Cole, S. R., Platt, R. W., Schisterman, E. F., Chu, H., Westreich, D., Richardson, D., & Poole, C. (2010). Illustrating bias due to conditioning on a collider. $\mathit{International \ Journal \ of \ Epidemiology, 39}$, 417-420. [doi.org/10.1093/ije/dyp334](https://doi.org/10.1093/ije/dyp334)
[ncbi.nlm.nih.gov/pmc/articles/PMC2846442/](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2846442/) 

University of Michigan - Ann Arbor

This contains the reference information for papers about causal inference. List of helpful papers about causal inference:

- Computer-Aided Experiment Planning toward Causal Discovery in Neuroscience
- Causal inference Based on Counterfactuals
- Illustrating bias due to conditioning on a collider
- Towards Clarifying the Theory of the Deconfounder
- On Geometry of Information Flow for Causal Inference
- Directed Acyclic Graphs and causal thinking in clinical risk prediction modeling
- A Crash Course in Good and Bad Controls
- The Seven Tools of Causal Inference, with Reﬂections on Machine Learning
- Generalizing Experimental Results by Leveraging Knowledge of Mechanisms
- Note on ‘‘Generalizability of Study Results‘‘
- THE LIMITATIONS OF OPAQUE LEARNING MACHINES
- Sensitivity Analysis of Linear Structural Causal Models
- The Environment and Disease: Association or Causation?
- Confounding and Collapsibility in Causal Inference
- Causal Inference-so much more than statistics

Causal Inference Papers

When a single node is caused by two other nodes we encounter something called "collider-bias" where one condition explains-away another. 

Since A and C both effect the outcome of B, by conditioning on B, A and C become **dependent**.

$A \rightarrow B \leftarrow C$: The Collider

Matiasz, N. J., Wood, J., Wang, W., Silva, A. J., & Hsu, W. (2017). Computer-Aided Experiment Planning toward Causal Discovery in Neuroscience. $\mathit{frontiers \ in \ Neuroinformatics, 11.}$ (12), 1-8. [doi.org/10.3389/fninf.2017.00012](https://doi.org/10.3389/fninf.2017.00012)
[https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5304468/](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5304468/) 

Computer-Aided Experiment Planning toward Causal Discovery in Neuroscience

Höfler, M. (2005). Causal inference based on counterfactuals. $\mathit{BMC \ Medical \ Research \ Methodology, 5}$(28), [doi.org/10.1186/1471-2288-5-28](https://doi.org/10.1186/1471-2288-5-28)
[www.ncbi.nlm.nih.gov/pmc/articles/PMC1239917/](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1239917/) 

Causal inference based on counterfactuals

Illustrating bias due to conditioning on a collider

Towards Clarifying the Theory of the Deconfounder

Slightly out of scope, but a very interesting read : 
[arxiv.org/abs/2002.02078](https://arxiv.org/abs/2002.02078) 

On Geometry of Information Flow for Causal Inference

More application based, but I enjoyed reading about the approach : 
[arxiv.org/abs/2002.09414](https://arxiv.org/abs/2002.09414) 

Directed Acyclic Graphs and causal thinking in clinical risk prediction modeling

Sutton-Tyrrell, K. (1991). Assessing bias in case-control studies. *AHA Journals*. 22(7),  938-939 from [www.ahajournals.org/doi/pdf/10.1161/01.STR.22.7.938 .](https://www.ahajournals.org/doi/pdf/10.1161/01.STR.22.7.938 .) 

Assessing bias in case-control studies.

