
Most questions in social and biomedical sciences are causal in nature: what would happen to individuals, or to groups, if part of their environment were changed? In this groundbreaking text, two world-renowned experts present statistical methods for studying such questions. This book starts with the notion of potential outcomes, each corresponding to the outcome that would be realized if a subject were exposed to a particular treatment or regime. In this approach, causal effects are comparisons of such potential outcomes. The fundamental problem of causal inference is that we can only observe one of the potential outcomes for a particular subject. The authors discuss how randomized experiments allow us to assess causal effects and then turn to observational studies. They lay out the assumptions needed for causal inference and describe the leading analysis methods, including, matching, propensity-score methods, and instrumental variables. Many detailed applications are included, with special focus on practical aspects for the empirical researcher.
For those on a more mathematical bend, check out "Causality" by the same author or "Causal Inference for Statistics, Social, and Biomedical Sciences" by Imbens and Rubin
- Mostly Harmless Econometrics by Joshua Angrist and Jorn Steffan Piscke
- Causal Inference for Statistics, Social, and Biomedical Sciences by Guido Imbens and Donald Rubin
- Data Analysis using Regression and Multilevel Models by Andrew Gelman and Jennifer Hill
Another technique we might use is a blocked (or stratified) random sample. Knowing that there will be both smokers and non-smokers, we recruit two separate samples, and randomize treatment assignment within each. This ensures that smoking status does not predict treatment assignment and guards against some potential threat from overall randomization.
We could also mitigate the imbalance that does exist by doing a matched analysis, where each treated unit is paired with a control unit that looks most like him (some control units are reused). Or we could match on propensity scores. Or we could weight on inverse propensity weights. Or we could weight using covariate balancing. Or...
My point in doing this info dump is to a) back up nerdponx's example, which is great and b) illustrate how there's a lot to learn about how statisticians have taken the problem of causal analysis seriously and developed techniques appropriate for answering causal questions.
People in the CS side of things tend to use Pearl's DAGS for conceptualizing this stuff. I'm in the stats/econ side of things so I use Neyman-Rubin. They're equivalent. Allow me to suggest Rubin and Imbens - Causal Inference for Statistics, Social and Biomedical Sciences as a good textbook that we assign to graduate students learning this stuff. Some of my students tell me the "Causal Inference Mixtape" is popular among people who want less statistical theory and more "what should I do as a practitioner". A virtue of both the resources I just mentioned is that they discuss not just experimental designs but also observational data studies, like the one the original post would have wanted to conduct.
[0] Causality, Judea Pearl
[1] Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction, Guido Imbens and Donald Rubin
Causal Inference for Statistics, Social, and Biomedical Sciences
and mention of this book: http://www.hsph.harvard.edu/miguel-hernan/causal-inference-b...
Does anyone have a comment on those? I've read Pearl's two earlier books, and found the one on causality quite hard to navigate. The basic ideas are cool, but it's hard to connect the more advanced theorems with anything I could actually implement.