Unbiased estimation in hierarchical models for Clinical trials

项目背景在这个项目中，我们的目标是开发无偏估计的分层数据，组织在多个层次或树模式结构。这些数据可能来自：聚类试验或多中心随机对照试验亚组分析试验的荟萃分析我们假设所有聚类（或荟萃分析中的研究中心/亚组/试验）都有共同的效应，每个聚类（或等）都有自己的聚类特异性效应。研究表明，对共同效应和聚类特异性效应的估计可能有偏差。偏倚会高估共同效应，导致误导性的虚假显著性结论。对于具有相对小的集群大小的大量集群，问题更加严重。在极端情况下，当每个聚类的大小为2时，对于二元结果，共同效应估计的相对偏差可以高达100%。学生奖学金将包含什么一个合理的解决方案是将聚类特异性效应视为潜在分布的随机变量。然而，分布的选择往往很难验证，并且由此产生的共同效应的推断可能对分布的选择很敏感。或者，可以使用条件/复合似然来通过消除估计中的集群特定效应来获得共同效应的无偏估计。基于一系列真实的临床试验数据，本项目将包括：1）理解和说明分层数据中的偏倚; 2）发展伪似然方法，用于具有不同类型结局的分层数据的无偏估计; 3）调查功效，4）建立随机共同效应和群特异性效应的期望最大化算法5）探索如何扩展现有的Meta分析方法来处理分层试验数据的异质性。

Background to the projectIn this project, we aim to develop unbiased estimation for hierarchical data, organised in multiple levels or a tree pattern structure. Such data can arise from:cluster trials or multisite randomised controlled trialssubgroup analysismeta-analysis of trialsWe assume there is a common effect across all clusters (or sites/subgroups/trials in a meta-analysis) and each cluster (or etc) has its own cluster-specific effect.Research shows that the estimates of the common and cluster-specific effects can be biased. The bias will overestimate the common effect and lead to misleading false significant conclusions. The problem is more severe for large number of clusters with relatively small cluster sizes. In the extreme case when the size of each cluster is 2, the relative bias for the estimate of the common effect can be as large as 100% for binary outcomes , .What the studentship will encompassOne plausible solution is to regard the cluster-specific effect as a random variable from a latent distribution. However, the choice of distribution is often difficult to verify, and the resulting inferences for the common effect may be sensitive to the choice of the distribution .Alternatively, one may use conditional/composite likelihoods to obtain unbiased estimate of the common effect by eliminating cluster-specific effects in estimation. The unbiased estimate of common effect then can be used to estimate unbiased cluster-specific effects using a profile likelihood method.Motivated by data from a series of real clinical trials, this project will involve1) Understanding and illustrating the bias in hierarchical data2) Developing pseudo-likelihood methods for unbiased estimation for hierarchical data with different types of outcomes3) Investigating the power, sample size needed and the impact of intra-cluster correlation on the unbiased estimators4) Developing Expectation-maximization algorithm for random common and cluster-specific effects 5) Exploring to extend existing methods in meta-analysis to handle heterogeneity in hierarchical trial data.