Unbiased estimation in hierarchical models for Clinical trials

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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.