Pearl, Judea. “The Seven Tools of Causal Inference, with Reflections on Machine Learning.” Communications of the ACM, vol. 62, no. 3, 2019, pp. 54–60., doi:10.1145/3241036.

https://dl.acm.org/doi/pdf/10.1145/3241036

The Seven Tools of Causal Inference, with Reﬂections on Machine Learning

Cinelli, Carlos, and Judea Pearl. “Generalizing Experimental Results by Leveraging Knowledge of Mechanisms.” Technical Report - UCLA, 10 Dec. 2019.

https://ftp.cs.ucla.edu/pub/stat_ser/r492.pdf

Generalizing Experimental Results by
Leveraging Knowledge of Mechanisms

Pearl, Judea, and Elias Bareinboim. “Note on ‘‘Generalizability of Study Results.’” Wolters Kluwer Health, vol. 30, no. 2, Mar. 2019.

https://journals.lww.com/epidem/Citation/2019/03000/Note_on___Generalizability_of_Study_Results__.5.aspx



Note on ‘‘Generalizability of Study Results‘‘

Pearl, Judea. “THE LIMITATIONS OF OPAQUE LEARNING MACHINES.” Technical Report - UCLA, May 2019.

THE LIMITATIONS OF OPAQUE LEARNING MACHINES

Pearl, Judea, et al. “Sensitivity Analysis of Linear Structural Causal Models.”

http://proceedings.mlr.press/v97/cinelli19a/cinelli19a.pdf

Sensitivity Analysis of Linear Structural Causal Models

Hill, A. B. (1965). The Environment and Disease: Association or Causation? Proceedings of the Royal Society of Medicine, 58(5), 295-300. doi:10.1177/003591576505800503
Link: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1898525/?page=1

The Environment and Disease: Association or Causation?

https://ftp.cs.ucla.edu/pub/stat_ser/r493.pdf

A Crash Course in Good and Bad Controls

Greenland, Sander; Robins, James M.; Pearl, Judea. Confounding and Collapsibility in Causal Inference. Statist. Sci. 14 (1999), no. 1, 29--46. doi:10.1214/ss/1009211805. https://projecteuclid.org/euclid.ss/1009211805

Confounding and Collapsibility in Causal Inference

Pearce, N., & Lawlor, D. A. (2016). Causal inference-so much more than statistics. International journal of epidemiology, 45(6), 1895–1903. https://doi.org/10.1093/ije/dyw328
Link: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5841844/

Causal inference-so much more than statistics

In a path that would impact both variables but also contains a collider, M-bias occurs when the variable in the center of the collider is adjusted for. 

The general structure for M-bias is A <- B -> C <- D -> E where adjusting for C would create bias. 

M-bias

This a subcategory of a collider bias (Collider is the selection of the data). When two factors individually are usually not severe enough to cause some effect but the combination of the two is. Usually both factors are not thought to be correlated with each other in real life settings but in a certain condition they are. This seems to occur because the resulting effect is being adjusted for by not considering the situations where both factors do not occur. This association is caused based on the conditional collider of the environment the data is selected. 

Berkson's Paradox

The statistical procedure of controlling for everthing that can be measured is misguided. 

For instance, in a collider $A\rightarrow B \leftarrow C$ where the path between $A$ and $C$ is initially independent, controlling for B would make them dependnet due to the explain-away effect. This means that a back-door is opened.

Also, controlling for descendents of the varibles we are interested in should also be avoided. This is like "partially" controlling for the interested variable itself. 

Controlling for everything is misguided

Proposed by Hans Reichenbach, the common cause principal argues against correlation doesn’t imply causation. It states that if there are two variables I and J and they are correlated, then I causes J or J causes I or there is another variable X that precedes and causes both I and J. 

This theory is not true because it doesn't account for how the data is selected and appeals to our human nature to look for casual explanations whenever there is a pattern. This is an example of collider bias.

Common Cause Principal 

A proxy is used as a substitute measure when a variable that is not directly measurable is needed for analysis.  For a variable to be a proxy for another variable, the proxy variable needs to be highly correlated with the variable of interest.  The proxy can be used for any variables such as a mediator, confounder, collider.  

Proxy

In the Book of Why, some of the classic examples of collider bias are discussed:

1. Celebrity's talent and beauty
2. Birth-weight paradox (Simpson's paradox)
3. Admission-rate bias (Berkson's paradox)

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