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Optimal Contract Design for End-of-Life Care Payments

Muyan Jiang, Ying Chen, Xin Chen, Javad Lavaei, Anil Aswani

TL;DR

This work develops a principal-agent framework for end-of-life care payments that blends fee-for-service with pay-for-performance to better align provider actions with patient outcomes and cost containment. It introduces three provider-risk models—free payment, non-negative payment, and risk-averse agent—and derives analytically tractable optimal contracts by converting bilevel formulations into single-level problems. A data-driven demonstration using MIMIC-IV ICP monitoring data for traumatic brain injury illustrates parameter estimation and how the non-negative model can yield a cost-effective contract, while risk aversion can undermine incentives to reduce high-cost interventions for poor responders. The study provides theoretical insights and a practical estimation approach for designing EOL payment schemes with potential implications for reducing wasteful spending while preserving or enhancing patient outcomes.

Abstract

A large fraction of total healthcare expenditure occurs due to end-of-life (EOL) care, which means it is important to study the problem of more carefully incentivizing necessary versus unnecessary EOL care because this has the potential to reduce overall healthcare spending. This paper introduces a principal-agent model that integrates a mixed payment system of fee-for-service and pay-for-performance in order to analyze whether it is possible to better align healthcare provider incentives with patient outcomes and cost-efficiency in EOL care. The primary contributions are to derive optimal contracts for EOL care payments using a principal-agent framework under three separate models for the healthcare provider, where each model considers a different level of risk tolerance for the provider. We derive these optimal contracts by converting the underlying principal-agent models from a bilevel optimization problem into a single-level optimization problem that can be analytically solved. Our results are demonstrated using a simulation where an optimal contract is used to price intracranial pressure monitoring for traumatic brain injuries.

Optimal Contract Design for End-of-Life Care Payments

TL;DR

This work develops a principal-agent framework for end-of-life care payments that blends fee-for-service with pay-for-performance to better align provider actions with patient outcomes and cost containment. It introduces three provider-risk models—free payment, non-negative payment, and risk-averse agent—and derives analytically tractable optimal contracts by converting bilevel formulations into single-level problems. A data-driven demonstration using MIMIC-IV ICP monitoring data for traumatic brain injury illustrates parameter estimation and how the non-negative model can yield a cost-effective contract, while risk aversion can undermine incentives to reduce high-cost interventions for poor responders. The study provides theoretical insights and a practical estimation approach for designing EOL payment schemes with potential implications for reducing wasteful spending while preserving or enhancing patient outcomes.

Abstract

A large fraction of total healthcare expenditure occurs due to end-of-life (EOL) care, which means it is important to study the problem of more carefully incentivizing necessary versus unnecessary EOL care because this has the potential to reduce overall healthcare spending. This paper introduces a principal-agent model that integrates a mixed payment system of fee-for-service and pay-for-performance in order to analyze whether it is possible to better align healthcare provider incentives with patient outcomes and cost-efficiency in EOL care. The primary contributions are to derive optimal contracts for EOL care payments using a principal-agent framework under three separate models for the healthcare provider, where each model considers a different level of risk tolerance for the provider. We derive these optimal contracts by converting the underlying principal-agent models from a bilevel optimization problem into a single-level optimization problem that can be analytically solved. Our results are demonstrated using a simulation where an optimal contract is used to price intracranial pressure monitoring for traumatic brain injuries.
Paper Structure (17 sections, 5 theorems, 24 equations, 2 figures, 1 table, 1 algorithm)

This paper contains 17 sections, 5 theorems, 24 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. Related Work on Payment Models
  3. Payment Models for EOL Care
  4. Contributions and Outline
  5. MODEL FORMULATIONS
  6. Payer's Utility Function
  7. Provider's Utility Function
  8. Principal-Agent Model Formulations
  9. Free Payment Model
  10. Non-Negative Payment Model
  11. Risk-Averse Agent Model
  12. OPTIMAL CONTRACTS
  13. Free Payment Model
  14. Non-Negative Payment Model
  15. Risk-Averse Agent Model
  16. ...and 2 more sections

Key Result

Proposition 1

The binding system of model:norm-basic admits a solution if and only if $(1 - \gamma) \pi_{01} + \gamma \pi_{11} < 1$.

Figures (2)

  • Figure 1: Response Scores Distribution
  • Figure 2: Simluation Comparison with Extreme Policies

Theorems & Definitions (14)

  • Remark 1
  • Proposition 1
  • proof
  • Theorem 1
  • proof
  • Remark 2
  • Remark 3
  • Theorem 2
  • proof
  • Proposition 2
  • ...and 4 more