Last observation carried forward: a crystal ball?

In spite of widespread criticism and notwithstanding the availability of flexible, broadly valid, and conveniently implemented methods like direct-likelihood and direct-Bayesian analyses, last observation carried forward (LOCF), baseline observation carried forward (BOCF), and complete case analysis remain popular for handling incomplete clinical trial data. To the well-known criticisms toward LOCF and BOCF, namely, that they can be either conservative or liberal depending on the context, that they can violate the intention-to-treat principle, and so on, we add that, with the exception of certain degenerate and unrealistic special cases, these methods are incompatible with the sensible requirement that the mechanism governing dropout be independent of future, unobserved measurements, given covariates, past observed measurements, and the current possibly missing measurement.