A decision‐theoretic evaluation of early stopping rules

We consider the decision‐theoretic evaluation of early stopping rules for clinical trials. We describe a hypothetical phase III, two‐arm trial with interim analysis, modelling it as a decision problem. We present methods for constructing a group‐sequential test that is optimal for a given utility and prior distribution, and for determining a utility and prior under which a given test is optimal. Using our methods, we construct optimal tests for utilities and priors representing a variety of perspectives: a view that seeks to maximize the long‐run response rate, a view that seeks to maximize the chance of a correct decision, and a personal view elicited from a medical oncologist. Characteristics of the optimal rules are sensitive to the input utilities and priors, and their critical values and sampling properties can differ markedly from those of group‐sequential tests. We also compute utility functions and priors under which some standard group‐sequential stopping rules are optimal. Our results suggest that the group‐sequential tests, considered as decision procedures, imply a symmetry in the decision problem that is inconsistent with the response‐rate perspective. We conclude that decision theory is a useful device for illuminating the sometimes conflicting goals of clinical research, and that the use of decision theory in designing clinical trials could lead to marked changes in statistical criteria for early termination.