Optimal staffing in community health centers to improve quality of care

Abstract

Objective

To explore optimal workforce configurations in the production of care quality in community health centers (CHCs), accounting for interactions among occupational categories, as well as contributions to the volume of services.

Data Sources

We linked the Uniform Data System from 2014 to 2016 with Internal Revenue Service nonprofit tax return data. The final database contained 3139 center‐year observations from 1178 CHCs.

Study Design

We estimated a system of two generalized linear production functions, with quality of care and volume of services as outputs, using the average percent of diabetic patients with controlled A1C level and hypertensive patients with controlled blood pressure as quality measures. To explore the substitutability and complementarity between staffing categories, we estimated a revenue function.

Findings

Primary care physicians and advanced practice clinicians achieve similar quality outcomes (3.2 percent and 3.0 percent improvement in chronic condition management per full‐time equivalent (FTE), respectively). Advanced practice clinicians generate less revenue per FTE but are generally less costly to employ.

Conclusion

As quality incentives are further integrated into payment systems, CHCs will need to optimize their workforce configuration to improve quality. Given the relative efficiency of advanced practice clinicians in producing quality, further hiring of these professionals is a cost‐effective investment for CHCs.

What is known on this topic

• Community health centers are undergoing rapid changes in staffing patterns with more advanced practice clinicians joining the workforce.

• Advanced practice clinicians tend to have higher productivity in community health centers where they have critical numbers.

What this study adds

• We successfully estimated the individual contributions to the management of chronic conditions of primary care physicians and advanced practice clinicians.

• We found that at the sample mean, an improvement of roughly 3 percentage points in the chronic condition management measure is attributed to every FTE of primary care physician and advanced practice clinician.

• Using a production function approach, we explicitly showed that primary care physicians and advanced practice clinicians could be substitutes (ie, negative Hicks elasticity of substitution).

1. INTRODUCTION

Community health centers (CHCs) are important safety net providers. In 2016, 1367 federally funded CHCs served 26 million patients or 1 in 12 Americans. ¹ , ² Health centers are a rapidly growing part of the health care system, experiencing a one‐third increase in their patient volumes nationwide from 2010 to 2016. ³ Meanwhile, researchers have documented significant changes in the workforce serving the underserved population, especially those in CHCs, with more advanced practice clinicians (APC, ie, nurse practitioners, physician assistants, certified nurse midwives) joining each year. ⁴ , ⁵ , ⁶ Despite the growing numbers of advanced practice clinicians in the CHC workforce, physicians remain the largest contributor to the total volume of services delivered at CHCs. ⁵

Different workforce configurations may affect the quality of care at CHCs, yet this question has not been sufficiently studied. To date, only a handful of studies have examined the impact of the workforce on the quality of care at CHCs. ⁷ , ⁸ , ⁹ , ¹⁰ , ¹¹ , ¹² Using key process measures, Kurtzman et al ⁷ approached the topic from the workforce perspective and found no impact of the regulatory environment of nurse practitioners on quality process measures in health centers. Similarly, Kurtzman et al ⁸ found no difference between nurse practitioners, physician assistants, and primary care physicians in achieving good outcomes in similar process measures. Given the movement toward value‐based health care, a more robust understanding of how different workforce configurations affect the quality of care in CHCs remains an important area of inquiry. Additionally, previous studies have not accounted for the relationship between the volume of services at CHCs and the quality of care they provide. More generally, there has been a strong interest in the impact of physician and nonphysician providers, and their team configurations on the quality of all primary care. For instance, some studies have found that adding nurses and pharmacists to the primary care team leads to improved patient satisfaction, ¹³ access to behavioral health services, ¹⁴ medication management, ¹⁵ and improved management of major chronic conditions such as diabetes ¹⁶ , ¹⁷ and hypertension. ¹⁸ , ¹⁹ Team‐based care is believed to improve quality of care and relieve physician burnout. ²⁰

However, despite the breadth of research on quality in primary care settings, previous studies have not fully examined the relative productivities of health professions within such teams, or the degree to which quality‐enhancing substitutions can efficiently occur. This leaves an important gap in the literature. As more and more states in the United States expand their scope of practice (SOP) laws aiming at broader treatment autonomy for APCs, ²¹ , ²² interest among health care leaders in gaining a more refined understanding of the potential contributions of APCs in the context of specific workforce and resources configurations is also growing.

