Gould A L
Merck Research Laboratories, West Point, PA 19486, USA.
Stat Med. 1998;17(15-16):1779-97; discussion 1799-800. doi: 10.1002/(sici)1097-0258(19980815/30)17:15/16<1779::aid-sim979>3.0.co;2-7.
Analyses of multi-centre trials must consider the effects of the individual centres and the possibility of non-constancy of treatment effect differences among centres. This usually means an ANOVA with terms for centres, treatments, and centre x treatment interactions in practice, at least in the U.S.A. Empirical and conventional Bayes methods provide attractive alternatives to conventional ANOVAs for analysing and reporting the findings from multi-centre trials and do not require more restrictive assumptions than the ANOVA approach. These approaches require regarding the centre effects as random instead of fixed, a view which often will reasonably describe outcomes of clinical trials in spite of the fact that the individual centres certainly do not comprise a random sample of all possible centres. The components of these approaches are well understood and have been employed in related applications such as meta-analysis. Combining them in a way that makes their application to routine multi-centre trial analysis relatively straightforward does not appear to have been described previously, and is what forms the topic of this paper. The empirical Bayes approach leads to useful graphical displays, including one with the data superimposed on probability contours of the joint distribution of the individual centre means and standard deviations, which provides a handy way to identify possible outliers. Covariates can be incorporated without difficulty. The Bayes approach, implemented with Gibbs sampling, provides a convenient way to construct posterior and predictive distributions for a variety of useful statistics. We compare the result of empirical and conventional Bayes analyses with the result of fixed and mixed model ANOVAs applied to data from a multi-centre trial.
多中心试验的分析必须考虑各个中心的影响以及各中心之间治疗效果差异非恒定的可能性。在实践中，这通常意味着要进行方差分析，至少在美国，要包含中心、治疗方法以及中心与治疗方法交互作用的项。经验贝叶斯方法和传统贝叶斯方法为分析和报告多中心试验结果提供了有吸引力的替代传统方差分析的方法，并且与方差分析方法相比，不需要更严格的假设。这些方法要求将中心效应视为随机效应而非固定效应，尽管各个中心肯定不是所有可能中心的随机样本，但这种观点通常能合理地描述临床试验的结果。这些方法的组成部分已得到充分理解，并已应用于诸如荟萃分析等相关领域。此前似乎尚未描述过以一种使其能相对直接地应用于常规多中心试验分析的方式将它们结合起来，而这正是本文的主题。经验贝叶斯方法能得出有用的图形展示，包括一种将数据叠加在各个中心均值和标准差联合分布的概率等高线上的展示，这提供了一种识别可能异常值的便捷方法。协变量可以毫无困难地纳入。通过吉布斯抽样实现的贝叶斯方法为构建各种有用统计量的后验分布和预测分布提供了一种便捷方式。我们将经验贝叶斯分析和传统贝叶斯分析的结果与应用于多中心试验数据的固定模型方差分析和混合模型方差分析的结果进行比较。
