Multiple Comparisons using Composite Likelihood in Clustered Data

TL;DR

This paper introduces composite likelihood-based methods for multiple hypothesis testing in correlated multidimensional data, offering a computationally feasible alternative to traditional maximum likelihood approaches.

Contribution

It proposes novel composite likelihood procedures for multiple comparisons in correlated data, applicable to Gaussian, probit, and quadratic exponential models, with demonstrated empirical effectiveness.

Findings

Composite likelihood methods control type I error well under intra-cluster correlation.

Ignoring correlation causes erratic error control in multiple testing.

Application to diabetic nephropathy data shows practical utility.

Abstract

We study the problem of multiple hypothesis testing for multidimensional data when inter-correlations are present. The problem of multiple comparisons is common in many applications. When the data is multivariate and correlated, existing multiple comparisons procedures based on maximum likelihood estimation could be prohibitively computationally intensive. We propose to construct multiple comparisons procedures based on composite likelihood statistics. We focus on data arising in three ubiquitous cases: multivariate Gaussian, probit, and quadratic exponential models. To help practitioners assess the quality of our proposed methods, we assess their empirical performance via Monte Carlo simulations. It is shown that composite likelihood based procedures maintain good control of the familywise type I error rate in the presence of intra-cluster correlation, whereas ignoring the correlation leads to erratic performance. Using data arising from a diabetic nephropathy study, we show how our composite likelihood approach makes an otherwise intractable analysis possible.