The transitive fallacy for randomized trials: If A bests B and B bests C in separate trials, is A better than C?

Abstract

Even with large sample sizes, combining results from a previous randomized trial of B versus C with results from a new randomized trial of A versus B will not guarantee correct inference about A versus C. A three-arm trial of A, B, and C would protect against this problem and should be considered when the sequential trials are performed in the context of changing secular trends in important omitted variables such as therapy in cancer screening trials.