David Maxwell Chickering, Judea Pearl
We describe a computer program to assist a clinician with assessing the efficacy of treatments in experimental studies for which treatment assignment is random but subject compliance is imperfect. The major difficulty in such studies is that treatment efficacy is not "identifiable", that is, it cannot be estimated from the data, even when the number of subjects is infinite, unless additional knowledge is provided. Our system combines Bayesian learning with Gibbs sampling using two inputs: (1) the investigator' s prior probabilities of the relative sizes of subpopulations and (2) the observed data from the experiment. The system outputs a histogram depicting the posterior distribution of the average treatment effect, that is, the probability that the average outcome (e.g., survival) would attain a given level, had the treatment been taken uniformly by the entire population. This paper describes the theoretical basis for the proposed approach and presents experimental results on both simulated and real data, showing agreement with the theoretical asymptotic bounds.