  We address the problem of modeling constrained hospital resources in the
midst of the COVID-19 pandemic in order to inform decision-makers of future
demand and assess the societal value of possible interventions. For broad
applicability, we focus on the common yet challenging scenario where
patient-level data for a region of interest are not available. Instead, given
daily admissions counts, we model aggregated counts of observed resource use,
such as the number of patients in the general ward, in the intensive care unit,
or on a ventilator. In order to explain how individual patient trajectories
produce these counts, we propose an aggregate count explicit-duration hidden
Markov model, nicknamed the ACED-HMM, with an interpretable, compact
parameterization. We develop an Approximate Bayesian Computation approach that
draws samples from the posterior distribution over the model's transition and
duration parameters given aggregate counts from a specific location, thus
adapting the model to a region or individual hospital site of interest. Samples
from this posterior can then be used to produce future forecasts of any counts
of interest. Using data from the United States and the United Kingdom, we show
our mechanistic approach provides competitive probabilistic forecasts for the
future even as the dynamics of the pandemic shift. Furthermore, we show how our
model provides insight about recovery probabilities or length of stay
distributions, and we suggest its potential to answer challenging what-if
questions about the societal value of possible interventions.
