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The Hybrid Hospital: Balancing On-Site and Remote Hospitalization

Noa Zychlinski, Gal Mendelson, Andrew Daw

TL;DR

This work introduces a Hybrid Hospital model that blends on-site and remote hospitalization via telemedicine, anchored by a Brownian-motion health-score dynamics and travel-time effects. The authors derive a tractable long-run cost framework $V(a)$ and characterize when remote care is cost-effective, both with unlimited and limited resources, using explicit threshold policies $a^*$ and their dependence on parameters such as the travel time $T$, initial health $x$, and relative costs. They extend the analysis to multiple patient types, establishing feasibility regions and a Gamma-adjusted equivalence that preserves solution structure under capacity constraints. A dynamic online swapping policy is proposed and demonstrated to improve performance in real-time decision-making, offering practical guidance for resource sharing and call-in policies in hybrid health networks. Overall, the paper provides structural insights and operational policies that challenge the assumption that telemedicine universally benefits rural patients, highlighting the critical roles of travel risk, resource scarcity, and patient heterogeneity in hybrid-health design.

Abstract

Hybrid hospitals offer on-site and remote hospitalization through telemedicine. These new healthcare models require novel operational policies to balance costs, efficiency, and patient well-being. Our study addresses two first-order questions: (i) how to direct patient admission and call-in based on individual characteristics and proximity and (ii) how to determine the optimal allocation of medical resources between these two hospitalization options and among different patient types. We develop a model that uses Brownian Motion to capture the patient's health evolution during remote/on-site hospitalization and during travel. Under cost-minimizing call-in policies, we find that remote hospitalization can be cost-effective for moderately distant patients, as the optimal call-in threshold is non-monotonic in the patient's travel time. Subject to scarce resources, the optimal solution structure becomes equivalent to a simultaneous, identically sized increase of remote and on-site costs under abundant resources. When limited resources must be divided among multiple patient types, the optimal thresholds shift in non-obvious ways as resource availability changes. Finally, we develop a practical and efficient policy that allows for swapping an on-site patient with a remote patient when the latter is called-in and sufficient resources are not available to treat both on-site. Contrary to the widely held view that telemedicine can mitigate rural and non-rural healthcare disparities, our research suggests that on-site care may actually be more cost-effective than remote hospitalization for patients in distant locations, due to (potentially overlooked) risks during patient travel. This finding may be of particular concern in light of the growing number of ``hospital deserts'' amid recent rural hospital closures, as these communities may in fact not be well-served through at-home care.

The Hybrid Hospital: Balancing On-Site and Remote Hospitalization

TL;DR

This work introduces a Hybrid Hospital model that blends on-site and remote hospitalization via telemedicine, anchored by a Brownian-motion health-score dynamics and travel-time effects. The authors derive a tractable long-run cost framework and characterize when remote care is cost-effective, both with unlimited and limited resources, using explicit threshold policies and their dependence on parameters such as the travel time , initial health , and relative costs. They extend the analysis to multiple patient types, establishing feasibility regions and a Gamma-adjusted equivalence that preserves solution structure under capacity constraints. A dynamic online swapping policy is proposed and demonstrated to improve performance in real-time decision-making, offering practical guidance for resource sharing and call-in policies in hybrid health networks. Overall, the paper provides structural insights and operational policies that challenge the assumption that telemedicine universally benefits rural patients, highlighting the critical roles of travel risk, resource scarcity, and patient heterogeneity in hybrid-health design.

Abstract

Hybrid hospitals offer on-site and remote hospitalization through telemedicine. These new healthcare models require novel operational policies to balance costs, efficiency, and patient well-being. Our study addresses two first-order questions: (i) how to direct patient admission and call-in based on individual characteristics and proximity and (ii) how to determine the optimal allocation of medical resources between these two hospitalization options and among different patient types. We develop a model that uses Brownian Motion to capture the patient's health evolution during remote/on-site hospitalization and during travel. Under cost-minimizing call-in policies, we find that remote hospitalization can be cost-effective for moderately distant patients, as the optimal call-in threshold is non-monotonic in the patient's travel time. Subject to scarce resources, the optimal solution structure becomes equivalent to a simultaneous, identically sized increase of remote and on-site costs under abundant resources. When limited resources must be divided among multiple patient types, the optimal thresholds shift in non-obvious ways as resource availability changes. Finally, we develop a practical and efficient policy that allows for swapping an on-site patient with a remote patient when the latter is called-in and sufficient resources are not available to treat both on-site. Contrary to the widely held view that telemedicine can mitigate rural and non-rural healthcare disparities, our research suggests that on-site care may actually be more cost-effective than remote hospitalization for patients in distant locations, due to (potentially overlooked) risks during patient travel. This finding may be of particular concern in light of the growing number of ``hospital deserts'' amid recent rural hospital closures, as these communities may in fact not be well-served through at-home care.
Paper Structure (35 sections, 13 theorems, 78 equations, 9 figures, 1 table)

This paper contains 35 sections, 13 theorems, 78 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Modeling Hybrid Hospitalization and Patient Health Progression
  4. Two-Station Network of Remote and On-Site Hospitalization
  5. Stochastic Dynamics of the Individual Health Score
  6. Cost Structure and Optimization
  7. Preliminary Analyses: Workload and Feasibility
  8. Analyzing the Shape of the Total Workload
  9. Identifying the Feasibility Region
  10. Minimizing the Cost-of-Care for Hybrid Hospitalization
  11. Identifying the Optimal Call-In Structure with Unlimited Resources
  12. Identifying the Optimal Call-In Structure with Limited Resources
  13. Generalizing the Insights to Multiple Patient Types
  14. Characterizing the Feasibility Region in Multiple Patient Dimensions
  15. Scaffolding to the Optimal Multi-Type Solution
  16. ...and 20 more sections

Key Result

Lemma 1

$W_H(a)$ is a strictly decreasing function of $a$; $W_R(a)$ is a strictly increasing function of $a$.

Figures (9)

  • Figure 1: Illustration of the hybrid hospital service network stations.
  • Figure 2: Three illustrative examples of patient's health score evolution.
  • Figure 3: An illustration of the total workload $W_T(a)$.
  • Figure 4: Optimal call-in threshold and call-in probability as a function of travel time for different initial health scores. The parameters are $\theta_H=0.05$, $\theta_R=0.06$, $\theta_T=0.1$, $h_H =2.65$, $h_R =5.1$, $h_T =2$, $\gamma = -32$, $\lambda = \sigma_R= 1$, $\bar{S}=15$.
  • Figure 5: Shifted call-in policy for different $\Gamma$ and $T$. The parameters are $\theta_T=0.1$, $h_R =5.1$, $h_T =2$, $x=8$, $\bar{S}=15$, $\lambda=\sigma_R=1$. In the left plot, $\theta_H=0.05$, $\theta_R=0.06$, $h_H =1$; on right, $\theta_H=0.1$, $\theta_R=0.05$, $h_H =7$.
  • ...and 4 more figures

Theorems & Definitions (15)

  • Remark 1
  • Remark 2
  • Lemma 1
  • Proposition 1
  • Proposition 2
  • Proposition 3: optimal call-in threshold
  • Theorem 1
  • Theorem 2
  • Proposition 4
  • Proposition 5
  • ...and 5 more