A non-homogeneous discrete time Markov model for admission scheduling and resource planning in a cost or capacity constrained healthcare system

Abstract

Healthcare resource planners need to develop policies that ensure optimal allocation of scarce healthcare resources. This goal can be achieved by forecasting daily resource requirements for a given admission policy. If resources are limited, admission should be scheduled according to the resource availability. Such resource availability or demand can change with time. We here model patient flow through the care system as a discrete time Markov chain. In order to have a more realistic representation, a nonhomogeneous model is developed which incorporates timedependent covariates, namely a patient's present age and the present calendar year. The model presented in this paper can be used for admission scheduling, resource requirement forecasting and resource allocation, so as to satisfy the demand or resource constraints or to meet the expansion or contraction plans in a hospital and community based integrated care system. Such a model can be used with both fixed and variable numbers of admissions per day and should prove to be a useful tool for care managers and policy makers who require to make strategic management decisions. We also describe an application of the model to an elderly care system, using a historical dataset from the geriatric department of a London hospital.

Costing hospital resources for stroke patients using phase-type models

“…The phasetype distribution is then used to calculate the length of time the patient spends in each phase of the model. The techniques used to achieve this include, Classification and Regression trees [5], Bayesian Belief Networks [16,27] and phase-type survival trees [14,15]. Figure 3 shows that the conditional component is implemented before the Coxian phase-type distribution and includes some techniques which can be used for the conditional component.…”

“…As each phase, except the last one, requires only 2 parameters for estimation and the last phase requires one parameter estimation, the degrees of freedom in our model are C= 2 K-1 [13,16,25] when there are K phases.…”

An extended phase type survival tree for patient pathway prognostication

“…Although the information about the discharge destination is not available at the time of admission, we can assign the probability to each discharge destination using cohort analysis. Using the resource planning model of [16], this information can be used for estimating bed requirements and cost of care separately for each patient group following homogeneous patient pathways and thus better estimations of resource requirements and cost of care for the whole care unit as it considers the effects of individual cluster (or cohort) of patients, their interactions in the whole care unit and the effect of demographic changes in the patient population.…”

Integrated decision making in healthcare : an operations research and management science perspective

“…The first situation negatively impacts quality of care as it can lead to increased morbidity and mortality [478] and the second negatively impacts both quality of care, as it may block admission of another patient, and efficient resource use [217,439]. Some multi-unit models explicitly take the patient's progress through multiple treatment or recovery stages into account and try to dimension the care units such that patients can in each stage be placed in the care units that are most suitable regarding their physical condition [104,108,123,172,192,199,240,245,246,259,347,439,480].…”

“…Methods: computer simulation [7,19,104,108,112,156,157,206,221,222,238,241,242,243,244,259,292,295,347,371,372,373,375,415,439,478,497,517,519,523,524], heuristics [309], Markov processes [7,68,172,192,199,245,246,247,335], mathematical programming [127,202,241,318,327,375,376], queueing theory [11,29,…”