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.

AMS subject classification (MSC2010) 92D20; 92D15, 92C50, 60C05, 62E17

Introduction

Cancers are thought to develop as clonal expansions from a single transformed, ancestral cell. Large-scale sequencing studies have shown that cancer genomes contain somatic mutations occurring in many genes; cf. Greenman et al., Sjöblom et al., Shah et al. Many of these mutations are thought to be passenger mutations (those that are not driving the behaviour of the tumour), and some are pathogenic driver mutations that influence the growth of the tumour. The dynamics of tumour evolution are not well understood, in part because serial observation of tumour growth in humans is not possible.

In an attempt to better understand tumour growth and structure, a number of evolutionary approaches have been described.