Health Care Manag Sci DOI 10.1007/s10729-014-9277-z

Public health capacity in the provision of health care services Vivian Valdmanis & Arianna DeNicola & Patrick Bernet

Received: 4 November 2013 / Accepted: 16 March 2014 # Springer Science+Business Media New York 2014

Abstract In this paper, we assess the capacity of Florida's public health departments. We achieve this by using bootstrapped data envelopment analysis (DEA) applied to Johansen's definition of capacity utilization. Our purpose in this paper is to measure if there is, theoretically, enough excess capacity available to handle a possible surge in the demand for primary care services especially after the implementation of the Affordable Care Act that includes provisions for expanded public health services. We measure subunit service availability using a comprehensive data source available for all 67 county health departments in the provision of diagnostic care and primary health care. In this research we aim to address two related research questions. First, we structure our analysis so as to fix budgets. This is based on the assumption that State spending on social and health services could be limited, but patient needs are not. Our second research question is that, given the dearth of primary care providers in Florida if budgets are allowed to vary is there enough medical labor to provide care to clients. Using a non-parametric approach, we also apply bootstrapping to the concept of plant capacity which adds to the productivity research. To preview our findings, we report that there exists excess plant capacity for patient treatment and care, but question whether resources may be better suited for more traditional types of public health services. V. Valdmanis (*) Health Policy and Public Health, University of the Sciences, Philadelphia, PA 19104, USA e-mail: [email protected] V. Valdmanis IESEG, Lille, Paris, France A. DeNicola University of Rome, Rome, Italy P. Bernet Florida Atlantic University, Boca Raton, FL, USA

Keywords DEA . Bootstapping . Public health clinics . Capacity utilization

1 Introduction The health care system in the U.S. is composed of private and public sectors, each with varying objective functions. Efficiency analysis has been carried out on the hospital system focusing on a number of factors, including ownership form, teaching status, quality of care, economies of scale, Malmquist productivity measures, specialty hospitals, and plant capacity. Hollingsworth has summarized the literature of productivity and efficiency studies in the health care industry [1–3]. One area that is missing in this vast literature is the efficiency and productivity of public health clinics. “The mission of the U.S. Public Health Service is to protect, promote, and advance the health and safety of the United States. According to the U.S. Public Health Service Commissioned Corps (PHSCC), this mission is achieved through the rapid response to public health needs, leadership, and excellence in public health practices, and the advancement of public health service” Each state in the U.S. has its own public health department which is organized to serve the needs of the state’s population. The organization form may vary, but in general terms each county, locality or territory has a local health department (LHD). LHDs are generally responsible for overall public health initiatives such as epidemiological surveillance and environmental interventions, as well as direct patient care services. In Florida, county health departments provide most of the public health services throughout the state. These services include disease control, primary care and personal health services, environmental initiatives, social/ health education services, and epidemiological studies. We provide a list of all the services provided by the Florida Public Health Departments in Appendix 1. Even though there

V. Valdmanis et al.

are many services provided by public health departments, the aspect we study here is direct medical and health care services. Another reason we focus on the direct care aspect of public health clinic production is that either (a) they may not be needed with the expansion of private health insurance under the Affordable Care Act (ACA) and the possibility that individuals previously treated in the public health clinics enter the private market if they can afford and purchase health care insurance in the market exchange, or (b) these services provided by the public health clinics are needed as substitutes to the private market because of supply or demand issues. If there is a reduced or increased need for direct health services the efficient allocation of these funds would require information on current capacity and from this information it could be inferred that direct health services provided by public health clinics should be expanded of contracted. This could permit decision makers to discern if expanded public health funding from the ACA should be allocated for community and clinical prevention services, public health infrastructure and public health training, [4]. Even though the data set we use is based on one state, Florida, policy changes from any type of health care reform can affect a wider variety of providers in which their budgets are determined by a governmental agency. Although the US healthcare delivery system is generally organized about private organizations and practices, people without insurance cannot easily access care; particularly for non-emergent conditions. Given the high proportion of people living without health insurance, personal health care has become more prominent in the service mix of public health agencies [5], and free clinics [6]. Higher than average rates of uninsured in Florida may be associated with more demand for personal health services from LHDs. In addition to a lack of insurance complicating the access to private health care services, Walls et al. [7] reported that for families who are poor, for African-Americans, for families headed by a woman, and for families with more children often seek care at alternative sites such as LHDs. Also affecting states such as Florida is the number of undocumented workers who are not eligible for insurance programs under the ACA, which has state officials concerned as to where these individuals can receive care [8]. It has also been estimated by Katz [9] that 23 million will remain uninsured under the ACA which may be exacerbated in Florida where the governor and legislature have refused federal money to expand Medicaid, the health insurance program for the poor. Even as the ACA is implemented with individual mandates for private insurance, public health departments will likely still be needed due to the dearth of primary care providers [10]. It has been reported that estimates demonstrate that Florida faces a worsening physician shortage [11] particularly in rural areas and poor inner cities [12]. Federal legislation has been proposed to increase the number of primary care providers (PCPs), a specialty in especially short supply, but

