Designing clinical trials requires evaluating multiple operating characteristics (OCs), such as the likelihood of an early stopping decision, the probability of detecting a treatment effect, and the Type I error rate. In most cases, these evaluations are based on computationally intensive Monte Carlo simulations. As the complexity of clinical trials and the use of adaptive designs increase, the computational burden can quickly become prohibitive. We introduce a strategy for rapidly approximating OCs, called the Q-approximation. Our approach is based on quadratic approximations of the log-likelihood and asymptotic arguments. The Q-approximation approach can be applied to any trial design that uses data analysis methods coherent with the likelihood principle, including multistage designs with early stopping, adaptively randomized designs, and designs that leverage external data. We illustrate the approach with several examples and show that it provides an accurate approximation of important OCs while reducing the computation time compared to Monte Carlo simulations. In particular, in our experiments, the standard Monte Carlo approximation of OCs requires 150 to 1,900 times greater computing budget than Q-approximations to achieve comparable levels of accuracy.

翻译：设计临床试验需要评估多个操作特征（OCs），例如提前停止决策的可能性、检测治疗效应的概率以及第一类错误率。在多数情况下，这些评估基于计算密集型的蒙特卡洛模拟。随着临床试验复杂性的增加以及适应性设计的广泛应用，计算负担可能迅速变得难以承受。我们提出了一种快速近似操作特征的策略，称为Q近似方法。该方法基于对数似然函数的二次近似以及渐近理论。Q近似方法可适用于任何采用符合似然原理的数据分析方法的试验设计，包括具有提前停止机制的多阶段设计、自适应随机化设计以及利用外部数据的设计。我们通过多个实例展示了该方法的应用，结果表明在将计算时间减少至蒙特卡洛模拟所需时间以下的同时，Q近似方法能精确逼近关键操作特征。具体而言，在我们的实验中，标准蒙特卡洛近似操作特征需要Q近似方法150至1900倍的计算量才能达到相当水平的精度。