Division of Biostatistics, Department of Population Health, New York University Grossman School of Medicine, New York, NY, USA.
Palliative and Advanced Illness Research (PAIR) Center, Department of Medicine, Perelman School of Medicine, University of Pennsylvania, 304 Blockley Hall, 423 Guardian Drive, Philadelphia, PA, 19104-6021, USA.
Trials. 2020 Nov 9;21(1):917. doi: 10.1186/s13063-020-04801-5.
In a five-arm randomized clinical trial (RCT) with stratified randomization across 54 sites, we encountered low primary outcome event proportions, resulting in multiple sites with zero events either overall or in one or more study arms. In this paper, we systematically evaluated different statistical methods of accounting for center in settings with low outcome event proportions.
We conducted a simulation study and a reanalysis of a completed RCT to compare five popular methods of estimating an odds ratio for multicenter trials with stratified randomization by center: (i) no center adjustment, (ii) random intercept model, (iii) Mantel-Haenszel model, (iv) generalized estimating equation (GEE) with an exchangeable correlation structure, and (v) GEE with small sample correction (GEE-small sample correction). We varied the number of total participants (200, 500, 1000, 5000), number of centers (5, 50, 100), control group outcome percentage (2%, 5%, 10%), true odds ratio (1, > 1), intra-class correlation coefficient (ICC) (0.025, 0.075), and distribution of participants across the centers (balanced, skewed).
Mantel-Haenszel methods generally performed poorly in terms of power and bias and led to the exclusion of participants from the analysis because some centers had no events. Failure to account for center in the analysis generally led to lower power and type I error rates than other methods, particularly with ICC = 0.075. GEE had an inflated type I error rate except in some settings with a large number of centers. GEE-small sample correction maintained the type I error rate at the nominal level but suffered from reduced power and convergence issues in some settings when the number of centers was small. Random intercept models generally performed well in most scenarios, except with a low event rate (i.e., 2% scenario) and small total sample size (n ≤ 500), when all methods had issues.
Random intercept models generally performed best across most scenarios. GEE-small sample correction performed well when the number of centers was large. We do not recommend the use of Mantel-Haenszel, GEE, or models that do not account for center. When the expected event rate is low, we suggest that the statistical analysis plan specify an alternative method in the case of non-convergence of the primary method.
在一项在 54 个地点进行分层随机分组的五臂随机临床试验（RCT）中，我们遇到了低主要结局事件比例的情况，导致多个地点在总体或一个或多个研究组中出现零事件。在本文中，我们系统地评估了在低结局事件比例情况下，考虑中心的不同统计方法。
我们进行了一项模拟研究和一项已完成 RCT 的重新分析，以比较在分层随机分组的多中心试验中估计优势比的五种流行方法：（i）不调整中心，（ii）随机截距模型，（iii）Mantel-Haenszel 模型，（iv）具有可交换相关结构的广义估计方程（GEE），以及（v）具有小样本校正的 GEE（GEE-小样本校正）。我们改变了总参与者人数（200、500、1000、5000）、中心数量（5、50、100）、对照组结局百分比（2%、5%、10%）、真实优势比（1、>1）、组内相关系数（ICC）（0.025、0.075）和参与者在中心的分布（平衡、偏斜）。
Mantel-Haenszel 方法在功效和偏差方面表现不佳，并且由于某些中心没有事件而导致参与者被排除在分析之外。在分析中不考虑中心通常会导致较低的功效和 I 型错误率，尤其是当 ICC=0.075 时。除了在一些中心数量较大的情况下，GEE 具有较高的 I 型错误率。除了在一些中心数量较小的情况下，GEE-小样本校正可以保持 I 型错误率在设定水平，但在功效和收敛问题方面表现不佳。随机截距模型在大多数情况下表现良好，除了在低事件率（即 2%的情况）和总样本量较小（n≤500）的情况下，所有方法都存在问题。
随机截距模型在大多数情况下表现最好。当中心数量较大时，GEE-小样本校正效果较好。我们不建议使用 Mantel-Haenszel、GEE 或不考虑中心的模型。当预期事件率较低时，我们建议在主要方法不收敛的情况下，统计分析计划指定替代方法。