increases in the number of these physicians will not be realized until 2024 [13]. This supply limitation in private physician markets may also impact public health clinics as a viable substitute for diagnostic and personal care. Another aspect of the ACA is the focus on public health providers. Provisions include an expansion in funding for US public health care of 9.2 billion dollars including a creation of new sites for the medically underserved including the expansion of preventive services, primary care, oral care, behavioral services enabling more care at existing sites [14]. Despite the social and public role public health plays in the entirety of the U.S. health care system, no systematic study has been carried out evaluating the productivity of this sector, and since public health clinics are important in providing care to vulnerable populations, it is also relevant to assess system capacity [15]. Studies have been carried out in other countries such as Nigeria [16], China [17], and Spain [18] In the U.S., studies have been conducted on specific aspects of public health, such as gauging the public health impact of health promotion interventions using the REAIM framework [19], effectiveness and efficiency of HIV programs [20], public health diabetes initiatives at one county level public health system [21, 22] and free clinics operating in Virginia [6]. These studies among others in the literature have provided information applying a micro-scale—disease specific focus. Glasgow et al. [19] indicate that the relationships among dimensions of public health are lacking. In this paper, we assess the plant capacity for health care services provided by the 67 county public health clinics operating in Florida. Rather than focus only on DEA efficiency, we incorporate the Johansen’s [23] definition of plant capacity which states: “capacity is the maximum amount that can be produced per unit of time with the existing plant and equipment, provided that the availability of variable factors of production is not restricted”. We use this approach for two reasons. First, even though expenditures expansion for public health services are proposed, we assume that budgets may be fixed, at least for the time being. Alternatively, even if budgets can be expanded, the question still arises: is there enough staff to care for patients? The second purpose of our paper is to analyze the capacity of public health clinics operating in Florida under various conditions to assess which factor is more constricting: expenditures in terms of budget or full time equivalency staff. Reasons for the budget constraint relate how best to allocate public money and the staffing constraint reflects the shortage of medical personal. By assessing productive capacity in these ways, we provide an approach that can be generalized to other settings providing public health care services. We also note that the capacity analysis performed here is not meant to represent a production technology in the assembly line definition. Rather given the best practice efficiency of the public health clinics in our sample we wish to determine if resources are being underutilized so that more

Plant capacity public health services

patients or clients could be treated without additional variable inputs. The policy question we address in this paper is given the production technology is there enough capacity to treat additional patients without relying on increased budgets from the ACA or increased private sector physician markets which may or may not be in practice in a timely fashion. Unfortunately, without access to quality of care data we are unable at this juncture to account for patient care differentials such as patient time with a provider. We state this at the outset to ensure research integrity and to alert readers to this caveat as we present our results. We also expand on the plant capacity measures used in the past by applying the bootstrapping techniques advocated by Kneip et al. [24]. This analysis will enable us to compare our findings with the more straightforward descriptive studies of public health clinics as well as to regress environmental factors on the clinic plant capacity measures to illuminate the county needs based on urban (inner city) and the percent of the population below poverty (poor) the two factors that could require more public health clinic services. In the next section, we provide a description of the plant capacity measure approach and the bootstrapping model we employ. In Section 3 we describe the data and results and conclude the paper with discussion and policy implications in Section 4. 1.1 Model and methods We apply the data envelopment approach (DEA) as described by Färe et al. [25] and the application of Johansen’s definition of plant capacity described by Färe et al. [26]. This approach was first applied to the health care setting in hospitals [27], used by Ferrier et al. [28] to assess possible hospital closure and by Valdmanis et al. [29] in order to estimate hospital capacity and capability of intensive care units. To review, this is a two-step process. In the first step we assess technical efficiency under variable returns to scale in which case all inputs can vary. In the second step, we assess technical efficiency with only the fixed variables included in the production set. Dividing the efficiency measure using the first step by the efficiency measure in the second step; we can derive the plant capacity measure. One of the main benefits of this approach is that we can also control for inefficiency, resulting in a measure that accounts for how much outputs can be efficiently expanded given plant capacity. In this way, we do not account for expansion that would need to increase the use of inefficient inputs. In order to assess efficiency and productivity of public health departments operating in the state of Florida, we use DEA. To briefly review, this method is non-parametric and determines efficiency as the maximum amount of outputs produced given level of inputs. This measure of the output based efficiency is derived using linear programming techniques to find the best practice public health clinics that are in

