Unbiased estimation in hierarchical models for Clinical trials

项目背景在这个项目中，我们的目标是开发对分层数据的无偏估计，这些数据组织在多个级别或树模式结构中。这类数据可以来自：集群试验或多点随机对照试验亚组分析试验的集合分析我们假设所有集群(或荟萃分析中的站点/子组/试验)都有共同的效应，每个集群(或其他)都有自己的集群特有效应。研究表明，对共同效应和集群特有效应的估计可能是有偏差的。这种偏差会高估共同效应，导致误导性的虚假显著结论。对于具有相对较小的集群大小的大量集群，该问题更为严重。在每个簇的大小为2的极端情况下，对于二元结果，对共同效应的估计的相对偏差可以高达100%。学生将包括的一个看似合理的解决方案是将簇特定的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，所得到的共同效应的推论可能对分布的选择敏感。或者，人们可以使用条件/复合似然来通过在估计中消除特定于簇的影响来获得对共同效应的无偏估计。在一系列真实临床试验数据的推动下，本项目将涉及：1)理解和说明分级数据中的偏差；2)为不同类型的结果的分级数据开发伪似然估计方法；3)调查功率、所需样本量以及簇内相关性对无偏估计器的影响；4)开发随机共同效应和特定于簇的效应的期望最大化算法；5)探索扩展Meta分析中的现有方法来处理分级试验数据中的异质性。

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.