The Productivity and Cost-Efficiency of Models for Involving Nurse Practitioners in Primary Care: A Perspective from Queueing Analysis

The Institute of Medicine has identified timely care as one of the six key aims for improving health in the United States (Institute of Medicine 2001). However, shortages of primary care physicians (PCPs) make it difficult for many patients to access care in a timely fashion (Blumenthal 2004; Arvantes 2007; Halsey 2009). With the recent passage of the health care reform bill, more than 30 million Americans may be included in health insurance plans. This could, however, exacerbate the existing imbalance between primary care needs and supply; demand for care could surge due to an increasing number of patients covered by health insurance, and waiting times could rise. In short, the goal of timely care may not be met despite the expansion of health insurance coverage. This article focuses on how to improve timely access to care in a cost-efficient way. We first operationalize “timeliness” by defining patient waiting time as the time elapsed from the point at which a patient makes an appointment to the point at which his or her medical service starts. We call this appointment waiting time (AWT). Long AWTs can potentially increase disease severity, resulting in more intensive treatment and higher costs. They can also constrain access to care. In states like Massachusetts, many clinics have stopped accepting new patients due to long AWTs for existing patients. To a large extent, cutting AWTs is equivalent to improving access to care. To achieve the goal of timely care, there are generally two ways to reduce patient AWTs. One is to reduce the average consultation time that a PCP spends with patients so that more patients can be seen in one day. The other way is simply to hire more PCPs. However, adjusting the average consultation time of PCPs by shortening visits might lead to reduced quality of service and patient dissatisfaction (Dugdale, Epstein, and Pantilat 1999), while hiring more PCPs is complicated by current shortages. Hence, alternative solutions must be sought. Nurse practitioners (NPs) are advanced practice nurses whose scope of practice includes health promotion, disease prevention, health education, and counseling, as well as the diagnosis and management of acute and chronic diseases (American Academy of Nurse Practitioners 2007). NPs can independently manage 80 percent of patients’ primary care needs (Kreitzer, Kligler, and Meeker 2009), and extensive studies show that NPs provide high-quality care (Horrocks, Anderson, and Salisbury 2002; Laurant et al. 2009). Clinical outcomes do not differ for patients who receive services from NPs compared to PCPs. Some studies conclude that care provided by NPs leads to better outcomes; patients appear to be as satisfied—and in some cases, more satisfied—with NP care as compared to PCPs. This literature supports engaging more NPs in primary care with even more autonomy. In fact, this way of expanding the primary care workforce has been recognized as a feasible and effective solution to solve the PCP shortage problem in Canada (Canadian Nurse Association 2006). Nonetheless, we know relatively little about how to organize the work of NPs and PCPs in primary care settings to maximize overall productivity and cost-efficiency. Laurant et al. (2005) indicate that nurse–doctor substitution has the potential to reduce doctor's workload and overall health care costs, but this benefit may not be realized for several reasons. First, nurses are not granted sufficient autonomy and doctors continue to provide the types of care that have been transferred to nurses. Second, nurses may generate new demands where previously there were none, for example, referrals. Third, cost savings due to salary differentials between nurses and doctors may be offset by nurses’ longer consultation times. However, until now, there has not been a general analytic framework for considering these factors. Using a systems modeling approach, we develop simple stylized models to investigate the productivity and cost-efficiencies of different health care delivery models (practice models) where NPs and PCPs work together in a salaried environment. These stylized models enable us to quantitatively examine the impact of those factors considered in Laurant et al. (2005). We study three models: (I) a solo-physician practice model, which serves as our benchmark; (II) a supervision model where NPs manage a certain amount of office visits under the supervision of PCPs and make referrals to PCPs if necessary; and (III) a shared-panel model where NPs work collaboratively with PCPs and provide care to patients with full autonomy. Model II resembles a practice where the NP and the PCP each maintains a panel of patients. Model III represents a group practice where providers work as a team. These models are useful in generating insights to the following questions related to staffing, productivity, and cost-efficiency. Is it always cost-efficient to employ NPs because they are paid less than PCPs? What factors affect the productivity and cost-efficiency of each practice model? And how? How can one improve the productivity and cost-efficiency of a practice model? This article addresses these questions by comparing the productivity and cost-efficiencies of different models across various parameter settings. These settings capture how providers organize their work, and the settings that result in good performance can be used to inform how a practice model can be designed or adjusted to reduce waiting and improve access while keeping costs contained. However, it only makes sense to conduct such comparisons if the care provided in these models is “equivalent” in some sense. We thus consider that two patients have received “equivalent” care if their AWTs are the same. Indeed, setting a requirement on AWTs can be regarded as an assurance for quality of care, because reducing AWTs improves timeliness-to-care and patient attendance rates and hence helps maintain continuity of care (Penchansky and Thomas 1981; Bean and Talaga 1995). Following Green and Savin (2008), we define the productivity of a practice model to be the maximum number of patients that can be accounted for by the model under a given AWT requirement; cost-efficiency is then measured by the corresponding annual cost per patient in that model under the same AWT requirement. Therefore, productivity is a measure of the maximum access to care that can be provided by a particular practice model, while cost-efficiency can be regarded as the minimum average annual cost (or more broadly speaking, medical resources) of serving a patient. The lower this cost, the higher the cost-efficiency. To develop an evaluation framework for the productivity and cost-efficiencies of these models while controlling for AWTs, we use a systems modeling method called queueing theory (Gross and Harris 1985). Queueing theory is an advanced mathematical modeling technique (see Appendix) that can estimate waiting times given customer arrival information and provider service patterns, and hence it is an ideal tool for our analysis. The next section describes how our models are developed using queueing theory.