Case-mix for assessing primary care value (CPCV)

Abstract

Measuring primary care (PC) performance and designing payment systems that reward value rather than volume have been a great challenge due in large part to lack of reliable risk adjustment mechanisms pertinent to primary care. Using risk scores designed for total resource needs to assess PC performance or set PC payment rates is inadequate because high-cost patients may not have high needs in PC and vice versa. The greatest challenge in developing a risk algorithm for PC is that significant components of PC providers’ workload are unobservable but needed in the modeling. In this study, we sought to overcome this challenge by analyzing 5,172,773 patients in the U.S. Veterans Affairs (VA) healthcare system to identify potential proxies of the unobservable PC workload. By combining the number of PC visits and prescription drug classes, we formed a proxy for the expected PC workload, which enabled us to develop a case-mix algorithm pertaining to primary care. The resultant algorithm with high explanatory power (R² = 0.702) is based on a publicly available patient classification system to account for patient comorbidities and thus can be used by other health systems to compare PC performance, workload, staffing levels, and to set more equitable payment rates.

Keywords

performance management primary care risk adjustment staffing

Introduction

From managed care in the 1980s to the latest value-based care models such as accountable care organizations (ACOs) and patient centered medical homes (PCMHs), primary care (PC) has taken center stage.^1–5 As healthcare expenditure continues to escalate, moving away from the traditional fee-for-service to value-based care has become more imperative. However, measuring PC performance and designing payment systems that reward value rather than volume has been a challenge,^6,7 in large part due to lack of reliable risk adjustment mechanisms.^8–11 To fill this gap, we developed a case-mix algorithm that can be used in benchmarking primary care performance and setting payment rates.

While the literature on case-mix for total disease burden or ambulatory care is abundant,^12–15 risk-adjustment algorithms designed specifically for PC is nonexistent except for one seminal study by Ash and Ellis.¹¹ Using total or ambulatory risk scores for assessing PC performance or setting payment rates is inadequate and could produce biased results because resource-intensive patients (e.g., transplant or cancer patients) with higher risk scores require more inpatient or specialized care while others (e.g., diabetic patients) with relatively lower risk scores need more primary care.

The greatest challenge to developing a case-mix algorithm for PC is that components of the PC providers (PCPs)' workload, devoted to improving quality of care and reducing overall cost, is not observable or not observed. Important services that are known to improve care and reduce cost such as coordination of care for patients seeing multiple specialists are often not done by PCPs and, even if done, they are either underpaid or not paid for at all.¹¹ In fact, we are not aware of any systematic records of PCP workload or effort (patient visit duration, time spent before and after the patient visits). Yet, to develop case-mix algorithms for PC, the workload at the patient level is needed as the dependent variable in the analyses.

To tackle the challenge of unobserved PCP workload, Ash and Ellis proposed a proxy of PC workload by augmenting the PC cost with the costs of specialty care, hospital care, emergency department visits, and prescription drugs.¹¹ The rationale behind this approach is that the unobservable PC workload is proportional to these non-PC costs.

In this study, we extended Ash and Ellis’ pioneering work on three fronts:

Developed a more robust proxy for PC workload by combining the number of PC visits and prescription drug classes, which avoids using arbitrary weights in constructing the dependent variable. Further, costs do not represent PC workload well because they are not the real cost of patient care; rather, they are the amounts paid or claimed, which vary from market to market and from country to country.

Employed a publicly available patient classification system to account for patient comorbidities,^15,16 which allows for potentially broad adoption, while Ash and Ellis used a proprietary system.

Assessed all the relevant statistical models and identified the one that performed best. OLS, as used in Ash and Ellis’ study, is sensitive to the long right-hand tail of the dependent variable and results in negative predicted values.

As in Ash and Ellis’ study, we only focus on the concurrent risk that can be used by hospitals and healthcare systems for risk adjustment in measuring and comparing PCPs’ workload (e.g., panel size and encounters), quality performance, staffing requirements, and setting payment rates.

