Statistical Methodology, Novartis Pharmaceuticals Corporation, East Hanover, New Jersey.
Stat Med. 2019 Oct 15;38(23):4656-4669. doi: 10.1002/sim.8325. Epub 2019 Jul 23.
Group sequential designs allow stopping a clinical trial for meeting its efficacy objectives based on interim evaluation of the accumulating data. Various methods to determine group sequential boundaries that control the probability of crossing the boundary at an interim or the final analysis have been proposed. To monitor trials with uncertainty in group sizes at each analysis, error spending functions are often used to derive stopping boundaries. Although flexible, most spending functions are generic increasing functions with parameters that are difficult to interpret. They are often selected arbitrarily, sometimes using trial and error, so that the corresponding boundaries approximate the desired behavior numerically. Lan and DeMets proposed a spending function that approximates in a natural way the O'Brien-Fleming boundary based on the Brownian motion process. We extend this approach to a general family that has an additive boundary for the Brownian motion process. The spending function and the group sequential boundary share a common parameter that regulates how fast the error is spent. Three subfamilies are considered with different additive terms. In the first subfamily, the parameter has an interpretation as the conditional error rate, which is the conditional probability to reject the null hypothesis at the final analysis. This parameter also provides a connection between group sequential and adaptive design methodology. More choices of designs are allowed in the other two subfamilies. Numerical results are provided to illustrate flexibility and interpretability of the proposed procedures. A clinical trial is described to illustrate the utility of conditional error in boundary determination.
群组序贯设计允许根据累积数据的中期评估，为达到疗效目标而停止临床试验。已经提出了各种方法来确定群组序贯边界，以控制在中期或最终分析时越过边界的概率。为了在每次分析时监测组大小不确定的试验，通常使用误差消耗函数来推导停止边界。虽然灵活，但大多数消耗函数都是具有难以解释的参数的通用递增函数。它们通常是任意选择的，有时使用试错法，以便相应的边界在数值上近似所需的行为。Lan 和 DeMets 提出了一种消耗函数，该函数基于布朗运动过程，以自然的方式近似 O'Brien-Fleming 边界。我们将这种方法扩展到一般家族，其中布朗运动过程的边界是可加的。消耗函数和群组序贯边界共享一个共同的参数，该参数调节错误消耗的速度。考虑了三个具有不同加性项的子族。在第一个子族中，参数具有条件错误率的解释，即最终分析时拒绝零假设的条件概率。该参数还提供了群组序贯和自适应设计方法之间的联系。在其他两个子族中允许更多的设计选择。提供了数值结果来说明所提出的程序的灵活性和可解释性。描述了一项临床试验来说明在边界确定中使用条件误差的效用。