In this study, we explored how the configuration and deployment of primary care health professionals affect the production of quality of care in CHCs. We defined the quality of care in CHCs in terms of management of patients’ most common chronic conditions (diabetes and hypertension) and posed the following research questions: (a) how do different staffing and capital configurations contribute to the production of quality of care?; (b) what is the relationship between quality and volume of services? That is, are there trade‐offs, potential economies of scale that result in both higher quality and volume of services delivered in CHCs?; and (c) how are different occupations substitutes or complements in the production process of CHCs? As a framework for answering these questions, we built on prior work on production functions of physician offices and other health care settings and estimated a set of interrelated production and revenue functions as detailed below.

2. METHODS

2.1. Conceptual framework

Economic theory posits that firms deploy labor and capital resources in different proportions to maximize their efficiency and overall performance, using a general model referred to as the production function. ²³ This general approach has been used to look at the maximization of the volume of services in health care facilities, such as hospitals, ²⁴ , ²⁵ , ²⁶ , ²⁷ , ²⁸ , ²⁹ , ³⁰ nursing homes, ³¹ , ³² , ³³ dialysis centers, ³⁴ , ³⁵ mental health clinics, ³⁶ and physician offices. ²⁹ , ³⁷ , ³⁸ , ³⁹ Another body of literature, based on the Grossman model, applies the production function theory to the “production” of health outcomes in households. ⁴⁰ , ⁴¹ , ⁴² , ⁴³ , ⁴⁴ More recently, Grieco and McDevitt ³⁴ developed a model that estimates the production functions of quality and volume jointly for dialysis centers. In this study, we combined these approaches to examine the impact of workforce inputs on both volume and quality in CHCs.

The production function of the volume of services (Y) in CHCs is summarized in Equation (1). In this equation, there are five categories of labor: primary care physicians (PCPs), advanced practice clinicians (nurse practitioners and physician assistants) (APCs), nurses (N), other medical support staff (eg, medical assistants) (S), and administrative and enabling staff (A). Additionally, the equation includes capital (K) and other CHC characteristics and socioeconomic and demographic characteristics of the underlying population ($\omega$) which may affect the quality of care. ⁴⁵ , ⁴⁶

$$Y=Y\left(PCP,APC,N,S,A,K,\omega \right)$$ (1)

The production function of CHC quality (Q) is similarly summarized in Equation (2).

$$Q=Q\left(PCP,APC,N,S,A,K,\omega ,Y\right)$$ (2)

Our conceptual model assumes that volume and quality are sequentially determined. Alternatively, volume and quality can be thought of as jointly determined: CHCs may employ strategies to manage volume that simultaneously impact quality, for example, delaying appointment scheduling or restricting access to new patient visits. In practice, however, federally funded CHCs are obligated to treat any patients regardless of their ability to pay, such that CHCs must meet basic demands in their communities. Quality could then be adjusted by the CHCs, within the constraints of their resources. To verify this assumption, we conducted robustness tests on whether the joint determination of quality and volume is a concern. Our empirical tests demonstrated that simultaneity was not an issue in our data (see our Robustness Checks section in the Results).

2.2. Empirical specification

For estimation purposes, there are many empirical specifications of the production function. Most notably, the Cobb‐Douglas production function is used to address substitutions between capital and labor. ²³ , ³⁸ A particular form that is relatively simple and suitable for estimating marginal productivity of different inputs on different scales and in the presence of multiple interaction terms between pairings of inputs is the Leontief production function (eg, Diewert ³⁷ ). In the context of the health care industry, this specification has been applied to the volume of services in physician offices in a study by Thurston and Libby. ³⁹ Here, we adopted the model to the case of CHCs, and the production functions of quality and volume are given as follows:

$$Y=\sum _{m\in Inputs}{\alpha }_{1,m}{I}_m^{1/2}+\sum _{m,n\in Inputs}{\alpha }_{1,mn}{I}_m^{1/2}{I}_n^{1/2}+{\theta }_{1}X+{\sigma }_1+{\delta }_1+{\epsilon }_1$$ (3)