Methods

Data source and variables

The VA Corporate Data Warehouse (CDW) was our primary data source. We included all 5,172,773 patients who had at least one PC visit in fiscal year (FY) 2017 (see Appendix for details). This study did not need or use any identifiable patient private information and, therefore is exempt from IRB review.

To develop a case-mix algorithm to compare PCP performance and set payment rates, the expected PCP workload is needed as the dependent variable in the analyses. However, few health systems or hospitals know the actual workload of their PCPs at the patient level, let alone the expected workload. To compensate for this data deficiency, Ash and Ellis constructed the dependent variable by augmenting the observed PC cost with other costs (amounts paid to providers):¹¹

\begin{array}{l} Y = AllPrimaryCareService $ + 0.0 6 \\ \times SpecialtyCareRelated $ + 0.0 6 \\ \times HospitalCareRelated $ + 0. 17 \\ \times EDVisitRelated $ \\ + 0. 12 \times PrescriptionDrugRelated $ + $ 65 \end{array}

where the first term “AllPrimaryCareService$” is the observed PC cost (amount paid to providers) for the visits of a patient during a year, the remainder costs are proxies of the unobserved PC workload, and the weights or coefficients are inputs from a group of PCPs. Ash and Ellis used the variable Y, observed plus unobserved, as the dependent variable in developing their risk model.

In this study, from a broader perspective, we considered three proxies for PCP workload: PC cost, RVUs (relative value units), and the number of PC visits.

The VA health system does track and record costs; however, PC cost at the patient level is inaccurate because the cost calculation is based on 30-minute intervals of the appointments rather than the actual time PCPs spend with patients before, during and after the visits. As a result, the cost in the VA system is an inadequate metric to measure PCP workload. It should be noted that payments to PCPs (used as cost in Ash and Ellis’ study¹¹) in non-VA settings are not based on actual time with the patients (inclusive of before, during and after) either.

RVUs, a product of the American Medical Association’s Relative Value Scale Update Committee, are used by CMS to compensate physicians for their services.¹⁷ Although the RVU scheme is a useful tool measuring procedure-oriented workload within each specialty, the current Evaluation and Management coding system and payment structure is inadequate to accurately capture PCP workload during a visit, which can range from a flu shot to managing multiple medical conditions and medications. The use of CPT-based RVUs to measure PCP workload and to set payments has been increasingly been called into question.^17–19

The number of PC visits for each patient recorded in the VA system is accurate (visit date and provider ID can be verified). But the actual duration of the visits, a function of the patient disease severity and comorbidities, is not available. To tackle this problem, we postulate the following at the patient level for the study period of a year:

\begin{array}{l} P C P W o r k l o a d = N u m b e r o f P C V i s i t s \\ \times A v e r a g e V i s i t D u r a t i o n \end{array}

Here we define the visit duration as all the time a PCP spends associated with the visits (e.g., reviewing patient records, coordinating care, phone calls, and text messaging). Since the average visit duration (for a patient during a year) is not observable, we explored all potential proxies that can mirror it. After an extensive literature search and consulting with primary care providers in the field (personal communications), we proposed the following potential options (all variables were based on FY 2017 full year data):

Average visit duration ≈ k × Average cost of the PC visits

Average visit duration ≈ k × Average number of RVUs of the PC visits

Average visit duration ≈ k × Average number of CPTs of the PC visits

Average visit duration ≈ k × Number of diagnoses (identified by ICD10 codes)

Average visit duration ≈ k × (1 + Number of prescription drugs)

Average visit duration ≈ k × (1 + Prescription drug cost)

Average visit duration ≈ k × (1 + Number of prescription drug classes)

Average visit duration ≈ k × (α + β × Number of prescription drug classes)

