Power for balanced linear mixed models with complex missing data processes

When designing repeated measures studies, both the amount and the pattern of missing outcome data can affect power. The chance that an observation is missing may vary across measurements, and missingness may be correlated across measurements. For example, in a physiotherapy study of patients with Parkinson’s disease, increasing intermittent dropout over time yielded missing measurements of physical function. In this example, we assume data are missing completely at random, since the chance that a data point was missing appears to be unrelated to either outcomes or covariates. For data missing completely at random, we propose noncentral <i>F</i> power approximations for the Wald test for balanced linear mixed models with Gaussian responses. The power approximations are based on moments of missing data summary statistics. The moments were derived assuming a conditional linear missingness process. The approach provides approximate power for both complete-case analyses, which include independent sampling units where all measurements are present, and observed-case analyses, which include all independent sampling units with at least one measurement. Monte Carlo simulations demonstrate the accuracy of the method in small samples. We illustrate the utility of the method by computing power for proposed replications of the Parkinson’s study.

在设计重复测量研究时，结局数据的缺失数量与缺失模式均会对检验效能产生影响。某一观测值出现缺失的概率可能随测量时点而异，且不同测量时点的缺失情况之间可存在相关性。例如，在一项针对帕金森病患者的物理治疗研究中，随着随访时间推移，间歇性失访人数逐渐增加，导致患者的躯体功能测量值出现缺失。在本示例中，我们假设数据为完全随机缺失（missing completely at random），因为某一数据点出现缺失的概率似乎与结局变量或协变量均无关联。针对完全随机缺失的数据，我们针对服从正态分布响应的平衡线性混合模型，提出了用于沃尔德检验（Wald test）的非中心<i>F</i>检验效能近似方法。该检验效能近似方法基于缺失数据汇总统计量的矩，其推导基于条件线性缺失过程假设。本方法可同时为完整病例分析（complete-case analyses，即仅纳入所有测量值均完整的独立抽样单元（independent sampling units））与观测病例分析（observed-case analyses，即纳入至少存在一项测量值的所有独立抽样单元）提供近似检验效能。蒙特卡洛（Monte Carlo）模拟结果证实了该方法在小样本场景下的准确性。我们通过计算该帕金森病研究拟开展的重复研究的检验效能，展示了本方法的应用价值。