The early evaluation of prognostic tumour markers is commonly performed by comparing the survival of two groups of patients identified on the basis of a cut-off value. The corresponding hazard ratio (HR) is usually estimated, representing a measure of the relative risk between patients with marker values above and below the cut-off. A posteriori methods identifying an optimal cut-off are appropriate when the functional form of the relation between the marker distribution and patient survival is unknown, but they are prone to an overestimation bias. In the presence of a small sample size, which is typical of rare diseases, the external validation sets are hardly available and internal cross-validation could be unfeasible. We describe a new method to obtain an unbiased estimate of the HR at an optimal cut-off, exploiting the simple relation between the HR and the associated p-value estimated by a random permutation analysis. We validate the method on both simulated data and set of gene expression profiles from two large, publicly available data sets. Furthermore, a reanalysis of a previously published study, which included 134 Stage 4S neuroblastoma patients, allowed for the identification of E2F1 as a new gene with potential oncogenic activity. This finding was confirmed by an immunofluorescence analysis on an independent cohort.
Keywords: Cox model; E2F1; hazard ratio; neuroblastoma; overestimation bias; survival analysis; tumour markers.