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.)