Manju Md Abu, Candel Math J J M, Berger Martijn P F
Stat Med. 2014 Jul 10;33(15):2538-53. doi: 10.1002/sim.6112.
In this paper, the optimal sample sizes at the cluster and person levels for each of two treatment arms are obtained for cluster randomized trials where the cost-effectiveness of treatments on a continuous scale is studied. The optimal sample sizes maximize the efficiency or power for a given budget or minimize the budget for a given efficiency or power. Optimal sample sizes require information on the intra-cluster correlations (ICCs) for effects and costs, the correlations between costs and effects at individual and cluster levels, the ratio of the variance of effects translated into costs to the variance of the costs (the variance ratio), sampling and measuring costs, and the budget. When planning, a study information on the model parameters usually is not available. To overcome this local optimality problem, the current paper also presents maximin sample sizes. The maximin sample sizes turn out to be rather robust against misspecifying the correlation between costs and effects at the cluster and individual levels but may lose much efficiency when misspecifying the variance ratio. The robustness of the maximin sample sizes against misspecifying the ICCs depends on the variance ratio. The maximin sample sizes are robust under misspecification of the ICC for costs for realistic values of the variance ratio greater than one but not robust under misspecification of the ICC for effects. Finally, we show how to calculate optimal or maximin sample sizes that yield sufficient power for a test on the cost-effectiveness of an intervention.
本文针对研究连续尺度上治疗成本效益的整群随机试验，得出了两个治疗组在整群和个体水平上的最优样本量。最优样本量在给定预算下使效率或功效最大化，或在给定效率或功效下使预算最小化。最优样本量需要效应和成本的组内相关系数（ICC）、个体和整群水平上成本与效应之间的相关性、效应转化为成本的方差与成本方差的比值（方差比）、抽样和测量成本以及预算等信息。在规划时，通常无法获得模型参数的研究信息。为克服这种局部最优性问题，本文还提出了极大极小样本量。结果表明，极大极小样本量对于在整群和个体水平上错误指定成本与效应之间的相关性具有相当的稳健性，但在错误指定方差比时可能会损失很多效率。极大极小样本量对于错误指定ICC的稳健性取决于方差比。对于大于1的实际方差比值，在错误指定成本的ICC时，极大极小样本量是稳健的，但在错误指定效应ICC时则不稳健。最后，我们展示了如何计算最优或极大极小样本量，以确保对干预措施的成本效益进行检验时有足够的功效。
