2016; 27: 368-377. |
Lecture9 Lucy's Slides: |
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| Oct 2 | Mediation Analyses | VanderWeele TJ (2015). Explanation in Causal Inference: Methods for Mediation and Interaction. Chapter 2, sections 2.1-2.6, 2.16, 2.10-2.15, 2.17-2.19. Appendix, sections A.2.1- A.2.2. | Lecture10 | Go over Homework 4 Homework 5 (due Oct 7) |
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| Oct 7 | Mediation Analyses | VanderWeele TJ (2015). Explanation in Causal Inference: Methods for Mediation and Interaction. Chapter 3, sections 3.2-3.4; Chapter 5, section 5.1. |
Go over Homework 5 Homework 5: With the JOBS II dataset, perform a mediation analysis estimating the controlled direct effect, the natural direct effect, and the natural indirect effect of job training on (a) depressive symptoms considering job_seek as a mediating variable, and on (b) employment status considering the mediating variable job_seek. The JOBS II dataset can be found at https://dataverse.harvard.edu/dataset.xhtml?persistentId=hdl:1902.1/14801. This contains the data and analyses for Imai K, Keele L, Tingley D. A general approach to causal mediation analysis. Psychological Methods 2010; 15: 309-334. Code up the analyses suggested in Chapter 2 of VanderWeele, but compare and contrast these estimates with those obtained using the approach of Imai and colleagues. Again, I would like a 1-page pdf document that contains all of the essentials and then also Supplementary Material that includes code and any other material you would like to include. |
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| Oct 9 | Compliance | Angrist JD, Imbens GW, Rubin DB (1996). Identification of causal effects using instrumental variables. JASA 91:444-455 | Lecture11 | ||||||||
| Oct 14 | Instrumental Variables | Baiocchi M, Cheng J, Small DS (2014). Tutorial in biostatistics: instrumental variable methods for causal inference. Statistics in Medicine 33: 2297-2340. Sections 1-4, 5.1-5.2, 6-8, and 13-14. | Lecture12 |
Go over Homework 6 Homework 6: The dataset listed below contains results from a simulated randomized trial. Participants were assigned to treatment or control (assign) and their CD4 count was measured after 3 months of follow-up (cd4). The treatment they actually took is also recorded (trt), as is a baseline measure of the patients health status (health.status). Estimate the effect of assignment to treatment on CD4 (ITT effect), and the compliers average causal effect (CACE or LATE). Describe the assumptions made for estimation and contrast these estimates with more naive estimates such as the per protocol estimate and the as-treated estimate. As usual, please provide a 1-page document that summarizes findings and put code and any diagnostics in Supplementary Material that can be as long as you would like. Due March 25. |
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| Oct 16 | Principal Stratification | Frangakis CE, Rubin DB (2002). Principal stratification in causal inference. Biometrics 58: 21-29. Gilbert PB, Bosch RJ, Hudgens MG (2003). Sensitivity analysis for the assessment of causal vaccine effects on viral loads in HIV vaccine trials. Biometrics 59; 531-541. Shepherd BE, Gilbert PB, Mehrotra DV (2007). Eliciting a counterfactual sensitivity parameter. The American Statistician 61: 1-8. |
Lecture13a, Lecture13b | ||||||||
| Oct 21 | Principal Stratification - Goal or Tool? | Pearl J (2011). Principal stratification - goal or a tool? International Journal of Biostatistics 7: 20. !VanderWeele TJ (2011). Principal stratification - uses and limitations. International Journal of Biostatistics 7:28. Joffe MM (2011). Principal stratification and attribution prohibition: good ideas taken too far. International Journal of Biostatistics 7: 35. Sjolander A (2011). Reaction to Pearls critique of principal stratification. International Journal of Biostatistics 7: 22. |
Lecture14 | A clinical trial was performed to evaluate the effect of an intervention (spontaneous breathing treatment in the ICU) on cognitive function. Cognitive function is only measured on survivors. 1) Perform an analysis comparing cognitive function among survivors; what problems does this analysis have that make it hard to interpret this causally? 2) Perform an intention-to-treat type analysis where those who die are assigned poor cognitive function; what problems does this analysis have? 3) Perform a principal stratification analysis estimating the causal effect of intervention on cognitive function among those who would have survived to 3 months regardless of treatment assignment. Perform a sensitivity analysis under under SUTVA, randomization, and monotonicity; derive large sample bounds and estimate with a sensitivity parameter. Data will be emailed to you and are not to be shared or posted. As always, please summarize results in a 1-page document. Code and other material can be provided in a Supplementary Material section that is as long as you would like. |
