ABSTRACT
The primary scientific goal of a randomized clinical trial of two treatments, A and B, is to compare their effects on the most important therapeutic outcome in the medical setting under study. Generally, this comparison may be formulated in terms of two real-valued parameters, θA and θB, which most often are based on probabilities or hazards under treatments A and B, respectively, possibly transformed or covariateadjusted. Scientists routinely base such comparisons on the A-versus-B treatment effect, δθ θA θB, implicitly assuming that a typical statistical estimator computed from their data actually estimates δθ . While it is well established that randomization will, on average, eliminate potential sources of bias,1,2 when patients are not randomized between A and B, standard statistical estimators may become scientifically invalid and substantively misleading.
