Department of Epidemiology and Public Health, Yong Loo Lin School of Medicine, National University of Singapore, Singapore.
Int J Radiat Oncol Biol Phys. 2011 Mar 15;79(4):1139-46. doi: 10.1016/j.ijrobp.2009.12.024. Epub 2010 May 14.
To accurately model the cumulative need for radiotherapy in trials designed to delay or avoid irradiation among children with malignant brain tumor, it is crucial to account for competing events and evaluate how each contributes to the timing of irradiation. An appropriate choice of statistical model is also important for adequate determination of sample size.
We describe the statistical modeling of competing events (A, radiotherapy after progression; B, no radiotherapy after progression; and C, elective radiotherapy) using proportional cause-specific and subdistribution hazard functions. The procedures of sample size estimation based on each method are outlined. These are illustrated by use of data comparing children with ependymoma and other malignant brain tumors. The results from these two approaches are compared.
The cause-specific hazard analysis showed a reduction in hazards among infants with ependymoma for all event types, including Event A (adjusted cause-specific hazard ratio, 0.76; 95% confidence interval, 0.45-1.28). Conversely, the subdistribution hazard analysis suggested an increase in hazard for Event A (adjusted subdistribution hazard ratio, 1.35; 95% confidence interval, 0.80-2.30), but the reduction in hazards for Events B and C remained. Analysis based on subdistribution hazard requires a larger sample size than the cause-specific hazard approach.
Notable differences in effect estimates and anticipated sample size were observed between methods when the main event showed a beneficial effect whereas the competing events showed an adverse effect on the cumulative incidence. The subdistribution hazard is the most appropriate for modeling treatment when its effects on both the main and competing events are of interest.
为了准确模拟恶性脑肿瘤患儿延迟或避免放疗的试验中放疗的累积需求，必须考虑竞争事件，并评估每个事件如何影响放疗的时机。选择适当的统计模型对于充分确定样本量也很重要。
我们使用比例病因特异性和亚分布风险函数描述了竞争事件（A，进展后放疗；B，进展后无放疗；和 C，选择性放疗）的统计建模。概述了基于每种方法的样本量估计程序。通过比较室管膜瘤和其他恶性脑肿瘤患儿的数据来说明这些方法。比较了这两种方法的结果。
病因特异性风险分析显示，所有事件类型的婴儿室管膜瘤的风险降低，包括事件 A（调整后的病因特异性风险比，0.76；95%置信区间，0.45-1.28）。相反，亚分布风险分析表明事件 A 的风险增加（调整后的亚分布风险比，1.35；95%置信区间，0.80-2.30），但事件 B 和 C 的风险降低仍然存在。亚分布风险分析需要比病因特异性风险方法更大的样本量。
当主要事件显示有益效果，而竞争事件对累积发生率有不利影响时，两种方法的效应估计和预期样本量存在显著差异。当对主要事件和竞争事件的效果都感兴趣时，亚分布风险最适合建模治疗。