In the eight options, k is an unknown constant, meaning the average visit duration at the patient level is proportional to the quantity on the righthand side; for example, high PC cost implies more PCP workload. Noteworthy is that k does not need to be estimated because k is same for all the patients and the risk score is relative. In options 7 and 8, the prescription drug classes (315 classes based on their therapeutic properties such as antivirals and antidepressants), developed by the VA Pharmacy Benefits Management Services to manage VA’s prescription drug formulary, are publicly available.²⁰

As noted earlier, costs and RVUs are poor indicators of PCP workload, thus options 1–3 are not viable. Conceptually, option 4 is most appealing; but it could result in a well-known statistical issue called endogeneity bias in regression analysis because diagnoses are also used as independent variables. Given that the number of prescription drugs taken by a patient is a good proxy of comorbidities,^21,22 options 5 and 6 are promising. We added 1 to the number of drugs and cost for a small number of patients had zero drugs and cost, which is a common practice in analyzing data with a small fraction of zero values.²³ Nevertheless, options 5 and 6 can be noisy because a patient could switch medications for the same condition due to side effects, or use one medication that is expensive (e.g. an otherwise healthy patient with hepatitis C) but does not require significant PCP work effort.

Option 7 seems to be able to overcome these two limitations. Theoretically, option 8 is more desirable compared to option 7 because the latter is a special case of the former if both α and β equal 1. However, it is infeasible to estimate α and β based on administrative data. Taken the pros and cons together, we chose option 7 to construct the dependent variable. As a result, we have the independent variable as:

\begin{array}{l} E x p e c t e d P C P W o r k l o a d \\ \approx k \times N u m b e r o f P C V i s i t s \\ \times (1 + N u m b e r o f p r e s c r i p t i o n d r u g c l a s s e s) \end{array}

Note that we added the word “Expected” to Workload. We define “expected workload” as the total time a PCP should spend (not actually spent) with a patient during a year (including the time for face-to-face visits, phone calls, text messaging, and coordination care, etc.) given the same ability of doctoring. The term “expected workload” denotes the work-effort or time expected by value-based health organizations intending to maximize quality and minimize cost rather than maximize revenue.

It is worth emphasizing that, in developing case-mix models, the expected workload is preferred to actual workload because actual workload or time spent with patients, even if observable, may not be optimal in reducing total cost and improve outcomes. Further, the number of prescription drug classes is an ideal proxy for the expected PCP workload: the more drugs a patient takes, the more comorbidities the patient has, the more specialists the patient must see, and the more PCP time the patient needs.

The independent variables in this study are age, gender, and comorbidities represented by the expanded CCS categories. CCS has been widely used to stratify patients for cohort analysis and to control for comorbidities in quality and outcome studies.¹⁶ However, CCS’ predictive power is limited because it groups patients into only 283 categories; for example, all diabetic and prediabetic patients are grouped into CCS49 (diabetes without complications) and CCS50 (diabetes with complications). For higher predictive power, CCS was later expanded to 762 categories.¹⁵ For instance, CCS49 was expanded to CCS49_E109 (type 1 diabetes), CCS49_E119 (type 2 diabetes), CCS49_R730 (impaired or abnormal glucose), and CCS49_R739 (hyperglycemia). The detailed expansion process, as well as the mapping between ICD-10 codes and the expanded categories, are available as Supplemental Digital Content from Medical Care.¹⁵

Statistical analyses

In developing their PC case-mix algorithm, Ellis and Ash used OLS to take the comorbidities into account. However, OLS often produces negative predicted values (e.g., in this study, OLS yielded 21.7% negative predicted values). In addition, OLS also produces overly dispersed risk scores if the dependent variable is not top-coded or truncated from the right. In this study, we ascertained the performance of OLS, log-linear, Box-Cox transformation, gamma (log link), Poisson, generalized Poisson, and negative binomial regressions (treating the dependent variable as count data) by comparing their goodness of fit (GOF) statistics, i.e., R-squared, mean absolute percentage error (MAPE), mean absolute error (MAE), and predictive ratios (see Supplement for more detailed discussions).^12,24–27 The GOF statistics of log-linear and Box-Cox regressions were calculated based on both the transformed and raw data scales with nonparametric smearing retransformations,^28,29 while the remaining models’ were only produced based on the original raw scale data.

