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The investigation of memristors has promoted the development of neuromorphic devices, which play a key role in in-memory computing and brain-inspired computation. In this work, we propose, for the first time, the concept of neuromorphic sensing-and-computing out of several cancer markers by memristive biosensors. Building upon memristive biosensors, each detecting a different cancer biomarker, our design directly converts biomolecular concentrations into spiking signals by employing a unipolar volatile memristor (UVM). These spikes can then serve as the input layer of a spiking neural network (SNN). Unlike conventional single-marker assays, the proposed approach supports multi-marker integration and multi-strategy analysis. Using dual-markers assessment of prostate cancer as an example, we provide preliminary validation of cancer risk prediction, highlighting the potential of neuromorphic sensing-and-computing as a new paradigm for disease diagnosis.