# Observational Studies

## 9. Internal Validity

### Causal Inference: Internal Validity

Modern discussions of causal inference are based on how statisticians have come to think about cause and effect. The statistical framework was developed by Neyman in 1923 and later extended by Rubin (1974) and Holland (1986). It is sometimes called the "Rubin Causal Model."

### Example 4

**Rubin defines a causal effect:**

Intuitively, the causal effect of one treatment, E, over another, C, for a particular unit and an interval of time from t1 to t2 is the difference between what would have happened at time t2 if the unit had been exposed to E initiated at t1 and what would have happened at t2 if the unit had been exposed to C initiated at t1: 'If an hour ago I had taken two aspirins instead of just a glass of water, my headache would now be gone,' or because an hour ago I took two aspirins instead of just a glass of water, my headache is now gone.' Our definition of the causal effect of the E versus C treatment will reflect this intuitive meaning.

According to the RCM, the causal effect of your taking or not taking aspirin one hour ago is the difference between how your head would have felt in case 1 (taking the aspirin) and case 2 (not taking the aspirin). If your headache would remain without aspirin but disappear if you took aspirin, then the causal effect of taking aspirin is headache relief (Rubin, 1974:689).