To prevent overfitting, we divided the study population randomly into a development sample (50%) and a validation sample (50%).³⁰ We fitted the regression models on the development sample, and then applied estimated coefficients to the validation sample. We produced all the GOF statistics based on the validation sample. The risk score for each patient is calculated as the predicted value divided by the mean predicted value.¹⁵ All the analyses were performed by using SAS 9.4 (see Appendix for more details on statistical modeling).

Results

All 5,172,773 patients who had at least one PC visit in FY 2017 were included in this study. Table 1 reports the descriptives of PC visits and drug classes, the combination of which was used as the dependent variable (proxy of PCP workload) in the regression analyses. Since the results from the development and validation samples were virtually identical, the results in Table 1 were based on the whole study population. As shown, the number of PC visits and drug classes, especially the latter, increased as age rose except for the last age group. Interestingly, female patients (8.5 percent) had a higher number of PC visits but a slightly lower number of drugs. Overall, the average number of PC visits was 3.22 and the number of medications prescribed in different drug classes was 8.58. It is noteworthy that 25 percent of the study population aged between 55 and 75 were prescribed at least 14 medications in different drug classes. Overall, 25 percent of the study population were prescribed at least 12 different drugs in FY 2017.

Table 1.

Average PC visits and drug classes by age and gender.

Age(Mean = 62.76)	Number of patients	Variable	Mean (95% CI) (P < 0.0001)^a	Median	Lower quartile	Upper quartile
Age < 35	404,332	PC Visits	2.43 (2.42–2.43)	2.00	1.00	3.00
Age < 35	404,332	Drug Classes	4.41 (4.39–4.42)	3.00	1.00	6.00
35 <= Age <45	393,457	PC Visits	2.73 (2.73–2.74)	2.00	1.00	3.42
35 <= Age <45	393,457	Drug Classes	6.10 (6.08–6.12)	4.00	2.00	9.00
45 <= Age <55	597,741	PC Visits	3.05 (3.04–3.06)	2.00	1.00	3.83
45 <= Age <55	597,741	Drug Classes	7.81 (7.80–7.83)	6.00	3.00	11.00
55 <= Age <65	961,461	PC Visits	3.56 (3.55–3.56)	2.67	1.42	4.42
55 <= Age <65	961,461	Drug Classes	9.94 (9.92–9.96)	8.00	4.00	14.00
65 <= Age <75	1,718,319	PC Visits	3.44 (3.43–3.44)	2.42	1.42	4.25
65 <= Age <75	1,718,319	Drug Classes	9.92 (9.90–9.93)	8.00	3.00	14.00
Age >=75	1,097,463	PC Visits	3.16 (3.15–3.17)	2.00	1.00	4.00
Age >=75	1,097,463	Drug Classes	8.15 (8.13–8.16)	6.00	2.00	12.00
Gender
Male	4,732,907	PC Visits	3.18 (3.18–3.18)	2.00	1.00	4.00
Male	4,732,907	Drug Classes	8.59 (8.58–8.60)	6.00	2.00	12.00
Female	439,866	PC Visits	3.69 (3.68–3.70)	2.80	1.42	4.77
Female	439,866	Drug Classes	8.46 (8.43–8.48)	6.00	3.00	12.00
Total	5,172,773	PC Visits	3.22 (2.25–3.22)	3.23	1.00	4.00
Total	5,172,773	Drug Classes	8.58 (6.00–8.58)	8.59	2.00	12.00

^aF-test for group means.

In statistical modeling, the 50/50 percent split-sample analyses produced near identical results, indicating no overfitting. As a result, all the model fit statistics reported in this study were based on the validation sample. Table 2 displays the model fit statistics. Overall, the Box-Cox regression outperformed other models with a R² of 0.702 in the transformed scale and 0.586 in the raw scale. The predictive power of OLS (R² = 0.541) was good too, but it yielded 21.7% negative predicted values. While the Poisson model performed reasonably well, the log-linear model in raw scale, the gamma regression with a log link, and the negative binomial model performed poorly based on the results of R² and MAE. The generalized Poisson model performed even worse, thus the results are not reported here.