$$Q=\sum _{m\in Inputs}{\alpha }_{2,m}{I}_m^{1/2}+\sum _{m,n\in Inputs}{\alpha }_{2,mn}{I}_m^{1/2}{I}_n^{1/2}+{\gamma }_{2}Y+{\theta }_{2}X+{\sigma }_2+{\delta }_2+{\epsilon }_2$$ (4)

$$Inputs:\left\{PCP,APC,N,S,A,K\right\}$$

For notational convenience, we suppressed the subscripts for year (t) and CHC (i). $Q$ is the quality of care, which is the main dependent variable of interest. Y is the total number of visits in the CHCs, $I$ is the full‐time equivalents (FTEs) of different medical occupational groups or units of capital expenditures, and $X$ is the other CHC and county‐level characteristics. $\sigma$ is CHC fixed effects, $\delta$ is year fixed effects, and $\epsilon$ is error terms. For a relatively short period, CHC fixed effects can account for the unobserved productivity heterogeneity among CHCs. ⁴⁷ , ⁴⁸ , ⁴⁹ , ⁵⁰ , ⁵¹ , ⁵² , ⁵³ Note that $\alpha$, $\theta$, and $\gamma$ are regression coefficients. Standard errors are clustered at the CHC level.

For Equations (3) and (4), the volume of services serves as a dependent variable in Equation (3) and an independent variable in Equation (4). This method is also known as mediation analysis, where the direct effect (ie, the effect of labor and capital inputs on quality in Equation (3)) and the indirect effect of independent variables (ie, the effect of labor and capital inputs on quality mediated through Equation (4) and volume term in Equation (3)) can be estimated separately. ⁵⁴ , ⁵⁵ , ⁵⁶ Appendix Figure S1 presents a conceptual path diagram for this mediation analysis. As discussed in above, the correct identification of Equations (3) and (4) relies on the exogeneity of volume in the quality equation. We performed statistical tests of endogeneity and found that the null hypothesis of exogeneity of volume in the quality equation cannot be rejected (refer to the section on Robustness Checks for more details).

Note that from Equations (3) and (4), we can only obtain the marginal products for volume and quality separately. However, for policy purposes, we were interested in obtaining the marginal products for the overall activity in the CHC, and, using those to calculate measures of substitutability and complementarity of inputs. The way to combine multiple outcomes in production functions is to estimate the revenue function. Stern ⁵⁷ has shown that the revenue function is an overall summary measure when the firm produces multiple outputs or multiple product attributes (ie, volume and quality). Further, it has been shown that both for‐profit and nonprofit health care facilities seek revenue maximization similarly. ⁵⁸ , ⁵⁹ , ⁶⁰ The revenue function is given as:

$$Ln\left(R\right)=\sum _{m\in Inputs}{\alpha }_{3,m}{I}_m^{1/2}+\sum _{m,n\in Inputs}{\alpha }_{3,mn}{I}_m^{1/2}{I}_n^{1/2}+{\theta }_{3}X+{\sigma }_3+{\delta }_3+{\epsilon }_3$$ (5)

where R is the total revenue and all other terms are similarly defined as in Equations (3) and (4). To accommodate the highly skewed nature of revenue, the revenue equation was specified with a family of gamma distribution and a log link function. Equation (5) was estimated using the correlated‐random effect estimator suggested by Mundlak. ⁶¹ , ⁶² All standard errors were clustered at the CHC level.

In theory, when estimating the revenue function, we need to control for output prices (ie, prices for volume and quality of care). In practice, however, data on market values for $p^y$ and $p^q$ are not readily available for several reasons. First, direct reimbursements for CHC services by public insurers are usually at, or below, the cost of services. Additionally, uninsured patients pay a heavily discounted fee, with supplementary federal grants covering shortfalls. Second, although quality reimbursement in CHCs ostensibly exists, the methodology behind it is still vague, and reporting of the price of quality is even more elusive. Similar to the volume of services, government programs often provide grant support for quality improvement efforts, making the true price of quality difficult to observe. Due to the relatively short study period (2014‐2016), however, it is reasonable to assume that the prices of both quality and volume of services are relatively stable and thus should be absorbed in CHC fixed effects.

