  In a comprehensive cohort study of two competing treatments (say, A and B),
clinically eligible individuals are first asked to enroll in a randomized trial
and, if they refuse, are then asked to enroll in a parallel observational study
in which they can choose treatment according to their own preference. We
consider estimation of two estimands: (1) comprehensive cohort causal effect --
the difference in mean potential outcomes had all patients in the comprehensive
cohort received treatment A vs. treatment B and (2) randomized trial causal
effect -- the difference in mean potential outcomes had all patients enrolled
in the randomized trial received treatment A vs. treatment B. For each
estimand, we consider inference under various sets of unconfoundedness
assumptions and construct semiparametric efficient and robust estimators. These
estimators depend on nuisance functions, which we estimate, for illustrative
purposes, using generalized additive models. Using the theory of sample
splitting, we establish the asymptotic properties of our proposed estimators.
We also illustrate our methodology using data from the Bypass Angioplasty
Revascularization Investigation (BARI) randomized trial and observational
registry to evaluate the effect of percutaneous transluminal coronary balloon
angioplasty versus coronary artery bypass grafting on 5-year mortality. To
evaluate the finite sample performance of our estimators, we use the BARI
dataset as the basis of a realistic simulation study.
