A mover-stayer mixture of Markov chain models for the assessment of dedifferentiation and tumour progression in breast cancer

Malignancy grade is a histological measure of attributes related to a breast tumour's aggressive potential. It is not established whether the grade is an inate characteristic which remains unchanged throughout the tumour's development or whether it evolves as the tumour grows. It is likely that a proportion of tumours have the potential to evolve, and so a statistical method was required to assess this hypothesis and, if possible, to estimate the proportion with the potential for evolution. Therefore, a mover-stayer mixture of Markov chain models was developed, with the complication that 'movers' were unobservable because tumours were excised on diagnosis. A quasi-likelihood method was used for estimation. The methods are demonstrated using data from the Swedish twocounty trial of breast-cancer screening.