How much is adequate staffing for a nursing home? Forecasting daily service need of its case mix

Staffing adequately in an economical manner is vital to nursing homes (NHs) in the United States. NHs strive for providing resident-centered differentiated service to their changing and diverse residents and service cases. In this paper, we present a novel Bayesian forecasting method to predict acuity category-specific resident volume and caregiver type-specific staff time on a daily basis for NHs. We utilize the Minimum Data Set (MDS) alongside the Resource Utilization Group (RUG) guidelines according to residents' acuity and the Patient Driven Payment Model (PDPM) specifications on recommended staff time in response to their staffing need, to generate two time series on daily NH service need, i.e., resident volume of each acuity group and staff time of each caregiver type in the entire facility, respectively. Given that the two multi-dimensional time-series above are nonstationary with potential correlations between dimensions, we propose prediction models with time-varying latent states to capture the dynamic patterns in the data and incorporate shared information between different categories. Specifically, we introduce a generalized mixture model to predict the discrete-valued resident volume and a generalized linear model to predict the continuous-valued staff time. Further, we propose a unified Bayesian estimation framework that allows convenient sequential updating and embed it in a forecasting procedure with rolling window to better capturing the nonstationarity inherent in the data. We demonstrate the superiority of the proposed model-based Bayesian forecasting method by comparing its performance against benchmark methods, using data from representative NHs.