turn used to define the best practice frontier. The best practice public health departments are those that produce a maximum level of outputs given inputs. Any public health department that is not on the frontier is deemed as inefficient and the measure of inefficiency is the radial distance between the hospital and the best practice frontier. In the case of multiple inputs and outputs, the technical efficiency of each observation (TEn, n=1,…,N) relative to the best-practice technology can be calculated by determining the proportion λ which is the radial distance of the observed inputs used that is technologically required to produce the observation’s given level of outputs: T E n ðx; yÞ ¼ maxfðλ : λyn ∈LðxÞg where TEn(x, y) is the Farrell [30] output-oriented measure of technical efficiency. L(y) denotes the observed level of outputs produced by all the observations in the sample. To define plant capacity given efficiency, we must solve two linear programming problems (given below). In addition to solving for plant capacity, we also apply bootstrapping techniques as described by Simar and Wilson [30] so that we can regress the capacity findings on an array of environmental variables that may be of interest for policy purposes. Following Simar and Wilson [31], we compute a bootstrapped DEA technique for two different models—(1) with all inputs variable and (2) with some inputs fixed. The ratio of the two efficiency scores is our measure of plant capacity. To review, we apply an output oriented DEA with variable return to scale (VRS) by solving θbit ¼ maxθλ θ s:t: xit ≥ X t λ θ yit ≤ Y t λ l 0λ ¼1 λ≥0

i ¼ 1; 2…; n;

i ¼ 1; 2…; n;


Where b θi and D are the Farrell [29] and Shepard’s [32] distance functions, n is the number of DMUs, Yt is a s×n matrix of s outputs, X is a r×n matrix of r inputs, λ represent a n×1 vector of weights which allows to obtain a convex combination between inputs and outputs and 1’ is a vector of ones. In the second step, we measure the maximum amount of outputs that can be produced given the fixed inputs and keeping the variable inputs unconstrained. We accomplish this by solving the second linear programming problem: θbit ¼ maxθλ θ s:t: x f it ≥ X f t λ θ yit ≤ Y t λ i ¼ 1; 2…; n; l 0λ ¼1 λ≥0

i ¼ 1; 2…; n;


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By dividing the solution from Eq. (1) by the solution in Eq. (2) we arrive at our measure of plant capacity which is consistent with Johansen’s definition. However, we do not know if the results from (1) and (2) are real, or merely an artifact. This uncertainty is because the true frontier, according to Simar and Wilson [31] cannot be derived from single point estimates via DEA and therefore bias arises. To overcome this problem and to obtain unbiased results, we use bootstrapping techniques, based on the idea of the Data Generating Program (DGP). These unbiased results can then be estimated using the given sample to generate a set of bootstrap samples from which parameters of interest can be calculated.. In this way, the estimates of the unknown true values of b θ 0 and b θit can be generated through the DGP process via a series of bootstrap estimations. Thus, for the generic unit i, we first compute the bias term: N   X * b BIAS b θi ¼ B−1 θi ; ∀i ¼ 1; …; n; ; ; θ i;b −b



where b θit the bootstrapped technical efficiency and B is is the number of bootstrap replications. So, the bias-corrected DEA efficiency score is given as: B   X c * b b θi ¼ θbi −BIAS b θi ¼ 2b θi −B−1 θi;b



Using this analysis, the results of the bootstrapped DEA are obtained from 2000 iterations using the FEAR software library linked to the statistical package R. It is also noted that the same iterations were used for both the output based model with fixed and variable inputs and the output based model with just the fixed inputs i.e., (1) and (2) so that the ratios are derived using the same bootstrap. Unlike the typical bootstrapped DEA, our plant capacity measures are both greater than and less than 1, therefore, we do not need to use a censored or truncated regression approach in assessing the effect environmental variables may have the public health centers’ capacity to treat patients. Rather, we simply employ ordinary least squares (OLS) since we do not have any a priori hypotheses that an alternative regression technique is preferable. The use of OLS is consistent with McDonald’s [33] contention that if there is no truncation or censoring of the results, then OLS is appropriate in the second stage analysis using DEA findings.

2 Data We use the data provided by the Florida State Department of Health for each county’s public health center. For inputs we

specify expenditures by service category (minus labor costs) as well as full time equivalent (FTE) labor inputs for the treatment and health services. The output is defined as the number of clients served by these sections of the public health center. As for output heterogeneity counts are typically included by some type of clustering such as by payer group, by case mix, by age group et cetera. Therefore, the use of number of individuals by whether they were treated in the health services or in the treatment services which are defined in Table 1. The inputs used in this study are also strictly allocated to the health care and treatment services mitigating the concern of double counting inputs. The descriptive statistics for the inputs and outputs we use for the bootstrapped DEA and plant capacity measures are given in Table 2. We also note a negative and statistically significant correlation (−0.30, p|t|

Intercept Percent urban Percent below poverty level

1.18 −2.0 0.39

8.2 −2.06 0.57

0.001 0.05 0.58

N=67 F~4.50 Pr|t|

Intercept Percent urban Percent below poverty level

0.68 0.56 2.12

2.8 3.26 1.83

0.007 0.002 0.07

N=67 F~5.32 Pr

Public health capacity in the provision of health care services.

In this paper, we assess the capacity of Florida's public health departments. We achieve this by using bootstrapped data envelopment analysis (DEA) ap...
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