Table 2.

Model goodness-of-fit statistics.

	OLS	Log-linear		Box-Cox		Gamma(log link)	Poisson	Negative binomial
	Raw scale	Transformedscale	Rawscale	Transformedscale	Raw scale	Raw scale	Raw scale
R-squared	0.541	0.635	0.083	0.702	0.586	N/A	N/A	N/A
Adj. R-squared	0.541	0.635	0.083	0.702	0.586	N/A	N/A	N/A
MAPE	2.620	0.343	6.648	0.646	1.598	6.732	2.253	1.576
MAE	28.05	0.724	42.73	2.682	23.30	43.27	25.86	55.38

To examine if Medicare use leads to biased estimates, we produced the predictive ratios (mean predicted risk divided by mean observed risk) by age groups (the age group 65–75 was split into two subsets due to the large number of patients) as reported in Table 3. Interestingly, Poisson model performed better than other models (predictive ratio close to 1 indicates good fit). It is also informative to note that none of the models’ predictive ratios significantly changed at age 65 when patients become eligible for Medicare.

Table 3.

Predictive ratios (predicted/observed) by age group.

		OLS	Log-linear		Box-Cox		Gamma(log-link)	Poisson	Negative binomial
Estimated risk level	Number of patients	Raw scale	Transformed scale	Raw scale	Transformed scale	Raw scale	Raw scale	Raw scale	Raw scale
Age < 35	202,212	0.86	1.00	2.39	1.00	1.12	1.27	1.01	1.21
35 <= Age <45	196,684	0.89	1.00	1.60	1.00	1.06	1.47	0.99	1.39
45 <= Age <55	298,563	0.97	1.00	1.16	1.00	1.01	1.78	1.00	1.66
55 <= Age <65	480,276	1.02	1.00	0.84	1.00	0.99	2.11	1.00	1.96
65 <= Age <70	458,373	1.03	0.99	0.85	0.99	0.99	2.02	0.99	1.89
70 <= Age <75	400,751	1.02	1.01	0.87	1.01	1.00	2.08	1.01	1.94
Age >=75	549,527	0.99	1.00	1.03	1.00	0.99	1.79	1.00	1.69

Discussion

Effective primary care is largely regarded as the foundation of our healthcare delivery systems and can be likened to the ‘quarterback role’ in improving overall care quality and cost efficiency.^5,7,11 However, assessing primary care performance has been a great challenge. Except for a few process measures, most outcome measures such as costs and avoidable hospitalizations require adequate risk adjustment. The same is true for setting PCP workload such as panel sizes (in salaried healthcare systems like the VA) or setting payment rates (in non-salaried systems). In addition, assessing staffing requirements at the practice or hospital level also requires reliable risk adjustment. Yet, robust case-mix algorithms that can reliably measure patient disease burden relevant to primary care is next to nonexistent. The greatest obstacle in developing such a risk algorithm lies in the fact that parts of the PCP workload are unobservable (not recorded systematically, not available for analyses, or can’t be measured).

In this study, we developed a case-mix algorithm by forming the dependent variable as the expected workload based on the observed workload (number of visits) and unobserved workload reflected by the number of prescription drug classes. This configuration offers several advantages. First, it more accurately accounts the unobservable workload such as reviewing patient records, coordination of care, phone calls and text messaging with patients. Second, it better reflects the expected workload which is preferred to actual workload (even if it were observable) in developing case-mix models. Third, it does not require any arbitrary weights in constructing the dependent variable. Finally, it yields great predictive power with R² = 0.70.

