Introduction to causal inference

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# Introduction to causal inference
### Dr. Olanrewaju Michael Akande
### Oct 31, 2019

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## Announcements

- Reminder: project presentations tomorrow at 10:00am.

- Everyone should be in class by 9:55 at most.

## Outline

- Association vs. causation; confounding

- Potential outcomes framework

- Causal estimands

- Assignment mechanisms

- Randomization vs observational studies

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# Association vs. causation; confounding

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## Causality

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<i class="fa fa-quote-left fa-2x fa-pull-left fa-border" aria-hidden="true"></i>
<i class="fa fa-quote-right fa-2x fa-pull-right fa-border" aria-hidden="true"></i>
We do not have knowledge of a thing until we have grasped its why, that is to say, <font color="red">its cause</font>.

-- Aristotle, Physics

</br>
- Over the next few classes, we will discuss causal inference, specifically, we will focus on measuring the .hlight[effects of causes].

- For today's class, we will simply lay the foundations for causal inference. We will get more into the actual methods in the next class.

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## Association vs. causation

- In the models we have covered so far, our focus has been on inferring .hlight[associations] using samples drawn from our population of interest.

- For example, we have been asking questions such as, do people who receive job training tend to earn more wages than people who do not?

- Causal inference goes further as we try to infer aspects of the actual data generating process, that is, .hlight[causation].

- For example, does receiving job training actually cause one to earn more wage than they would have without the training?

- The additional information needed to move from association to causation is often provided by .hlight[causal assumptions] (often untestable).

- Note: in most cases, .hlight[association does not imply causation]!

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## Confounding

- Why is it that association does not often imply causation? .hlight[confounding variables or confounders]!

- Causal relationship
<div id="htmlwidget-b1d2a9b26625270e53e5" style="width:2100px;height:180px;" class="DiagrammeR html-widget"></div>
<script type="application/json" data-for="htmlwidget-b1d2a9b26625270e53e5">{"x":{"diagram":"\n\t        graph LR\n\t        W(Treatment)-->Y(Outcome)\n\t        "},"evals":[],"jsHooks":[]}</script>

- Confounding
<div id="htmlwidget-e486787b6eca8f29e89c" style="width:2100px;height:180px;" class="DiagrammeR html-widget"></div>
<script type="application/json" data-for="htmlwidget-e486787b6eca8f29e89c">{"x":{"diagram":"\n\t        graph TB\n\t        C(Confounder)-->W(Treatment)\n\t        C-->Y(Outcome)\n\t        "},"evals":[],"jsHooks":[]}</script>

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## Examples of confounding

- Ice cream consumption and number of people who drowned.  
  .hlight[Confounder: temperature]; people tend to consume more ice cream and also swim more when it is hot.

- Medical treatment and patient outcome.  
  .hlight[Confounders: age, sex, other complications]
  
--

- Education and income.  
  .hlight[Confounder: socio-economic status of family]
  
--

- An extreme example of confounding is Simpson’s paradox: where  a confounder reverses the sign of the correlation between treatment and outcome

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## Simpson's paradox

- Example: kidney stone treatment (Charig et al., BMJ, 1986).
  + Compare the success rates of two treatments for kidney stones
  + Treatment A: open surgery; treatment B: small puncture

<br />       | Treatment A | Treatment B   |
:----------- | :--------- | :---------   |
Small stones | <b>93%</b> (81/87) | 87% (234/270) |
Large stones | <b>73%</b> (192/263) | 69% (55/80) |
Both         | 78% (273/350) | <b>83%</b> (289/350) |

+ What is the confounder here? Severity of the case/type of stones.
  
  
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## Simpson's paradox or Yule-Simpson effect

- Simpson’s paradox: a trend appears in different groups of data but disappears or reverses when these groups are combined.

- Mathematically, it is about conditioning.

- Another well-known example is the Berkeley admission gender bias (Bickel et al., Science, 1976).

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## General notation

- .hlight[W]: Treatment (e.g. job training); we will focus on binary treatments.

- .hlight[Y]: Outcome (e.g. annual wages).

- .hlight[X]: Observed predictors or confounders (e.g. age, education, etc).

- .hlight[U]: Unobserved predictors or confounders.

</br>

- Examples of causal questions:
  + Causal effect of exposure to a disease.
  
  + Comparative effectiveness research such as in clinical trials: whether one drug or medical procedure is better than the other.
  
  + Program evaluation in economics and policy.

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# Potential outcomes framework