Louis T A
Division of Biostatistics, University of Minnesota, School of Public Health, Minneapolis.
Stat Med. 1991 Jun;10(6):811-27; discussion 828-9. doi: 10.1002/sim.4780100604.
A compound sampling model, where a unit-specific parameter is sampled from a prior distribution and then observed are generated by a sampling distribution depending on the parameter, underlies a wide variety of biopharmaceutical data. For example, in a multi-centre clinical trial the true treatment effect varies from centre to centre. Observed treatment effects deviate from these true effects through sampling variation. Knowledge of the prior distribution allows use of Bayesian analysis to compute the posterior distribution of clinic-specific treatment effects (frequently summarized by the posterior mean and variance). More commonly, with the prior not completely specified, observed data can be used to estimate the prior and use it to produce the posterior distribution: an empirical Bayes (or variance component) analysis. In the empirical Bayes model the estimated prior mean gives the typical treatment effect and the estimated prior standard deviation indicates the heterogeneity of treatment effects. In both the Bayes and empirical Bayes approaches, estimated clinic effects are shrunken towards a common value from estimates based on single clinics. This shrinkage produces more efficient estimates. In addition, the compound model helps structure approaches to ranking and selection, provides adjustments for multiplicity, allows estimation of the histogram of clinic-specific effects, and structures incorporation of external information. This paper outlines the empirical Bayes approach. Coverage will include development and comparison of approaches based on parametric priors (for example, a Gaussian prior with unknown mean and variance) and non-parametric priors, discussion of the importance of accounting for uncertainty in the estimated prior, comparison of the output and interpretation of fixed and random effects approaches to estimating population values, estimating histograms, and identification of key considerations in the use and interpretation of empirical Bayes methods.
复合抽样模型是多种生物制药数据的基础，在该模型中，特定单元的参数是从先验分布中抽样得到的，然后根据该参数通过抽样分布生成观测值。例如，在多中心临床试验中，真实的治疗效果因中心而异。观测到的治疗效果会因抽样变异而偏离这些真实效果。先验分布的知识允许使用贝叶斯分析来计算特定临床中心治疗效果的后验分布（通常以后验均值和方差来总结）。更常见的情况是，在先验分布未完全指定时，可以使用观测数据来估计先验分布并用于生成后验分布：即经验贝叶斯（或方差分量）分析。在经验贝叶斯模型中，估计的先验均值给出典型的治疗效果，估计的先验标准差表明治疗效果的异质性。在贝叶斯方法和经验贝叶斯方法中，估计的临床中心效果都会从基于单个临床中心的估计值向一个共同值收缩。这种收缩产生了更有效的估计。此外，复合模型有助于构建排名和选择方法，提供多重性调整，允许估计特定临床中心效果的直方图，并构建外部信息的纳入方式。本文概述了经验贝叶斯方法。内容将包括基于参数先验（例如，均值和方差未知的高斯先验）和非参数先验的方法的开发与比较，讨论在估计先验分布时考虑不确定性的重要性，比较估计总体值的固定效应和随机效应方法的输出及解释、估计直方图以及确定经验贝叶斯方法使用和解释中的关键考虑因素。
