Bayesian clustering with uncertain data
Authors: Nicholls Kath , Kirk Paul D W , Wallace Chris 
Published: December 2022

Clustering is widely used in bioinformatics and many other fields, with applications from exploratory analysis to prediction. Many types of data have associated uncertainty or measurement error, but this is rarely used to inform the clustering.

We present Dirichlet Process Mixtures with Uncertainty (DPMUnc), an extension of a Bayesian nonparametric clustering algorithm which makes use of the uncertainty associated with data points. We show that DPMUnc out-performs existing methods on simulated data. We cluster immune-mediated diseases (IMD) using GWAS summary statistics, which have uncertainty linked with the sample size of the study. DPMUnc separates autoimmune from autoinflammatory diseases and isolates other subgroups such as adult-onset arthritis.

We additionally consider how DPMUnc can be used to cluster gene expression datasets that have been summarised using gene signatures. We first introduce a novel procedure for generating a summary of a gene signature on a dataset different to the one where it was discovered. Since the genes in the gene signature are unlikely to be as strongly correlated as in the original dataset, it is important to quantify the variance of the gene signature for each individual. We summarise three public gene expression datasets containing patients with a range of IMD, using three relevant gene signatures. We find association between disease and the clusters returned by DPMUnc, with clustering structure replicated across the datasets.

The significance of this work is two-fold. Firstly, we demonstrate that when data has associated uncertainty, this uncertainty should be used to inform clustering and we present a method which does this, DPMUnc. Secondly, we present a procedure for using gene signatures in datasets other than where they were originally defined. We show the value of this procedure by summarising gene expression data from patients with immune-mediated diseases using relevant gene signatures, and clustering these patients using DPMUnc.

Author Summary

Identifying groups of items that are similar to each other, a process called clustering, has a range of applications. For example, if patients split into two distinct groups this suggests that a disease may have subtypes which should be treated differently. Real data often has measurement error associated with it, but this error is frequently discarded by clustering methods. We propose a clustering method which makes use of the measurement error and use it to cluster diseases linked to the immune system.

Gene expression datasets measure the activity level of all ~20,000 genes in the human genome. We propose a procedure for summarising gene expression data using gene signatures, lists of genes produced by highly focused studies. For example, a study might list the genes which increase activity after exposure to a particular virus. The genes in the gene signature may not be as tightly correlated in a new dataset, and so our procedure measures the strength of the gene signature in the new dataset, effectively defining measurement error for the summary. We summarise gene expression datasets related to the immune system using relevant gene signatures and find that our method groups patients with the same disease.