Girling Alan J, Watson Samuel I
Institute of Applied Health Research, University of Birmingham, Birmingham, UK.
Stat Med. 2025 Jun;44(13-14):e70100. doi: 10.1002/sim.70100.
Stepped-wedge studies usually entail regular sampling of clusters over time. Yet the precision of the treatment effect estimator can sometimes be improved if the regular sampling scheme is replaced by one with preferential allocation of observations to particular time-epochs within each cluster. We present some exact results for optimizing the allocation for a general experimental layout under a mixed effects model with a time-varying cluster-autocorrelation structure, together with an algorithm for generating optimal allocations. An index of cluster variation is introduced, an increasing function of both the intra-class correlation and the total sample size, which encapsulates the influence of cluster-level variation on the optimal allocation. For any specified layout there is a sampling scheme (the 'best natural allocation') that solves the optimization problem for all values of this index up to a threshold value which depends only on the cluster autocorrelations. Under such a scheme the treatment effect estimator is equal to a simple difference between the means of the treated and control observations. Best natural allocations stand alongside conventional parallel and cross-over designs in giving equal weight to observations from all participants, even under stepped-wedge layouts with irreversible interventions. When applied to a recent study of primary care training programmes in low- and middle- income countries (The REaCH study), the results lead to substantial reductions in total sample size, without loss of precision. For stepped-wedge layouts with block-exchangeable or time-decaying cluster autocorrelations, we present explicit conditions for the optimality of staircase-type sampling schemes, which can arise as best natural allocations in such cases.
阶梯楔形研究通常需要随着时间的推移对群组进行定期抽样。然而，如果将常规抽样方案替换为一种在每个群组内将观察值优先分配到特定时间段的方案，有时可以提高治疗效果估计量的精度。我们给出了一些精确结果，用于在具有随时间变化的群组自相关结构的混合效应模型下优化一般实验布局的分配，同时还给出了一种生成最优分配的算法。引入了一个群组变异指数，它是组内相关系数和总样本量的增函数，该指数概括了群组水平变异对最优分配的影响。对于任何指定的布局，都存在一种抽样方案（“最佳自然分配”），该方案可以解决该指数所有值直至一个仅取决于群组自相关的阈值的优化问题。在这种方案下，治疗效果估计量等于治疗组和对照组观察值均值之间的简单差值。即使在具有不可逆干预的阶梯楔形布局下，最佳自然分配与传统的平行设计和交叉设计一样，对所有参与者的观察值给予同等权重。将其应用于最近一项关于低收入和中等收入国家初级保健培训项目的研究（REaCH研究）时，结果可大幅减少总样本量，且不会损失精度。对于具有块可交换或时间衰减群组自相关的阶梯楔形布局，我们给出了阶梯型抽样方案最优性的明确条件，在这种情况下，阶梯型抽样方案可能会作为最佳自然分配出现。
