Van Lancker Kelly, Betz Joshua F, Rosenblum Michael
Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21205, United States.
Department of Mathematics, Computer Science and Statistics, Ghent University, Ghent 9000, Belgium.
Biometrics. 2025 Jan 7;81(1). doi: 10.1093/biomtc/ujaf020.
Group sequential designs (GSDs), which involve preplanned interim analyses that allow for early stopping for efficacy or futility, are commonly used for ethical and efficiency reasons. Covariate adjustment, which involves appropriately adjusting for prespecified prognostic baseline variables, can improve precision and is generally recommended by regulators. Combining these, that is, using adjusted estimators at interim and final analyses of a GSD, has potential for dual benefits. We address 2 challenges involved in combining these methods. First, adjusted estimators may lack the independent increments structure (asymptotically) that is required to directly apply standard stopping boundaries for GSDs. We address this by applying a linear transformation to the sequence of adjusted estimators across analysis times, resulting in a new sequence of consistent, asymptotically normal estimators with the independent increments property that either improves or leaves precision unchanged. This approach generalizes foundational results on GSDs with semiparametric efficient estimators to any sequence of regular, asymptotically linear estimators. Second, we address the practical problem of handling uncertainty about how much (if any) precision gain will result from covariate adjustment. This is important for trial planning, since an incorrect projection of a covariate's prognostic value risks an over- or underpowered trial. We propose using information-adaptive designs, that is, continuing the trial until the required information level is achieved. This design enables faster, more efficient trials, without sacrificing validity or power.
成组序贯设计（GSDs）出于伦理和效率原因通常被采用，该设计涉及预先计划好的期中分析，允许基于疗效或无效性提前终止试验。协变量调整，即对预先指定的预后基线变量进行适当调整，可以提高精度，并且通常受到监管机构的推荐。将这两者结合起来，即在GSD的期中分析和最终分析中使用调整后的估计量，可能会带来双重益处。我们解决了结合这些方法所涉及的两个挑战。首先，调整后的估计量可能缺乏（渐近地）直接应用GSD标准停止边界所需的独立增量结构。我们通过对跨分析时间的调整后估计量序列应用线性变换来解决这个问题，从而得到一个具有独立增量性质的新的一致、渐近正态估计量序列，该序列要么提高精度，要么保持精度不变。这种方法将关于具有半参数有效估计量的GSD的基础结果推广到任何正则、渐近线性估计量序列。其次，我们解决了处理协变量调整将带来多少（如果有的话）精度增益的不确定性这一实际问题。这对于试验规划很重要，因为对协变量预后价值的错误预测会使试验面临效能过高或过低的风险。我们建议使用信息自适应设计，即持续试验直到达到所需的信息水平。这种设计能够实现更快、更高效的试验，同时不牺牲有效性或效能。