In a production or revenue function, substitutions or complementarities are best shown by the Hicks elasticity, defined as (Equation 6):

$$\text{Hicks Elasticity}=\frac{\%\text{Change in Ratio of the Inputs}}{\%\text{Change in the Ratio of marginal products}}$$ (6)

In the case of substitutes (negative elasticity), an increase in the productivity of some input m relative to an input n is in response to a decrease in the amount of input n used in production relative to input m. In the case of complements (positive elasticity), an increase in the productivity of input m relative to input n is in response to an increase in the amount of input n used in production relative to input m. The Hicks elasticity from the revenue function is given by (Equation 7):

$${\text{Hicks Elasticity}}_{\mathit{mn}}=(R\ast R_{\mathit{mn}})/(R_m\ast R_n)\forall m\ne n$$ (7)

where subscripts indicate the partial derivatives with respect to input m and n.

In a production function, the regression coefficients are difficult to interpret owing to the many interaction terms between the variables. Therefore, we opt to present marginal products derived from the coefficients in the Results section whereas the regression coefficients are presented in the Appendix. A marginal product of an input describes the change in the level of some output as a result of a unit change in that input. The marginal products of volume, quality, and revenue can be derived from Equations (3), (4), [Link], respectively. The direct marginal product on quality of care of input factor m is given by Equation (8). The indirect marginal product on quality of care of input factor m is given by the product of the marginal effect on volume of input m (given by Equation (9)) and the coefficient of volume in the quality production function (${\gamma }_2$). The total marginal product on quality of care of input factor m is the sum of the direct marginal product and the indirect marginal product (given by Equation (10)). The marginal revenue product (MRP) is given by Equation (11). Notationally, these can be described as follows:

$$\text{Direct Marginal Product of Input}m\text{on Quality}=0.5\left({\alpha }_{1,mm}+\sum _{n\in Inputs}{\alpha }_{1,mn}{\left(I_m/I_n\right)}^{1/2}\right)$$ (8)

$$\text{Marginal Product of Input}m\text{on Volume}=0.5\left({\alpha }_{2,mm}+\sum _{n\in Inputs}{\alpha }_{2,mn}{\left(I_m/I_n\right)}^{1/2}\right)$$ (9)

$$\text{Total Marginal Product of Input}m\text{on Quality}=\left(\text{Direct Marginal Product of Input}m\text{on Quality}\right)+{\gamma }_2·\left(\text{Marginal Product of Input}m\text{on Volume}\right)$$ (10)

$$\text{Marginal Revenue Product of Input}M=0.5\left({\alpha }_{3,mm}+\sum _{n\in P}{\alpha }_{3,mn}{\left(I_m/I_n\right)}^{1/2}\right)\ast R$$ (11)

2.3. Data sources and sample

The primary data source for this study was the Uniform Data System (UDS) from 2014 to 2016. To avoid confounding the results with Medicaid expansions in the Affordable Care Act, we did not consider the pre‐expansion years. All CHCs that receive Section 330 grants under the Public Health Service Act are required to report annually to the Bureau of Primary Health Care in the UDS. These reports include information on staffing, utilization, quality of care, revenue, and patient characteristics of the CHC. UDS data consisted of 3931 center‐year level observations (1354 unique CHCs) in 50 states and DC.

The other important data source was the Internal Revenue Services (IRS) Form 990 nonprofit tax return form database to obtain information on the capital of CHCs. The tax return database provided rich information on capital costs for nonprofit CHCs. Electronically filed Form 990s were publicly available from the IRS, hosted by Amazon Web Services. Paper filed Form 990s were publicly available from ProPublica Nonprofit Explorer.

There was no existing crosswalk between IRS 990 forms and the UDS data. Therefore, we used an iterative matching process to match the 990 forms with the UDS data, using the address, zip code, city name, and organization name. Of the 3931 center‐year observations, 294 observations (107 CHCs) were deleted, as they were for state and local government, or tribal organization‐operated CHCs, for which there are no matching IRS records. We also deleted another 300 observations (254 CHCs) for which we found no IRS tax return data. Some of these may have been due to filed forms other than the 990 or 990‐EZ. In a side analysis, we compared the means of FTEs and capital inputs between CHCs with and without matched Form 990s. Given that we found statistically significant differences (CHCs that lack tax return information tend to be smaller in size), results from this study should not be extrapolated to CHCs that do not file Form 990s. The analytical dataset consists of 3139 CHC‐year observations and 1178 unique CHCs (see Appendix Table S1 for a detailed comparison).