It is worth emphasizing that the use of the number of drug classes to augment the dependent variable does not create perverse incentives. This is because the final risk score is calculated based on the independent variables, i.e., age, gender, and diagnoses (defined by ICD-10 codes), which reflect patients’ disease severity and comorbidities pertaining to PCP workload. On the other hand, perverse incentives could result if variables such as medication use or visits to specialists were used as independent variables in the analyses – a PCP’s risk score would be higher if the provider prescribed more drugs or made more referrals to specialists.

In addition, by comparing different statistical models, we found the Box-Cox regression model superior to others: it is easy to understand and straightforward to implement, it has the highest predictive power (R² = 0.70 and 0.59 for transformed and raw scales, respectively), it does not need the dependent variable to be top coded, and it does not produce negative predicted values. Apparently, the advantage of the Box-Cox model stems from its flexibility in rescaling the righthand side tail of the dependent variable.

Of special note, although socioeconomic variables can significantly affect PC workload and outcomes, we purposely leave them out as independent variables in our model development. This is because most, if not all, commercial case-mix models only use age, gender and diagnoses as explanatory variables; we intend to use the same variables so that the performance of our model can be compared with others. In addition, the objective of the present study is to produce a risk score that can be used in models to assess PC workload, performance, and payment. It is important to note that such models (beyond the scope of this study) can and should include other variables such as patient socioeconomic factors (e.g., income and education level), provider characteristics (e.g., teaching and rural status), etc.

Finally, it should be noted that this study has several limitations. First, by no means, is PC visits augmented by drug classes the optimal surrogate of PCP workload; however, it is the best choice of all the options available to us at the time. Apparently, more research is warranted. Second, this study was based on an adult population with only 8.5 percent female patients, which resulted in fewer CCS groups in female, infant and adolescent care. Third, Veterans receive care from non-VA providers, notably under their Medicare benefits, and we only focused on VA care. However, the predictive ratios by age groups revealed no indication of bias – no discernable shift of the predictive ratios around age 65 when patients start to use Medicare. Of special note, in the context of performance measurement, the predictive ratio should not be used as the primary metric to gauge model fit. This is because the observed value may not be optimal (see Appendix for more discussion). In any event, one can reasonably assume that within an inclusive system the model’s explanatory power would be higher. Obviously, further studies in these areas are warranted.

Nevertheless, we emphasize that it is the framework and methodology rather than the resultant risk score of this study that can be readily applied by other value-based care organizations to compare PCPs’ performance, benchmark workload, and set payment rates. For large health systems like the VA and Kaiser Permanente, it can also be used to risk-adjust staffing requirements at the facility or hospital level.

Supplemental Material

sj-pdf-1-hsm-10.1177_0951484820931063 - Supplemental material for Case-mix for assessing primary care value (CPCV)

Supplemental material, sj-pdf-1-hsm-10.1177_0951484820931063 for Case-mix for assessing primary care value (CPCV) by Jian Gao, Eileen Moran, Amy Schwartz and Christopher Ruser in Health Services Management Research

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Jian Gao

References

Butler

Sherman

Rhinehart

, et al. Managed care: new challenges, new roles for the primary care physician. Geriatrics 1996; 51: 35–36, 39–41, 45–46.

Forrest

Shi

Schrader

, et al. Managed care, primary care, and the patient-practitioner relationship. J Gen Intern Med 2002; 17: 270–277.

Fisher

Shortell

SM.

Accountable care organizations – accountable for what, to whom, and how. JAMA 2010; 304: 1715–1756.

Rittenhouse

Shortell

Fisher

ES.

Primary care and accountable care – two essential elements of delivery-system reform. N Engl J Med 2009; 361: 2301–2303.

Watson

Salisbury

Jani

, et al. Better value primary care is needed now more than ever. BMJ 2017; 359: j4944.

Litvin

Ornstein

Wessell

, et al. “ Meaningful” clinical quality measures for primary care physicians. Am J Manag Care 2015; 21: e583–e590.

Young

Roberts

Holden

RJ.

The challenges of measuring, improving, and reporting quality in primary care. Ann Fam Med 2017; 15: 175–182.

