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First, do no harm? A framework for evaluating new versus reprocessed medical devices

  • Case-Oriented Paper
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Journal of the Operational Research Society

Abstract

More than ever before, health care providers are under intense pressure to control costs. Medical devices represent a significant ‘hard’ cost, with worldwide spending exceeding USD 235 billion. A growing number of health care providers are engaging in the practice of reprocessing—sterilizing and reusing medical devices labelled only for a single use. The ethical and technical dimensions of this practice have received much attention, but its economic aspects remain largely unexamined. This paper presents a Markov decision process framework that a health care provider can use to decide whether to use new or reprocessed devices in a given context. Two cases are studied: completely observable device condition and partially observable device condition. After briefly discussing structural results for the two cases, several examples are presented to illustrate how the model can be applied in practice. Useful results can be computed quickly with minimal data. A key insight of the model is that perfect information regarding the device condition is often not required to make a sound decision.

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Authors and Affiliations

  1. University of Massachusetts Lowell, Lowell, MA, USA

    T Sloan

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  1. T Sloan
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Correspondence to T Sloan.

Appendices

Appendix A. Main technical results

The main technical results of the model are summarized here. For more details and for proofs, please refer to Sloan (2008).

A.1. COMDP: indifference points

Proposition A.1

  • With respect to the repair probability of a used device (p10u), comparing policies A1=[r,n,n,n] and A2=[r,u,n,n] yields the following indifference point:

    When p10u>ρ1*(A1,A2), using a refurbished device is optimal in state 1; when p10u<ρ1*(A1,A2), using a new device is optimal in state 1.

Proposition A.2

  • With respect to the repair probability of a used device (p20u), comparing policies A2=[r,u,n,n] and A3=[r,u,u,n] yields the following indifference point:

    When p20u>ρ2*(A2,A3), using a refurbished device is optimal in state 2; when p20u<ρ2*(A2,A3), using a new device is optimal in state 2.

A.2. COMDP: monotonicity conditions

In this context, one condition is sufficient to ensure the monotonicity of the optimal policy: as the condition of a used device gets worse, the likelihood of returning it to like-new condition is non-increasing. In other words, as long as the repair probability does not increase as the state gets worse, the optimal policy will call for increasingly effective (and costly) maintenance actions. The next proposition formalizes this intuitive result.

Proposition A.3

  • If pi0u⩾pj0u for each j>i, then the optimal policy will be monotone with respect to the process state.

A.3. POMDP: existence of an optimal policy

Proposition A.4

  • A bounded solution to Equation (5) exists, and a unique, stationary policy exists that minimizes the average expected cost. Furthermore, the average cost per unit time is constant; that is, g(α)=g*, independent of the initial belief vector.

The result follows direction from Theorem 4.2 of Fernández-Gaucherand et al (1991).

Appendix B. Data for example problems

Most of the data used for the example problems are reported in Section 4. This section reports all of the remaining data necessary to solve the problem variants discussed. Cost data are based on numbers from Klein (2005) and Landro (2008) unless otherwise noted.

B.1. Post-procedure observation probabilities

Table B1 reports the post-procedure observation probabilities, q jk r, used for in the example problems. By definition, a device cannot be in state 0 (perfect condition) after a procedure is performed, so corresponding observation probabilities are not relevant. In addition, the probability of observing state 0 after a procedure is performed is 0.

Table 2 Information matrices for example problems
Full size table

B.2. Post-reprocessing observation probabilities

For all example problems, a Very High information quality level refers to the following observation probabilities:

where j (row) is the observed state and k (column) is the actual state.

B.3. Parameters for example 1: angioplasty balloon

Costs and rewards: N=515, U=250, C=1 000 000, R=−16 000.

Transition probabilities:

B.4. Parameters for example 2: pulse oximetry sensor

Costs and rewards: N=10, U=6, C=10 000, R=−15.

Transition probabilities:

B.5. Parameters for example 3: orthopaedic blade

Costs and rewards: N=30, U=15, C=100 000, R=−650.

Transition probabilities:

B.6. Parameters for example 4: laparoscopic surgery

Costs and rewards: N=1200, U=250, C=1 000 000, R=−8000.

Transition probabilities:

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Sloan, T. First, do no harm? A framework for evaluating new versus reprocessed medical devices. J Oper Res Soc 61, 191–201 (2010). https://doi.org/10.1057/jors.2008.137

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