We have previously derived power calculation formulas for cohort studies and clinical trials using the longitudinal mixed effects model with random slopes and intercepts to compare rate of change across groups [Ard & Edland, Power calculations for clinical trials in Alzheimer’s disease. J Alzheim Dis 2011;21:369–77]. We here generalize these power formulas to accommodate 1) missing data due to study subject attrition common to longitudinal studies, 2) unequal sample size across groups, and 3) unequal variance parameters across groups. We demonstrate how these formulas can be used to power a future study even when the design of available pilot study data (i.e., number and interval between longitudinal observations) does not match the design of the planned future study. We demonstrate how differences in variance parameters across groups, typically overlooked in power calculations, can have a dramatic effect on statistical power. This is especially relevant to clinical trials, where changes over time in the treatment arm reflect background variability in progression observed in the placebo control arm plus variability in response to treatment, meaning that power calculations based only on the placebo arm covariance structure may be anticonservative. These more general power formulas are a useful resource for understanding the relative influence of these multiple factors on the efficiency of cohort studies and clinical trials, and for designing future trials under the random slopes and intercepts model.

中文翻译：

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具有随机斜率和截距的混合效应模型的功效公式比较组间变化率


我们之前使用具有随机斜率和截距的纵向混合效应模型导出了队列研究和临床试验的功效计算公式，以比较各组之间的变化率[Ard & Edland，阿尔茨海默病临床试验的功效计算。 J Alzheim Dis 2011；21：369–77]。我们在这里概括这些功效公式以适应 1) 由于纵向研究中常见的研究对象流失而导致的缺失数据，2) 各组之间样本量不等，以及 3) 各组之间方差参数不等。我们展示了如何使用这些公式来支持未来的研究，即使现有试点研究数据的设计（即纵向观察之间的数量和间隔）与计划的未来研究的设计不匹配。我们证明了不同组间方差参数的差异（通常在功效计算中被忽视）如何对统计功效产生巨大影响。这与临床试验尤其相关，其中治疗组随时间的变化反映了安慰剂对照组中观察到的进展的背景变异性以及对治疗反应的变异性，这意味着仅基于安慰剂组协方差结构的功效计算可能是反保守的。这些更通用的功效公式是了解这些多个因素对队列研究和临床试验效率的相对影响以及在随机斜率和截距模型下设计未来试验的有用资源。