2.4. Outcome variables

The main dependent variable of interest was the average percentage of patients in a CHC whose conditions of diabetes or hypertension were well controlled. For patients with diabetes, a well‐controlled condition means that the patient's A1C (blood sugar) level is lower than 9 percent for a given year (as defined by the UDS data). For patients with hypertension, a well‐controlled condition means that the patient's blood pressure is less than 140/90 mm Hg. These outcome measures were calculated in UDS as the average of the proportion of patients with diabetes whose A1C level was under control, and the proportion of patients with hypertension whose blood pressure was under control. The final outcome measure used, namely the percentage of diabetic or hypertensive patients under control, had a mean of 63.91 percent during the study period.

The second dependent variable was the total revenue of the CHC, defined as the sum of the patient‐related revenue, and grants and contracts. One important distinction between the previously described quality variable and this dependent variable is that the former pertains to chronic disease management activities, whereas the latter describes the center more generally. Patient‐related revenues are primarily third‐party reimbursements, with Medicaid being the dominant third‐party payer. Grants and contracts were mostly made by federal, state, and local governments, while private foundation grants accounted for a small proportion. As previously stated, many quality improvement projects are supported by government grants as part of the financing structure of CHCs. Therefore, it is reasonable to include patient‐related as well as other types of revenues, when estimating the revenue function. The mean of the total revenue was $15.87 million during the study period.

The total number of CHC visits serves as the outcome variable inhe mean number of visits was 70 366 during the period.

2.5. Independent variables

The key independent variables of interest were health workforce variables and the capital expenditure variable. In the estimation, PCPs and PACs, nurses, other medical support staff, and administrative and enabling staff, as measured by the number of FTEs, were included as labor inputs. We used units of $100 000 for capital expenditure, including rental and depreciation cost of office buildings and equipment.

2.6. Control variables

We obtained county‐level socioeconomic and demographic control variables, including poverty rates, uninsurance rates, area median income, unemployment rates, percentage of female population, percentage of black population, and percentage of Hispanic population from the US Census Bureau. We controlled for a CHC wage index that reflects the overall price of labor used by CHCs in the labor market (Metropolitan area or state rural areas as defined by the Occupational Employment Statistics (OES) from the Bureau of Labor Statistics (BLS)). We further controlled for the disease prevalence of hypertension and diabetes from the Centers for Disease Control and Prevention, and the PCP to population ratio calculated using the Area Health Resource File from the Health Resources and Services Administration. Those control variables are constructed at the county level, and CHCs might serve multiple counties. Thus, a direct county to CHC headquarter match might lead to inaccurate control of population and market characteristics. We resolved this issue by matching CHCs to weighted county covariates. Weights were created using the share of patients in a county visiting a given CHC, calculated from patient origination data in the UDS. We then calculated weighted averages of all county‐level covariates.

We further controlled for CHC level characteristics including behavioral health, dental health, and laboratory FTEs, case‐mix index, the fraction of patients under the poverty line; the fractions of adult, female, White, Black, and Hispanic patients; fractions of uninsured, Medicaid, and Medicare patients; the fraction of patients with English as a second language (ESL); and the number of delivery sites.

3. RESULTS

Table 1 presents the summary statistics of the key variables. There are large variations in staffing levels across CHCs, and CHCs often do not employ staff for all possible occupational categories. Appendix Table S2 presents the full regressions. Our results were stable in specifications with and without control variables on demographic, socioeconomic, and disease prevalence.

TABLE 1.

Characteristics of community health centers in the study sample

	Mean	SD	Min	Median	Max
Products
Pct. Chronic condition managed well	63.914	9.573	29.566	64.576	96.905
Total visits (in 1000s)	70.366	81.792	0.826	42.106	713.316
Revenue (in million $)	15.867	19.098	0.293	9.365	206.900
Labor Inputs (FTEs)
Primary care physicians	6.792	8.561	0.000	4.000	75.690
Advanced practice clinicians	7.727	7.782	0.000	5.320	64.510
Nurses	11.988	16.024	0.000	6.740	167.280
Other medical support staff	20.783	29.504	0.000	10.520	337.930
Administrative and enabling staff	18.482	23.568	0.000	10.550	222.090
Capital input
K (in $100 000)	11.324	13.798	0.000	6.635	98.270

