The effect of the Katz parameter on node ranking, with a medical application

Abstract The Medical Extensible Dynamic Probabilistic Risk Assessment Tool (MEDPRAT), developed by NASA, is an event-based risk modeling tool that assesses human health and medical risk during space exploration missions. The Susceptibility Inference Network (SIN), a sub-element of MEDPRAT, is a prototype model informed with data that represents the probabilities of medical conditions progressing from one to another and the expected quality time lost associated with the disease progression for each condition. The work presented in this paper aims to determine which conditions in the SIN have the greatest effect on MEDPRAT-predicted medical risk. Here, we propose to measure this expected quality time lost using a weighted version of Katz centrality and investigate the effect of the $$\alpha$$ α -parameter on the lengths of walks that significantly affect the ranking of nodes. To do this, we introduce a tool to compare different centrality measures in their node rankings. This general tool is of independent interest, as it considers that a relative ranking of two nodes by a centrality measure is unreliable if their scores are within a margin of error. In particular, we find an upper bound on the lengths of the walks that determine the node ranking up to this margin of error. If an application imposes a realistic bound on possible walk lengths, this set of tools may help determine a suitable value for $$\alpha$$ α .