On synthetic interval data with predetermined subject partitioning, and partial control of the variables' marginal correlation structure

TL;DR

This paper introduces a method for generating synthetic interval data with controlled correlation structures to evaluate clustering models, especially in genomics, and explores the dependence between variables and subject clusters.

Contribution

It presents a novel algorithm for precisely controlling the marginal correlation structure of interval variables in synthetic data, enhancing model assessment in genomic studies.

Findings

The algorithm effectively controls correlation within variable groups.

Synthetic data closely mimics real genomic data.

The approach aids in evaluating clustering performance.

Abstract

A standard approach for assessing the performance of partition models is to create synthetic data sets with a prespecified clustering structure, and assess how well the model reveals this structure. A common format is that subjects are assigned to different clusters, with observations simulated so that subjects within the same cluster have similar profiles, allowing for some variability. In this manuscript, we consider observations from interval variables, taking a finite number of values. Interval data are commonly observed in cohort and Genome Wide Association studies, and our focus is on Single Nucleotide Polymorphisms. Theoretical and empirical results are utilized to explore the dependence structure between the variables, in relation with the clustering structure for the subjects. A novel algorithm is proposed that allows to control the marginal stratified correlation structure of the variables, specifying exact correlation values within groups of variables. Practical examples are shown, and a synthetic dataset is compared to a real one, to demonstrate similarities and differences.