Assessing molecular variability in cancer genomes

TL;DR

This paper introduces a statistical framework based on the Ewens Sampling Formula to evaluate molecular variation across different regions of colorectal tumors, aiding understanding of tumor evolution.

Contribution

It develops a multi-sample statistical model and simulation methods for analyzing tumor heterogeneity, along with asymptotic theory to guide interpretation.

Findings

Provides a simulation procedure for reference distributions.

Derives large-sample asymptotics for variation distributions.

Offers theoretical guidelines for data analysis.

Abstract

The dynamics of tumour evolution are not well understood. In this paper we provide a statistical framework for evaluating the molecular variation observed in different parts of a colorectal tumour. A multi-sample version of the Ewens Sampling Formula forms the basis for our modelling of the data, and we provide a simulation procedure for use in obtaining reference distributions for the statistics of interest. We also describe the large-sample asymptotics of the joint distributions of the variation observed in different parts of the tumour. While actual data should be evaluated with reference to the simulation procedure, the asymptotics serve to provide theoretical guidelines, for instance with reference to the choice of possible statistics.