Mathematically optimised public access defibrillator placement - fairness or accessibility?

Abstract

Background - Mathematical optimisation can be used to maximise public access defibrillator (PAD) accessibility for out-ofhospital cardiac arrests (OHCA). It is unclear whether enforcing 'fairness' (defined as parity of PAD accessibilty) across city wards would impact resulting PAD accessibility compared to an unconstrained approach. Method We included all suspected OHCAs responded to by the Scottish Ambulance Service (SAS) in the cities of Glasgow, Edinburgh, Aberdeen, and Dundee between Jan. 2011 - Sept. 2017, and PADs registered with SAS as of Feb. 2020. We computed the accessibility (defined as within 100 m of OHCA) for existing PADs and developed a mathematical model to select locations for additional PADs under two scenarios: (1) select optimal locations across whole cities, and (2) select optimal locations distributed equally between city wards. Up to 20 additional PAD locations per ward were considered. For both scenarios, we compared PAD accessibility on out-of-sample OHCAs using McNemar's test and fairness across wards using the Nash social welfare function. Results We identified 14,674 OHCA responses and 424 existing PADs. Existing PADs were within range of 1.1% of OHCAs (0.4-2.0% per city). Optimising new PAD locations per city, regardless of wards, increased PAD accessibility to 15.4% of OHCAs (14.9-17.9% per city). Constraining an equal number of PADs in each ward resulted in accessibility loss of 0.2-1.4 percentage points depending on the quantity of PADs placed (P<0.05 for 18 of 20 cases) but improved fairness values by up to 89% for smaller quantities of PADs. Conclusion Enforcing ward-level parity when selecting optimal new PAD locations results in fairer but less accessible PADs for OHCA. This is an Open Access article distributed in accordance with the Creative Commons Attribution Non Commercial (CC BY-NC 4.0) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited and the use is non-commercial. See: http://creativecommons.org/licenses/by-nc/4.0/