Platform trials are randomized clinical trials that allow simultaneous comparison of multiple interventions, usually against a common control. Arms to test experimental interventions may enter and leave the platform over time. This implies that the number of experimental intervention arms in the trial may change over time. Determining optimal allocation rates to allocate patients to the treatment and control arms in platform trials is challenging because the change in treatment arms implies that also the optimal allocation rates will change when treatments enter or leave the platform. In addition, the optimal allocation depends on the analysis strategy used. In this paper, we derive optimal treatment allocation rates for platform trials with shared controls, assuming that a stratified estimation and testing procedure based on a regression model, is used to adjust for time trends. We consider both, analysis using concurrent controls only as well as analysis methods based on also non-concurrent controls and assume that the total sample size is fixed. The objective function to be minimized is the maximum of the variances of the effect estimators. We show that the optimal solution depends on the entry time of the arms in the trial and, in general, does not correspond to the square root of $k$ allocation rule used in the classical multi-arm trials. We illustrate the optimal allocation and evaluate the power and type 1 error rate compared to trials using one-to-one and square root of $k$ allocations by means of a case study.

翻译：平台试验是一种随机化临床试验，允许同时比较多种干预措施，通常与共同对照组进行比较。用于测试实验性干预措施的治疗组可随时间进入或退出平台，这意味着试验中实验性干预组别的数量会动态变化。确定平台试验中患者分配到治疗组和对照组的最优分配率颇具挑战性，因为治疗组的变化意味着当新治疗组进入或退出平台时，最优分配率也会随之改变。此外，最优分配率还取决于所采用的分析策略。本文假设使用基于回归模型的分层估计与检验程序来调整时间趋势，推导了共享对照平台试验中实验性治疗的最优分配率。我们同时考虑了仅使用同期对照的分析方法以及基于非同期对照的分析方法，并假设总样本量固定。需最小化的目标函数为效应估计量方差的最大值。研究表明，最优解取决于各治疗组进入试验的时间，且通常不适用于经典多臂试验中的$k$平方根分配规则。我们通过案例研究展示了最优分配方案，并评估了其与一对一分配及$k$平方根分配相比的统计功效与第一类错误率。