March 20, 2019

- correlation
- two problems:
- confounding/bias
- random association

- design-based vs. adjustment-based
- conditioning
- what is it?
- how does it work?

We start with a causal claim

- Turn claim into a causal theory
- causal logic, independent \(X\)/dependent \(Y\) variables

- Turn causal logic and \(X\)/\(Y\) into hypotheses
- expect that
**potential outcomes**of \(Y\) change with \(X\)

- expect that
B/C of FPCI: imperfectly test hypotheses using

**correlation**of__observed__values of \(X\) and \(Y\)- Infer causality if:
- assumptions about cases we compare let us ignore
**confounding**/**bias** - correlation unlikely to have occured
**by chance**

- assumptions about cases we compare let us ignore

Equivalently:

- Observed cases with different values of \(X\) have different potential outcomes of \(Y\)
- Observed cases with different values of \(X\) have different values of \(W\), which is related to \(Y\)
- There is a "backdoor" causal path from \(X\) to \(Y\)

- Correlation between \(X\) and \(Y\) is by chance and reflects no change in \(Y\) due to \(X\).

**adjustment-based**solutions**design-based**solutions

- Increase number of
**independent**cases - Take courses in statistics

- Identify possible
**confounding**variables (e.g. \(W, Z, V, U\)) - Measure these variables
**adjust**correlation of \(X\) and \(Y\) by "**conditioning**" on confounding variables

- Compare cases that,
__by assumption__, are- similar in terms of confounding variables \(W\)/ potential outcomes of \(Y\)
- exposed to \(X\) in a manner unrelated to \(W\)/potential outcomes of \(Y\)

Adjustment-based approaches start from the…

Sometimes called the "method of difference" (via John Stuart Mill), this assesses whether \(X\) causes \(Y\) by…

- comparing two cases that are the same in
**all relevant**respects, except for value of \(X\) - assess for these two cases whether \(Y\) changes when \(X\) changes (correlation)

What causes the spread of **cholera**?

Contaminated water causes cholera outbreaks

19th Century London saw repeated outbreaks of cholera, with mass death

- Dominant view was that "miasmas" or bad air caused diseases like cholera

John Snow, MD