Tiered Service Architecture for Remote Patient Monitoring

TL;DR

The paper addresses how to optimally allocate remote patient monitoring effort between ordinary and intensive tiers under health dynamics and costs. It models the system as a two-tier controlled Markov process with an absorbing state at health $0$ and solves via discounted dynamic programming, deriving conditions under which monitoring should remain always ordinary or switch at a health threshold. In the asymptotic regime of many health states, it proves a threshold structure and provides a closed-form criterion involving $\phi$ and cost ratios; numerical results show the same threshold behavior extends to finite health states and illustrate parameter sensitivities. The framework offers a general methodology for RPM design across conditions and highlights extensions to non-zero switching costs and state-dependent parameters.

Abstract

We develop a remote patient monitoring (RPM) service architecture, which has two tiers of monitoring: ordinary and intensive. The patient's health state improves or worsens in each time period according to certain probabilities, which depend on the monitoring tier. The patient incurs a "loss of quality of life" cost or an "invasiveness" cost, which is higher under intensive monitoring than under ordinary. On the other hand, their health improves faster under intensive monitoring than under ordinary. In each period, the service decides which monitoring tier to use, based on the health of the patient. We investigate the optimal policy for making that choice by formulating the problem using dynamic programming. We first provide analytic conditions for selecting ordinary vs intensive monitoring in the asymptotic regime where the number of health states is large. In the general case, we investigate the optimal policy numerically. We observe a threshold behavior, that is, when the patient's health drops below a certain threshold the service switches them to intensive monitoring, while ordinary monitoring is used during adequately good health states of the patient. The modeling and analysis provides a general framework for managing RPM services for various health conditions with medically/clinically defined system parameters.

Figures (4)

• Figure 1: The Simplified RPM Service. The blue and red arrows represent the possible transitions from state $(o,3)$ for actions $o$ and $i$ respectively. The arrows are labeled with probability of transition and cost incurred.
• Figure 2: Optimal policies (numerically computed) for $H=6$ and two different parameter sets. (a) For $\lambda_o=0.2, \lambda_i=0.3,C_c=20, C_i=1, C_o=0, \gamma=0.9$ the optimal policy is $\pi_o$ (using ordinary monitoring at all health states). (b) For $\lambda_o=0.2, \lambda_i=0.3,C_c=60, C_i=1, C_o=0, \gamma=0.9$ the optimal policy is $\pi_{t,\bar{h}}$ with $\bar{h}=3$, that is, ordinary monitoring is used for $h>3$ and intensive for $h\le3$.
• Figure 3: The optimal (blue) value function $V^*(h)$ (numerically computed) compared to its asymptotic counterpart (red, $V_o(h)$ obtained from Lemma \ref{['lemma:out']}) for various health states $h$ in a system with $H=5, \lambda_o=0.2, \lambda_i=0.4,C_c=5, C_i=1, C_o=0, \gamma=0.9$. Note the close proximity of the two plots.
• Figure 4: Dependence of the (numerically computed) optimal monitoring policy on the (a) cost ratio $C_c/C_i$ (with fixed $\lambda_o=0.2, \lambda_i=0.4, C_i=1, C_o=0, \gamma=0.9$); on (b) $\lambda_i$ (with fixed $\lambda_o=0.2, C_c=50, C_i=1, C_o=0, \gamma=0.9$); and on (c) $\gamma$ (with fixed $\lambda_o=0.2,\lambda_i=0.4, C_c=50, C_i=1, C_o=0$). We set $H=10$ in all cases. Below the vertical orange dashed line, the optimal policy is $\pi_o$ (ordinary monitoring is used for all health states). This line is positioned at the point where the condition of Theorem \ref{['thm:out']} achieves equality. Above this value the policy changes to $\pi_{t,\bar{h}}$ and each threshold $\bar{h}$ is marked in blue.

Theorems & Definitions (10)

• Definition 1
• Lemma 1
• proof
• Theorem 1
• proof
• Theorem 2
• proof
• proof
• proof
• proof