Bayesian sequential analysis for multiple-arm clinical trials
Use of full Bayesian decision-theoretic approaches to obtain optimal stopping rules for clinical trial designs typically requires the use of Backward Induction. However, the implementation of Backward Induction, apart from simple trial designs, is generally impossible due to analytical and computational difficulties. In this paper we present a numerical approximation of Backward Induction in a multiple-arm clinical trial design comparing k experimental treatments with a standard treatment where patient response is binary. We propose a novel stopping rule, denoted by tau (p) , as an approximation of the optimal stopping rule, using the optimal stopping rule of a single-arm clinical trial obtained by Backward Induction. We then present an example of a double-arm (k=2) clinical trial where we use a simulation-based algorithm together with tau (p) to estimate the expected utility of continuing and compare our estimates with exact values obtained by an implementation of Backward Induction. For trials with more than two treatment arms, we evaluate tau (p) by studying its operating characteristics in a three-arm trial example. Results from these examples show that our approximate trial design has attractive properties and hence offers a relevant solution to the problem posed by Backward Induction.
clinical trials stopping rule backward induction expected utility one-arm look-ahead approximation