Flexible Modelling in Survival Analysis. Structuring Biological Complexity from the Information Provided by Tumor Markers

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Abstract
The aim of the present article is to introduce and discuss the problem of optimal modelling of the prognostic information provided by putative prognostic variables, possibly measured on a quantitative scale. A number of methodological aspects will be treated, with particular reference to the role of spline functions and artificial neural networks, which will be discussed in the context of the analysis of survival data. The problem of the evaluation and the choice of the optimal statistical models will be examined, with particular attention to the critical aspects related to the definition of prognostic indexes on the basis of the results of the selected models. Clinical examples in breast cancer on the evaluation of the prognostic impact of several tumor markers are provided. This paper is addressed to all researchers who are interested in the evaluation of the prognostic role of tumor markers, therefore we will stress the necessity of integrating the methodologies of biological, clinical and statistical research in the assessment of prognosis.