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| Oct 23 | Econometric Causality | Heckman JJ (2008). Econometric causality. International Statistical Review 76: 1-27. | Lecture15a, Lecture15b | ||||||||
| Oct 28 | Difference in Differences | Thome JC, Rebeiro PF, Shepherd BE. Understanding difference-in-differences methods to evaluate policy effects with staggered adoption: An application to Medicaid and HIV. (submitted) [pre-print at https://arxiv.org/abs/2402.12576] | |||||||||
| Oct 30 | Regression Discontinuity | Moscoe E, Bor J, Barnighausen T (2015). Regression discontinuity designs are underutilized in medicine, epidemiology, and public health: a review of current and best practice. Journal of Clinical Epidemiology 2015; 68: 132-143. | |||||||||
| Nov 4 | Time-varying confounding | Daniel RM, Cousens SN, De Stavola BL, Kenward MG, Sterne JAC (2012). Methods for dealing with time-dependent confounding. Statistics in Medicine 32: 1584-1618. Sections 1-4. | Reproduce Simple Example g-computation and IPW of MSM in Section 4; Reproduce simulations of section 5. Due April 11. | ||||||||
| Nov 6 | Marginal structural models | Daniel RM, Cousens SN, De Stavola BL, Kenward MG, Sterne JAC (2012). Methods for dealing with time-dependent confounding. Statistics in Medicine 32: 1584-1618. Sections 5, 7-9. | |||||||||
| Nov 11 | Marginal structural models | Daniel RM, Cousens SN, De Stavola BL, Kenward MG, Sterne JAC (2012). Methods for dealing with time-dependent confounding. Statistics in Medicine 32: 1584-1618. Sections 5, 7-9. | Lecture16; simulation-code | ||||||||
| Nov 13 | MSM | Robins JM, Hernan MA, Brumback B (2000). Marginal structural models and causal inference in epidemiology. Epidemiology 11: 550-560. Hernan MA, Brumback B, Robins JM (2000). Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men. Epidemiology 11: 561-570. |
Lecture17 | Perform a marginal structural model analysis. Estimate the causal effect of HAART on mortality using the simulated HIV data attached below. Your analysis should be similar to that of Hernan, Brumback, and Robins (2000). More details are in the attached document. Due April 27. msm-assignment-instructions Simulated-HIV-data.zip | |||||||
| Nov 25 | NO CLASS | Thanksgiving Break | |||||||||
| Nov 27 | NO CLASS | Thanksgiving Break | |||||||||
| Dec 2 | Dynamic Marginal Structural Models | Hernan MA, Lanoy E, Costagliola D, Robins JM (2006). Comparison of dynamic treatment regimes via inverse probability weighting. Basic and Clinical Pharmacology and Toxicology 98: 237-242. [BONUS:] Cain LE, Robins JM, Lanoy E, Logan R, Costagliola D, Hernan MA (2010). When to start treatment? A systematic approach to the comparison of dynamic regimes using observational data. International Journal of Biostatistics 6: 18. |
Lecture18 | ||||||||
| Dec 4 | Applications of Dynamic Marginal Structural Models | Shepherd BE, Jenkins CA, Rebeiro PF, Stinnette SE, Bebawy SS, McGowan CC, Hulgan T, Sterling TR (2010). Estimating the optimal CD4 count for HIV-infected persons to start antiretroviral therapy. Epidemiology 21: 698-705. [BONUS:] Shepherd BE, Liu Q, Mercaldo N, Jenkins CA, Lau B, Cole SR, Saag MS, Sterling TR (2016). Comparing results from multiple imputation and dynamic marginal structural models for estimating when to start antiretroviral therapy. Statistics in Medicine 35: 4335-4351. |
Lecture19 | ||||||||
| Apr 25 | Catch up day | The C-word; scientific euphimisms do not improve causal inference from observational data. AJPH; 108: 616-619, with discussion. | |||||||||
| Extra | Targeted maximum likelihood estimation | Schuler MS, Rose S (2017). Targeted maximum likelihood estimation for causal inference in observational studies. American Journal of Epidemiology 185: 65-73. | replicating-Schuler-Rose-simulations.R | ||||||||
| Extra | Causal inference never a dull topic | Dawid P (2000). Causal inference without counterfactuals, with Discussion. JASA 95: 407-448. Hernan MA (2018). The C-word; scientific euphimisms do not improve causal inference from observational data. AJPH; 108: 616-619, with discussion. |
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| Extra | Propensity Scores in Practice (continued) | Lecture7c-PS-continuous.pptx, | |||||||||
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