Bayesian decision-theoretic trial design: Operating characteristics and ethics, an approximate method, and time -trend bias

Background. The design of clinical trials to evaluate new therapies for the treatment of unusual but devastating acute illnesses is a challenging but important problem. Using a Bayesian, decision-theoretic approach, it is possible to design and evaluate group-sequential clinical trials that coherently incorporate pre-existing information with the accumulating data so that all available information is brought to bear, while minimizing a particular loss function. It is often assumed that incorporating adaptive features---such as adding response-adaptive, adaptive randomization---into the trial design will have positive ethical implications.;Methods. We develop software that designs Bayesian, decision-theoretic trials that compare two treatments with dichotomous outcomes, and explore the operating characteristics that result from adding adaptive randomization and a term (in the loss function) for a subject experiencing the worse outcome. Separately, we consider the use of a variable-step look-ahead technique for overcoming some limitations imposed by backward induction, the traditional method of solving such trial designs. Finally, we explore a bias that results from the use of adaptive randomization in the setting of a background trend in risk of disease, and derive bias formulas that can be used with a sensitivity analysis.;Conclusions. (1) The addition of adaptive randomization to trial designs generally confers increased efficiency; however, goals which are not explicitly included in the loss function are ignored and even compromised. Without an appropriate loss function, a trial that uses adaptive randomization does not by itself imply a more ethical trial design. Controlling error rates curtails the impact of including competing goals. (2) Variable-step look-ahead is a viable alternative to full backward induction, and may be especially useful for the first groups enrolled in a sequential trial where differences in optimal actions may have significant impact on the overall operating characteristics. (3) Confounding may occur with adaptive randomization in the setting of a time trend in baseline risk of disease, and may be dealt with through the use of Bayesian hierarchical modeling, stratification, or the derived bias factors with an appropriate sensitivity analysis.