In recent years, the biomedical field has witnessed the emergence of novel tools and modelling techniques driven by the rise of the so-called Big Data. In this paper, we address the issue of predictability in biomedical Big Data models of cancer patients, with the aim of determining the extent to which computationally driven predictions can be implemented by medical doctors in their clinical practice. We show that for a specific class of approaches, called k-Nearest Neighbour algorithms, the ability to draw (...) predictive inferences relies on a geometrical, or topological, notion of similarity encoded in a well-defined metric, which determines how close the characteristics of distinct patients are on average. We then discuss the conditions under which the relevant models can yield reliable and trustworthy predictive outcomes. (shrink)