Department of Biostatistics, University of North Carolina, Chapel Hill, NC 27599, U.S.A.
Stat Med. 2011 Aug 15;30(18):2295-309. doi: 10.1002/sim.4263. Epub 2011 May 17.
Owing to the rapid development of biomarkers in clinical trials, joint modeling of longitudinal and survival data has gained its popularity in the recent years because it reduces bias and provides improvements of efficiency in the assessment of treatment effects and other prognostic factors. Although much effort has been put into inferential methods in joint modeling, such as estimation and hypothesis testing, design aspects have not been formally considered. Statistical design, such as sample size and power calculations, is a crucial first step in clinical trials. In this paper, we derive a closed-form sample size formula for estimating the effect of the longitudinal process in joint modeling, and extend Schoenfeld's sample size formula to the joint modeling setting for estimating the overall treatment effect. The sample size formula we develop is quite general, allowing for p-degree polynomial trajectories. The robustness of our model is demonstrated in simulation studies with linear and quadratic trajectories. We discuss the impact of the within-subject variability on power and data collection strategies, such as spacing and frequency of repeated measurements, in order to maximize the power. When the within-subject variability is large, different data collection strategies can influence the power of the study in a significant way. Optimal frequency of repeated measurements also depends on the nature of the trajectory with higher polynomial trajectories and larger measurement error requiring more frequent measurements.
由于临床试验中生物标志物的快速发展，近年来纵向和生存数据的联合建模因其能够减少偏差并提高治疗效果和其他预后因素评估的效率而受到关注。尽管在联合建模的推断方法（如估计和假设检验）方面已经做了很多工作，但设计方面尚未得到正式考虑。统计设计，如样本量和功效计算，是临床试验的关键第一步。在本文中，我们推导出了一种用于估计联合建模中纵向过程效果的闭式样本量公式，并将 Schoenfeld 的样本量公式扩展到联合建模环境中，以估计总体治疗效果。我们开发的样本量公式非常通用，允许 p 度多项式轨迹。线性和二次轨迹的模拟研究证明了我们模型的稳健性。我们讨论了个体内变异性对功效的影响以及数据收集策略，如重复测量的间隔和频率，以最大程度地提高功效。当个体内变异性较大时，不同的数据收集策略会对研究的功效产生重大影响。最佳重复测量频率还取决于轨迹的性质，具有较高多项式轨迹和较大测量误差的轨迹需要更频繁的测量。
