Modelling tumour biology-progression relationships in screening trials.

There has been some recent work in the statistical literature for modelling the relationship between tumour biology properties and tumour progression in screening trials. While non-parametric methods have been proposed for estimation of the tumour size distribution at which metastatic transition occurs, their asymptotic properties have not been studied. In addition, no testing or regression methods are available so that potential confounders and prognostic factors can be adjusted for. We develop a unified approach to non-parametric and semi-parametric analysis of modelling tumour size-metastasis data in this article. An association between the models considered by previous authors with survival data structures is discussed. Based on this relationship, we develop non-parametric testing procedures and semi-parametric regression methodology of modelling the effect of size of tumour on the probability at which metastatic transitions occur in two situations. Asymptotic properties of these estimators are provided. The proposed methodology is applied to data from a screening study in lung cancer. Copyright 2005 John Wiley & Sons, Ltd.