Table 2 presents the marginal effects estimated from the regression results. PCPs (0.260, P = .055) and APCs (0.252, P = .062) had similar direct marginal effects on quality. Both marginal effects were statistically significant. Nurses had a positive, but not statistically significant, direct quality effect (0.076, P = .277), while other medical support staff (−0.022, P = .107) and administrative and enabling staff (−0.64, P = .107) had a negative, but not statistically significant, direct marginal effects on quality. Capital had a positive, but not statistically significant, quality effect (0.033, P = .663). In an alternative specification, results remained the same when we excluded disease prevalence and county‐level control variables. Similarly, PCPs (0.059, P = .099) and APCs (0.047, P = .099) had positive indirect marginal products of quality. Both effects were statistically significant. No other factor had significant indirect quality effects.

TABLE 2.

Marginal products by occupational categories and capital

	Quality			Volume	Revenue
	Direct	Indirect	Total
Primary care physicians	0.260*	0.059*	0.319**	1.736***	326 875***
	(0.134)	(0.036)	(0.132)	(0.194)	(42 376)
Advanced practice clinicians	0.252*	0.047*	0.299**	1.383***	183 915***
	(0.135)	(0.028)	(0.131)	(0.166)	(33 578)
Nurses	0.076	0.009	0.085	0.268***	60 694***
	(0.070)	(0.006)	(0.071)	(0.092)	(16 767)
Other medical support staff	−0.022	0.002	−0.019	0.065	38 580***
	(0.038)	(0.003)	(0.038)	(0.087)	(9462)
Administrative and enabling staff	−0.064	0.004	−0.060	0.116*	53 118***
	(0.040)	(0.003)	(0.040)	(0.059)	(12 175)
Capital inputs	0.033	0.005	0.038	0.159	64 523***
	(0.075)	(0.005)	(0.073)	(0.101)	(21 026)

Marginal products are estimated at sample means from regressions shown in Appendix Table S2.

Standard errors derived from delta method in parentheses.

^*** P < .01, **P < .05, *P < .1

As for the total quality effect, PCPs (0.319, P = .015) and APCs (0.299, P = .022) had similar total quality effects. These effects were statistically significant. The total quality effects of other factors were not statistically significant.

Table 2 also presents the marginal effects of additional FTEs on the volume of services and revenue at the sample mean. PCPs and APCs had different marginal volume and revenue effects. For the volume of services, each additional PCP could perform 1736 visits (P < .001), whereas an additional APC could perform 1382 visits (P < .001), an additional nurse could increase the number of visits by 268 (P = .004), and an additional administrative and enabling staff member could increase the number of visits by 116.

(P = .048). For revenues, each additional PCP could generate $326 875 (P < .001), while an additional APC could generate $183 914 (P < .001), an additional nurse could generate $60 694 (P < .001), an additional other medical support staff member could generate $38 580 (P < .001), and an additional administrative and enabling staff member could generate $53 118 (P < .001).

Table 3 provides a comparison between the average wage and the corresponding mean marginal revenue product of labor (MRPLs) by type of occupation. The third column presents the ratio of wages to MRPLs. Economic theory would predict that optimal results would be obtained when the ratios of wages to MRPLs are equal across different occupations. However, from the table, we observe wide variations in wage/MRPL by occupation. Note that although PCPs are 78 percent more productive than APCs ($326 875/$183 914 = 178 percent), on average, they are 107 percent more expensive ($208 000/$100 538 = 207 percent).

TABLE 3.

Average wage and marginal revenue product of labor (MRPL)

Provider occupation	Average wage a	MRPL	Wage/MRPL
Primary care physicians	$208 000	$326 875	0.64
Advanced practice clinicians	$100 538	$183 915	0.55
Nurses	$57 543	$60 694	0.95
Other medical support staff	$36 122	$38 580	0.94
Administrative and enabling staff	$44 542	$53 118	0.84

^aSource: Occupational Employment Statistics, Bureau of Labor Statistics.

These results suggest that there are potential efficiency gains from hiring more APCs instead of PCPs in the CHC workforce. One PCP is equal to 1.78 APCs in terms of overall productivity measured by revenue; however, given the lower wage of APCs, hiring 1.78 APC instead of 1 PCP would generate 13.96 percent savings in salaries ($100 538*1.78‐$208 000)/$208 000).

