There has been some recent work in the statistical literature for modelling the relationship between the size of primary cancers and the occurrences of metastases. While nonparametric methods have been proposed for estimation of the tumor 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 nonparametric and semiparametric analysis of modelling tumor size-metastasis data in this article. An equivalence between the models considered by previous authors with survival data structures. Based on this relationship, we develop nonparametric testing procedures and semiparametric regression methodology of modelling the effect of size of tumor on the probability at which metastatic transitions occur in two situations. Asymptotic properties of these estimators are provided. Procedures that achieve the semiparametric information bound are also considered. The proposed methodology is applied to data from a screening study in lung cancer.
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