Majeed

Bindman

Weiner

JP.

Use of risk adjustment in setting budgets and measuring performance in primary care I: advantages, disadvantages, and practicalities. BMJ 2001; 323: 604–607.

Goroll

AH.

Risk adjustment for primary care: an essential tool for health system reform. Med Care 2012; 50: 637–639.

10.

Grazier

KL.

Risk-adjusted payment for and performance assessment of primary care. Med Care 2012; 50: 640–642.

11.

Ash

Ellis

RP.

Risk-adjusted payment and performance assessment for primary care. Med Care 2012; 50: 643–653.

12.

Schone

Brown

RS.

Risk adjustment: what is the current state of the art and how can it be improved? Robert Wood Johnson Foundation, www.rwjf.org/en/library/research/2013/07/risk-adjustment---what-is-the-current-state-of-the-art-and-how-c.html (2013, accessed 26 August 2018).

13.

Thomas

Grazier

Ward

Comparing accuracy of risk-adjustment methodologies used in economic profiling of physicians. Inquiry 2004; 41: 218–231.

14.

CMS risk adjustment discussion paper, www.cms.gov/CCIIO/Resources/Forms-Reports-and-Other-Resources/Downloads/RA-March-31-White-Paper-032416.pdf (accessed 26 August 2018).

15.

Gao

Moran

Almenoff

PL.

Case-mix for performance management: a risk algorithm based on ICD-10-CM. Med Care 2018; 56: 537–543.

16.

Clinical classifications software (CCS) for ICD-10-CM, www.hcup-us.ahrq.gov/toolssoftware/ccs10/ccs10.jsp (accessed 26 August 2018).

17.

Reinhardt

UE.

The little-known decision-makers for medicare physicians fees, https://economix.blogs.nytimes.com/2010/12/10/the-little-known-decision-makers-for-medicare-physicans-fees/ (2010, accessed 26 Aug 2018).

18.

Goodson

JD.

Unintended consequences of resource-based relative value scale reimbursement. JAMA 2007; 298: 2308–2310.

19.

Young

Burge

Kumar

, et al. The full scope of family physicians’ work is not reflected by current procedural terminology codes. J Am Board Fam Med 2017; 30: 724–732.

20.

VA National Formulary by classes, www.pbm.va.gov/nationalformulary.asp (accessed 26 August 2018).

21.

Sales

Liu

Sloan

, et al. Predicting costs of care using a pharmacy-based measure risk adjustment in a veteran population. Med Care 2003; 41: 753–760.

22.

Liu

Sales

Sharp

, et al. Case-mix adjusting performance measures in a veteran population: pharmacy- and diagnosis-based approaches. Health Serv Res 2003; 38: 1319–1337.

23.

Pettengill

Vertrees

Reliability and validity in hospital case-mix measurement. Health Care Financ Rev 198; 4: 101–128.

24.

Diehr

Yanez

Ash

, et al. Methods for analyzing health care utilization and costs. Annu Rev Public Health 1999; 20: 125–144.

25.

Basu

Manning

WG.

Issues for the next generation of health care cost analyses. Med Care 2009; 47: S109–S114.

26.

Manning

Basu

Mullahy

Generalized modeling approaches to risk adjustment of skewed outcomes data. J Health Econ 2005; 24: 465–488.

27.

Winkelman

Mehmud

A comparative analysis of claims-based tools for health risk assessment. Schaumburg, IL: Society of Actuaries, 2007.

28.

Duan

Manning

Morris

, et al. A comparison of alternative models for the demand for medical care. J Bus Econ Stat 1983; 1: 115–126.

29.

Mihaylova

Briggs

O’Hagan

, et al. Review of statistical methods for analysing healthcare resources and costs. Health Econ 2011; 20: 897–916.

30.

Efron

Estimating the error rate of a prediction rule: improvement on cross-validation. J Am Stat Assoc 1983; 78: 316–331.

Supplementary Material

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