Physician education mix and patient case-mix in hospital

Previous literature pays little attention on relationship between hospital case-mix and physicians’ human capital, while it is truly important topic in studies about health workforce. A multi-tiered medical education system resulted in substantial variation in physician education mix in hospital. We rst exploit this heterogeneity in physician human capital across hospitals to explore its role as one of determinants of hospital case-mix. The hospital case-mix index (CMI) from DRGs system is dependent variable. The school years of medical education is used to measure variation in physician human capital, that can be aggregated and averaged by each hospital. The study uses both descriptive analysis and regression modelling to investigate this association. Descriptive results show a positive relationship between physician human capital and patient case-mix in hospital. The model results illustrated that hospitals have higher level of physician education tend to have more serious case mix. In specic, when average medical school years increased by one, the hospital CMI increased by nearly 0.05. The study ndings highlight the importance and inuences of physicians’ education mix in patients’ and lower more


Introduction
Becker and Steinwald rst examined the determinants that affect hospital case-mix complexity in their Health Services Research paper in 1981 [1], while one major limitation of the study is the missing of medical staffs' characteristics in hospitals. We adopt the framework of Becker and Steinwald (1981) and extend it to include physician human capital, because complexity in health care often represented by a more serious case mix, while physicians with higher human capital are more capable to manage and treat inpatient volume. The aggregation of patients with serious illness is not random, but may implies heterogeneity in physician human capital or education mix. We will further review a brief conceptual framework about hospital case-mix and its determinants.
This paper employs hospital case-mix index (CMI) extracted from DRGs system to measure the concept of case-mix. Technically, case mix can be of prime importance in hospital reimbursement or physicians' payment design. Case-mix can represent both patients' searching and matching in health care market, and physicians' efforts of diagnosis and treatment, or even physicians' case-mix management. Factors that underlie CMI variation among hospitals still need to be investigated. The behavioural framework in Becker and Steinwald (1981) assumes that variations in hospital case-mix complexity are a function of variables of hospitals, patients, and local areas. The critical limitation of the previous study is lacking of consideration of physician's characteristics, in particularly the years of the medical training or physician human capital.
Heterogeneity in physicians' medical education Hsieh and Tang illustrated that the heterogeneity of different types of medical students in China's medical education is a long-term phenomenon and will not phase out in a short time [2]. There are at least three approaches for a medical student to become a physician with full licensure in China. The most common approach for a medical student with a bachelor degree is taking the national exam for medical practitioners and receiving hospital training as a resident for at least three years. Afterwards, the medical graduate earns the opportunity to become a licensed doctor. However, this is the most common approach to become a doctor, this approach only accounts for half of all new licensed doctors even till 2015. The second approach to become a physician is for medical graduates from junior medical colleges to earn a vocational diploma that requires three years of study after secondary school. The third approach involves secondary-level medical education through secondary vocational schools that provide very limited medical training after junior middle school. This program leads to a secondary vocational diploma (equal to a high school education) [2][3][4][5].
The heterogeneity in physicians' medical education resulted in huge variation in their training and further in uence the education mix of hospital physician in labour market. Therefore, it is a direct and forward question whether and what kind of effects of physician education mix will be, while there are no previous studies ever examined the role of physician education mix and its impacts on hospital outcomes, like patient case-mix. By exploiting multi-tiered medical education system and relevant physician human capital variation across hospitals, this study aims to re-examine this topic and address this gap in the literature. This paper offers a useful perspective on the topic of medical education and health care market interaction and extends our previous study on heterogeneous physician human capital in a more general way [2]. The rest of this article is organised as follows: The Methods section details the hospitals data and variables, and the regression model. The Results section presents descriptive results and empirical analysis. Finally, we make discusses and conclusion in the last section.

Study data
China has launched a pilot program to implement hospital reimbursement based on diagnosis-related groups (DRGs) system since 2019. Before the program, the infrastructure of health care information from provincial health department to each hospital, in particular for secondary and tertiary hospital that are highly standardised and regulated by governments, have been built and prepared effectually over last decade.
This study utilized the DRG data extracted from a provincial health information system. The present population-based DRG system annually collects over sixteen million inpatient medical records from a large province with more than 83 million populations. To construct case-mix index, the system will process a uni ed International Classi cation of Disease (ICD-10) coding of diagnoses and treatment procedures from inpatient face-sheet. This DRG data provides annual CMI for each secondary and tertiary hospitals based on 2017 inpatient records, so it enables us to measure a hospital's case-mix complexity, and comparing it with other hospitals.
Measuring the impact of physician human capital on hospital CMI requires information about physicians, therefore a de-identi ed hospital staff dataset including age, gender, education level, professional quali cation and working hospital from provincial medical workforce system will be aggregated and linked to the main data. The hospital annual report dataset was also included to provide background variables for each hospital. All three datasets were cross-sectional and come from the study year in 2017.