To get a more precise measurement of the degree of substitution, we calculated the Hicks elasticity of substitution. Table 4 presents the estimated Hicks elasticity of substitution between pairs of inputs at sample means. Only two pairs were significant, yet in different directions: PCPs and APCs as substitutes (−2.253, P = .011), and PCPs and other medical support staff as complements (2.246, P = .089). At current wages, considering the substitution effects, hiring one additional PCP is equal to hiring 1.77 APCs in terms of the overall productivity measured by revenue; hiring 1.77 APCs would generate 14.5 percent savings in salaries. Although the complementarity and substitutability between other inputs were inconclusive (possibly due to the small sample size), the directions and magnitudes of Hicks elasticity were reasonable. For instance, other medical support staff and capital were potential substitutes, whereas capital was a potential complement of PCP and APC.

TABLE 4.

Degree of substitution or complementarity between input pairs (measured by Hicks elasticity of substitution)

	Primary care physician	Advanced practice clinicians	Nurses	Other medical support staff	Administrative and enabling staff
Advanced practice clinicians	−2.253**
	(0.888)
Nurses	−0.327	0.010
	(1.295)	(1.552)
Other medical support staff	2.246*	−2.791	−1.901
	(1.319)	(2.013)	(2.781)
Administrative and enabling staff	0.775	0.251	−3.903	−3.516
	(1.402)	(1.539)	(2.877)	(2.756)
Capital inputs	2.214	1.990	1.330	−6.415	−0.079
	(1.481)	(2.069)	(3.024)	(4.394)	(2.806)

Standard errors derived from delta method in parentheses.

^*** P < .01, **P < .05, *P < .1.

3.1. Robustness checks

3.1.1. Tests of endogeneity

To test the possibility that the production of quality and volume are endogenous, we performed a Durbin‐Wu‐Hausman test (augmented regression test) using three instrumental variables: county Hispanic population, county Black population, and the interaction term between the county Hispanic and Black populations. The rationale behind using county Hispanic and Black population as instrumental variables is that they are a proxy for the potential demand of services for CHCs; however, these populations will not affect the quality measures of CHCs unless they are patients of the CHCs (ie, those populations can only affect the quality measures through service utilization). This satisfied the relevance and exclusion restrictions for the instrumental variables.

The results are shown in Table 5. The instrumental variables passed the overidentification and under‐identification instrumental variable tests. The rejection of the null hypothesis (P = .016) of the under‐identification test indicates that the instruments were relevant. We were unable to reject the null hypothesis of the overidentification tests, indicating that instrumental variables are likely to satisfy the exclusion restriction (ie, be overidentified). (P = .560). We saved the residual from the first stage regression and used it as a covariate in the second stage regression. The coefficient on the residual term was not statistically significant. Therefore, the null hypothesis of the Durbin‐Wu‐Hausman test (ie, the volume is exogenous of quality) could not be rejected. Since the Durbin‐Wu‐Hausman test might not be robust to clustered standard errors, we also performed Hansen's J test which is implemented in the STATA IVREG2 package. This endogeneity test also could not reject the null hypothesis of exogeneity.

TABLE 5.

Robustness check on endogeneity regarding quality and volume

Dependent variable	First stage	Second stage
	Number of visits	Percentage of chronic conditions managed well
Instrumental variables
County Hispanic population (in 1000)	0.071**
	(0.028)
County Black population (in 1000)	−0.085**
	(0.043)
Hispanic X Black /1000	−0.037*
	(0.019)
Second stage variables
Number of visits		0.403
		(0.279)
First stage residual		−0.362
		(0.280)
Input factors	Yes	Yes
Controls	Yes	Yes
Community health center fixed effects	Yes	Yes
Year fixed effects	Yes	Yes
Endogeneity test (C‐statistic [P‐value])	1.193 [.275]
Under‐identification test (SW F‐statistic [P‐value])	10.290** [.016]
Overidentification test (Hansen J‐statistic [P‐value])	1.160 [.560]
N	3139

Standard errors are clustered at the Community Health Center level.

^*** P < .01, **P < .05, *P < .1.

