This week, we discussed:

Little, R. J., & Rubin, D. B. (2000). Causal effects in clinical and epidemiological studies via potential outcomes: concepts and analytical approaches. Annual Review of Public Health, 21(1), 121–145.

In this article, Little and Rubin lay down some of their requirements for causal inference, including a variety of approaches. Read the full post for some notes and links to python code and angry physicists.

### Nailing down our assumptions

Of critical importance is the authors' claim that a “stable unit-treatment value” assumption (SUTVA) is necessary for causal inference. Put simply, SUTVA breaks down into the following:

- If one bunny is given a treatment, it doesn’t affect other bunnies.
- There is no (relevant) variation in treatment.

However, it seems that there are certainly situations in which we could claim causal effects (and can’t assume homogeneity of treatments) – for example, in psychoterapeutic settings, or when compliance with a protocol is violated by some participants.

Michael claims another paper of interest (*Interference between units in
randomized experiments*, by Paul R. Rosenbaum) lays out a version of causal
inference that does not require SUTVA.

The authors present three forms of inference.

- Fisherian: We demand full randomization, and perform Null-Hypothesis Significance Testing (NHST) on differences between groups.
- Neyman’s: We still demand full randomization, and generate a (frequentist) confidence interval around the difference.
- Model-based: Compute a bayesian confidence interval. The authors find this to be the most satisfying approach.

A breakdown of these different forms of confidence intervals, including python code is given in this well-circulated blog post by Jake VanderPlas. (But note that it’s not hard to find folks who argue that Jake’s specific examples are ignorant.)