Innovative Applications of O.R.Optimizing healthcare network design under reference pricing and parameter uncertainty
Introduction
In the United States, healthcare providers can charge very different prices for the same procedure. A study by Hsia, Kothari, Srebotnjak, and Maselli (2012) reports prices ranging from $1529 to $182,955 for an appendectomy, although no clear difference in care quality could account for this range. The Health Care Cost Institute states in a 2014 report: “Rising prices, rather than utilization, were the primary drivers of spending growth for all medical service categories and brand prescriptions” (Health Care Cost Institute, 2014). In the fee-for-service system, patients are not incentivized to choose the best value provider, and providers are not incentivized to be cost-efficient; but as an indirect consequence, costs for payers and premiums for patients are increasing.
One of the emerging tools for payers to protect themselves and patients from this high-price spiral is Reference Pricing (RP). In RP, the payer’s liability is capped to a predefined amount, hereby referred to as “reference price”. Patients are asked to pay the difference between the posted price and the reference price, if there is one. This system has the potential to increase value for all stakeholders: for payers, it can help containing the price rise. It can steer patients towards providers with the highest quality/price ratio. It can shift patients’ attention towards their care quality, and help them make more price-conscious choices. It can also improve cooperation between payers and providers, and allow more visibility for the best performing providers. Yet there exist important, although not insurmountable caveats: RP needs price transparency as well as reliable data regarding providers quality. It is also not applicable to any kind of health procedure: emergency or routine procedures are out of the scope. Implementation programs should be focused on specific procedures with a large and volatile price range. It also has the inconvenience that providers could redistribute the effect of the reimbursement decrease on other procedures with less control.
Another cost-containing measure is for payers to design Tiered Networks (TN), also known as tiered plans or tiered products. Providers are grouped in tiers based on criteria such as price, quality or location. Patients are subject to different co-payments according to the tier of provider they visit. Emanuel et al. (2012) strongly advocate the implementation of tiered plans for payers.
Inspired by a pilot experiment described in the next section, we provide the first decision model for the combination of RP and TN for a healthcare procedure, including the choice of providers subjected to this payment scheme instead of fee-for-service. Our main contribution is to present a methodological framework that captures the impact of quality, volume and out-of-pocket payment on patient usage of specific facilities. The specificities of this framework, namely a choice model where demand depends on binary decision variables, as well as the linearization of the resulting fractional model, are also a novelty for healthcare optimization problems.
The following section contains a literature review for different research streams to which this paper contributes. Section 3 includes a presentation of the model with analytical insights. Section 4 discusses how to address parameter uncertainty and Section 5 consists of numerical experiments. Section 6 concludes the paper.
Section snippets
Reference pricing: brief history and relevant literature
RP is not new to the healthcare industry and quite used in the pharmaceutical sector: it was introduced in Germany in 1989 with the Statutory Health Insurance System, and later in many European and Commonwealth countries (Brekke, Königbauer, & Straume, 2007). An abundant stream of empirical literature exists on the impact of RP on drugs prices and competition. In a broad cross-country study, Danzon and Ketcham (2003) argue that the goals of RP (such as encouraging price competition) are not
Model scope
We consider an ecosystem composed of one payer (the decision-maker) and her network of providers. We isolate a single procedure, characterized by a large price value and volatility. Each provider is characterized, regarding this specific procedure, with his own posted price, volume of patients (or market share), and quality measure. The payer observes this set of parameters and decides which providers to exempt from RP, and which ones to set on an RP contract.
The payer minimizes her expected
Uncertainty on demand parameters: Robust model
The main difficulty for practitioners remains to estimate the choice parameters, even after implementation of a pilot. We develop in this section an optimization model that incorporates uncertainty in the logit parameters of our model. We combine the modeling of Bertsimas and Sim (2004), where an uncertainty budget is allocated to all uncertain parameters, with the results in Schaible (1976).
We start from the deterministic problem (M) and introduce interval uncertainty on (a, d). We assume a
Data simulation and model calibration
For our numerical experiments, we generated independent random vectors for the providers’ prices, volumes, and quality:
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Quality scores qi are drawn from the set {1, 2, 3, 4, 5} with a distribution inspired by the Centers for Medicare and Medicaid Services (2012) (CMS) 5-star rating system. Details on the exact distribution of stars can be found in CMS Five-Star Quality Rating System Technical Users’ Guide (2012).
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Volumes are drawn uniformly from the interval [10, 100]. This range is based on
Conclusion
This paper develops a structured framework for practitioners willing to pursue the experiment of reference pricing for healthcare and wish to incorporate cost and quality criteria in the selection of providers. The optimization model captures the impact of the network selection on patients choices, modeling flows of patients based on their preferences. One important theoretical result, in Theorem 3.5, establishes a threshold policy to determine which providers should be exempted from reference
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