Fedorov Valerii, Jones Byron
Research Statistics Unit, GlaxoSmithKline Pharmaceuticals, Philadelphia, PA, USA.
Stat Methods Med Res. 2005 Jun;14(3):205-48. doi: 10.1191/0962280205sm399oa.
The analysis of data collected in multicentre trials offers challenges because the data from the individual centres must be combined in some way to give an overall evaluation of the differences between the treatments in the trial. We propose that the combined response to treatment (CRT) be used as this overall measure. The definition and estimation of the CRT can be derived from either a fixed-effects or a random-effects model. For the latter we introduce the ECRT--the expected combined response to treatment. We describe and compare both types of model and express our preference for the random-effects model. We stress that the number of patients enrolled at a centre is a random variable and show that this source of randomness inflates the variance of the estimated ECRT. Variability in enrolment rates over the centres further inflates this variance. A simple conclusion from our results is that if variability in the treatment and centre effects, in the enrolment time, in the number of patients enrolled at a centre and in the enrolment rates is not properly accounted for, then an underpowered trial may result. Using properties of estimators generated by the random-effects model we propose methods for determining the optimal number of centres and total number of patients to enrol in a trial to minimize a loss function that accounts for centre and patient costs and loss of revenue. We discuss variants of the loss function and corresponding optimization problems for different types of enrolment. We end the paper with brief generalizations of the developed techniques to the case where the response is binary.
多中心试验中收集的数据的分析存在挑战，因为各个中心的数据必须以某种方式合并起来，以便对试验中各治疗方法之间的差异进行总体评估。我们建议将综合治疗反应（CRT）用作这一总体衡量指标。CRT的定义和估计可以从固定效应模型或随机效应模型中推导得出。对于后者，我们引入了ECRT——预期综合治疗反应。我们描述并比较了这两种模型类型，并表明我们更倾向于随机效应模型。我们强调，一个中心招募的患者数量是一个随机变量，并表明这种随机性来源会使估计的ECRT的方差膨胀。各中心招募率的变异性会进一步增大这种方差。我们的结果得出的一个简单结论是，如果治疗和中心效应、招募时间、一个中心招募的患者数量以及招募率的变异性没有得到妥善考虑，那么可能会导致一项效能不足的试验。利用随机效应模型生成的估计量的性质，我们提出了一些方法，用于确定试验中要招募的最佳中心数量和患者总数，以使一个考虑了中心和患者成本以及收入损失的损失函数最小化。我们讨论了损失函数的变体以及针对不同类型招募的相应优化问题。本文最后简要将所开发的技术推广到反应为二元的情况。