3.1.2. Alternative specification of revenues

As previously noted, the two largest sources of CHC revenue are Medicaid reimbursements and federal Section 330 grants. Section 330 grants are sometimes earmarked for designated purposes. In practice, community health centers may be able to allocate and shift funds between their various activities. Therefore, we opted to emphasize the results with all revenue sources included. However, we also examined total patient revenues only excluding the grants. As expected, the marginal effects of labor and capital inputs on patient‐related revenue are smaller compared to the model where all revenue sources were included. Moreover, the results were similar for the Hicks elasticity of complementarity. These results are available in Appendix Tables S3 and S4.

4. DISCUSSION

We observed that all inputs, including occupational categories and capital expenditures, are significantly and positively associated with overall CHC quality productivity and revenue maximization. However, our results identify PCPs and APCs as the primary contributors to quality of care. These results are consistent with findings in the CHC workforce literature ⁵ , ⁸ as well as those in the more general literature on the primary care workforce. ⁶³ , ⁶⁴ While administrative and enabling staff contribute significantly to the volume of services, they do not appear to contribute significantly to CHC quality measures.

Further, these findings demonstrate that APCs and PCPs are substitutes in CHC operations. Given that wages of APCs tend to be substantially lower than PCP wages, hiring additional APCs rather than PCPs appears to be a cost‐effective option. The apparent undervaluation of APCs in the labor market during our study period may at least partially explain the surge in APC staffing in CHCs in recent years. ⁵ , ⁶

We also found that PCPs and other medical support staff are complements in CHCs. This complementarity is consistent with traditional physician practice models where the main function of medical assistants is to support PCPs, but not necessarily APCs, in care delivery. ²⁰ , ⁶⁵ , ⁶⁶ , ⁶⁷ Another part of our analysis shows that there is no tradeoff between quality and volume in health centers.

These findings are important to consider in the context of the transition to value‐based payment. We know that few CHCs currently participate in such programs, but that an increase is likely in the future. Currently, outside of certain targeted grants, ⁶⁸ , ⁶⁹ CHC payment systems rarely reward quality directly. ⁷⁰ Notably, Medicaid and Medicare Prospective Payment System (PPS) methods for CHCs are based mostly on historical costs. ⁷⁰ Moreover, while Medicaid CHC Alternative Payment Models allow for payments above the PPS rate in some states, quality is not a reimbursable factor, with the rare exception of Minnesota. ⁷¹ Additionally, the participation of CHCs in Medicaid Accountable Care Organizations (ACOs) remains limited. ⁷² To the extent that ACOs may penalize participating CHCs for lower quality, in practice, penalties are subsidized by state wraparound payments. ⁷¹ An important implication of our results, then, is that incorporating quality incentives into payment systems may have the added benefit of encouraging CHCs to optimize their workforce configuration to improve quality, in this case by deploying more APCs.

While our study did focus directly on SOP laws due to sample size limitations, our results on the contributions of APCs to quality of care are well aligned with the premise behind reforms in SOP laws. However, related studies have shown that SOP reforms alone have not had a significant effective on either increasing patient utilization, ²¹ or the labor supply of APCs. ²² The implication of all of these studies combined may be that such reforms need to be enhanced with tangible incentives.

Certain limitations of the present study should be noted. First, while the main quality measure used, namely chronic disease management, is a reliable indicator of quality, other quality measures could be used in future research. Second, as mentioned above, given the many permutations of SOP laws and our sample size, we opted to not stratify the data by SOP groupings and instead relied on state fixed effects to account for policy differences. When stratified by type of nurse practitioner SOP laws, there were 243 CHCs in full SOP states, 244 CHCs in reduced SOP states, and 662 CHCs in restricted SOP states.

Our analysis suggests that policies that promote APC employment in primary care are likely to be a cost‐effective approach to improving the quality of care in CHCs. The finding that APCs and PCPs achieve similar quality outcomes is well aligned with incentives in current Medicaid and Medicare payment methodologies for CHCs (these provide for equal reimbursement rates for primary care services rendered by APCs and PCPs). Expansion of CHC participation in value‐based programs in the future could further encourage CHCs to hire more APCs. Given the variations in staffing across CHCs, the next step in this line of research may be to use estimates such as ours to identify the most cost‐effective workforce configurations for specific types of CHCs to enhance the quality of care.

Supporting information

Author Matrix

Supplementary Material

Luo Q, Dor A, Pittman P. Optimal staffing in community health centers to improve quality of care. Health Serv Res 2021;56:112–122. 10.1111/1475-6773.13566