Modelling tumour biology–progression relationships in screening trials

Abstract

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.

Proportional Hazards Regression for Cancer Studies

“…We will refer to these as Models I and II. In Ghosh (2006), it is shown that Model I corresponds to treating S as a right‐censored version of Y . Here and in the sequel, only Model I is considered.…”

“…We first use the analysis method outlined in Ghosh (2006). This corresponds to treating the tumor size as a right‐censored random variable and fitting a proportional hazards analysis that ignores the biased sampling and the two‐stage design.…”

“…Such a question requires a regression formulation. Recently, an approach to this problem has been outlined by Ghosh (2006). The regression model utilized there was the additive hazards model (Breslow and Day, 1980; pp.…”

“…The way this was incorporated by Kimmel and Flehinger (1991) is to assume that the missingness mechanism for the distribution of tumor sizes is missing completely at random (Little and Rubin, 2002). This issue is not addressed in the statistical framework of Ghosh (2006). It seems that this might not be a completely reasonable assumption.…”

Modeling the transition of lung cancer from early to advanced stage

“…From data on patients who were detected in advanced stage, one can infer that the size at transition must be smaller than the size at detection. The majority of models that aim to infer primary tumor size at stage transition have been applied to breast cancer [11,12,[17][18][19][20][21][22][23][24], but we have found that they can not be directly applied to lung cancer. When modeling the natural history of breast cancer, a common assumption made is that disease stage does not impact the detection of the disease due to clinical symptoms.…”