Inferred attractiveness gravity-based models for estimating realized access at rural hospitals

Operating obstetric units in rural America is financially challenging in part due to low birth volume. Birth volume at a hospital decreases when birthers bypass it to go to a farther hospital. Beyond financial considerations, it is important from a healthcare equity perspective for hospitals to know whether certain subgroups of birthers avoid utilizing the hospital's services. This can better inform resource allocation decisions targeting those subgroups. In this paper, we use a nonlinear programming optimization model, inferred attractiveness gravity-based model (GBM), to estimate realized access to obstetric care at hospitals in Montana. We compare three variations of GBM and benchmark our results to a regression-based conditional logit model. Results indicate that hospital attractiveness varies across the level of obstetric care provided and depends on the subgroup of birthers considered. While all GBMs produced smaller errors for hospitals with higher birth volumes, our novel variant was more accurate for low-volume hospitals. Bootstrapping analyses and resolving the models for population subgroups indicated large variations in hospital attractiveness. Research findings contribute to new knowledge about equity in access to obstetric care, the importance of considering population heterogeneity in GBMs, and the benefit of using hospital demand-based thresholds for GBMs in rural settings.