Review

# Review

**Session 13**

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![](img/diagramming/d14.png)

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# Asking good causal questions

.box-inv-1.medium[the claim]

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.box-inv-1.medium[the evidence]

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# Asking good causal questions

.box-inv-1.medium[the claim]
Smoking causes lung cancer
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.box-inv-1.medium[the evidence]

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class: title title-1

# Asking good causal questions

.box-inv-1.medium[the claim]
Smoking causes lung cancer
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.box-inv-1.medium[the evidence]
For people who smoking 15+cigarettes a day, reducing smoking by 50% reduces the risk of lung cancer over 5-10 years
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.box-1.medium[do these match?]
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# Asking good causal questions

.box-1.medium[the question]
Does smoking cause lung cancer?
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.box-inv-1.medium[the evidence]
For people who smoking 15+cigarettes a day, reducing smoking by 50% reduces the risk of lung cancer over 5-10 years
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.box-1.medium[do these match?]

# Asking good causal questions

.box-inv-1.medium[the question]
For people who smoke 15+ cigarettes a day, does reducing smoking by 50% reduce the lung cancer risk over 5-10 years? 
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.box-inv-1.medium[the evidence]
For people who smoking 15+cigarettes a day, reducing smoking by 50% reduces the risk of lung cancer over 5-10 years
]

.box-1.medium[do these match?]

# What is a causal effect

.box-inv-1.medium[The causal effect is the comparison of the potential outcomes for the same unit at the same moment in time post-exposure]

.box-inv-1.medium[Whether the effect is **causal** depends on the potential outcomes but it **does not** depend on which outcome is actually observed]

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# Potential Outcome

<br> <br>
.box-1[

What *will* happen to you in the future given you have a particular exposure

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<br>

.box-inv-1.medium[

**fixed** but **unknown**

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## Stable Unit Treatment Value Assumption

.box-inv-1[
The potential outcomes for any unit do not vary with the exposures assigned to other units, and, for each unit, there are no different forms or versions of each exposure level, which lead to different potential outcomes.]

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# Exposure assignment

.box-inv-1[Understanding the **assignment mechanism** is crucial for understanding the causal effect]

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# Summary of assumptions

Assumption | Classic Randomized Trial| Randomized Trial| Observational Study
------------|-----------------|-------------------
No Interference | 🤷 | 🤷 | 🤷
Consistency | 😄 | 😄 | 🤷
Individualistic | 😄| 🤷| 🤷
Probabilistic |😄| 😄| 🤷
Unconfounded |😄| 🤷| 🤷

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# Compontents of a target trial

.box-inv-1.medium[consistent exposure]

.box-inv-1.medium[assignment procedures]

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.pull-right[
.box-inv-1.medium[follow-up period]

.box-inv-1.medium[outcome]

.box-inv-1.medium[causal contrasts of interest]

.box-inv-1.medium[analysis plan]

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<img src = "img/diagram/diagram/diagram.009.jpeg" width = "80%"></img>
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<img src = "img/diagram/diagram/diagram.010.jpeg" width = "80%"></img>
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<img src = "img/diagram/diagram/diagram.013.jpeg" width = "80%"></img>
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<figure>
<img src = "img/diagram/diagram/diagram.021.jpeg" width = "80%"></img>
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<img src = "img/diagram/diagram/diagram.022.jpeg" width = "80%"></img>
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# Causal Diagrams: DAGs

.box-inv-1.medium[directed]

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.box-inv-1.medium[acyclic]

.box-inv-1.medium[graph]

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# Directed Acyclic Graphs!

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# Spurious associations

![](img/dags-cars/dags-cars.001.png)

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# Eliminate backdoor paths

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.pull-right[
.box-1[What isn't here? Why?]
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# Identify adjustment sets

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# Spurious associations

![](img/dags-cars/dags-cars.001.png)

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![](img/estimand.jpeg)
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# Randomized Trials

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.box-1[
Estimand: `$\tau = E[Y(1) - Y(0)]$`
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.box-1[
Estimator: `$\hat\tau = \frac{1}{N}\sum_{i=1}^N\left(\frac{Y^{obs}X_i}{N_e/N }-\frac{Y^{obs}(1-X_i)}{N_c/N}\right)$`
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# Randomized Trials

`$$E[\hat\tau | Y(1), Y(0)]=\\ E\left[\frac{1}{N}\sum_{i=1}^N\left(\frac{Y(1)X_i}{N_e/N }-\frac{Y(0)(1-X_i)}{N_c/N}\right)\Big|Y(1), Y(0)\right]$$`
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# Randomized Trials

.box-1[
`$$E[\hat\tau | Y(1), Y(0)]=\\\frac{1}{N}\sum_{i=1}^N\left(\frac{Y(1)E[X_i|Y(1), Y(0)]}{N_e/N }-\frac{Y(0)E[(1-X_i)|Y(1), Y(0)]}{N_c/N}\right)$$`
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# Propensity score: The average unit assignment probability for units where `$Z_i=z$`

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# Observational studies

.box-1[
Estimator: `$\frac{1}{N}\sum_{i=1}^N\left(\frac{Y^{obs}X_i}{N_e/N }-\frac{Y^{obs}(1-X_i)}{N_c/N}\right)$`
]

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# Observational studies

.box-inv-1.medium[Propensity score weighting]

.box-inv-1.medium[Propensity score matching]

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# <svg aria-hidden="true" role="img" viewBox="0 0 640 512" style="height:1em;width:1.25em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M624 416H381.54c-.74 19.81-14.71 32-32.74 32H288c-18.69 0-33.02-17.47-32.77-32H16c-8.8 0-16 7.2-16 16v16c0 35.2 28.8 64 64 64h512c35.2 0 64-28.8 64-64v-16c0-8.8-7.2-16-16-16zM576 48c0-26.4-21.6-48-48-48H112C85.6 0 64 21.6 64 48v336h512V48zm-64 272H128V64h384v256z"/></svg> Application Exercise