Dependent variable
The DRG provides a systematic approach to group patients based on a diagnosis classi cation and a similar resource consumption and length. Case-mix index is de ned as the sum of all DRG relative weights (RW) dividing by the number of inpatient admission for a hospital. Relative weight is a value number that have been technically calculated by clinical experts and assigned to a group of patients, namely diagnosis-related group (DRG). The RW for each DRG usually measure the relative resource consumption and re ect clinical complexity associated with this DRG. Overall, the average DRG weight determines the hospital CMI and represent a comprehensive severity and relative resource consumption of the hospital.
An easy approach to understand hospital CMI is to compare it with a student's Grade Point Average (GPA). The higher GPA may re ect the student's academic achievement, in a similar way, the higher CMI is able to re ect the ability of a hospital or the workshop of physicians to diagnosis and manage to treat a more serious case mix. The most common application of CMI is to help insurance organization adjust and determine how much they should pay the hospital for cases.
We plotted hospital CMI distribution by hospital level in the Fig. 1. As we see, the CMI for both secondary and tertiary hospital are nearly normal distributed that allow for a statistically sound regression for a small sample size. In addition, the average CMI of tertiary hospitals and its distribution are signi cantly larger than the average CMI of secondary hospitals.

Independent variable
In terms of physician human capital for a hospital, we used average years of medical training of all physicians for the measurement because the substantial differences in medical education programs caused a large variation in training years. The rst type is bachelor-degree-oriented medical education which includes at least four to ve years of undergraduate study in medical college. The second type is still a tertiary-level medical education which provide 3 years of study after high school and lead to a vocational diploma. The third type is secondary level medical education that provide very limited medical training, commonly for two years, after junior middle school and lead to a secondary vocational diploma (SVD) [3][4][5]. Finally, some doctors may continue to do their master or doctoral program by extending the training years after undergraduate study. Those post-graduate programs generally need seven years to nish the whole medical education training.
As the present legislation allows medical students without bachelor degree to become assistant doctors and then they have the chance to obtain the full doctor licensure after they accumulate certain years of work experience and pass an examination [2,5,6]. At a given point in time, the pool of Chinese physicians containing at least four types of physicians with different level of education training, thus, we use school years of medical education for each physician to measure physician human capital, that have been aggregated and averaged by each hospital.  Beyond physicians' variable, other independent variables are from the conceptual framework in Becker and Steinwald (1981), which covers hospital, patients and local areas characteristics. First, to account for different aspects of hospital, we include binary variables identifying Teaching hospital, Government owned, Tertiary hospital, Specialty hospital, and TCM (Traditional Chinese Medicine) hospital service. In addition, both Occupancy rate and Outpatient per admission featured the hospital's patient ow. The former indicates the number of occupied beds compared to the total number of available beds annually; the latter refers to a ratio of outpatient visits to inpatient days. Second, the previous model considered the composition of hospital medical staff proxied by hospital service distribution: Proportion of internal medicine, Proportion of OBG. Third, the model speci cation includes three variables to represent the association between health insurance distribution and case-mix: the proportion of hospital income from Urban residents insurance, Employee insurance, Rural residents insurance, respectively. Finally, the regression models used prefecture-level city xed effects to account for local areas characteristics (See Table 1). Descriptive analysis and empirical strategy Figure 3 depicts hospital CMI distribution by physician human capital measured by average years of medical schooling. We see that hospitals with higher level of physician human capital treat patients' volume with higher case-mix index. Even though the number of hospital is much smaller than the number of secondary hospital, this relationship between CMI and physician human capital is stronger and signi cant for tertiary hospital. There are three explanations for this striking relationship: rst, the casual effect of additional medical training; second, patients' sorting across hospitals (or physicians); third, physicians' ability bring about higher medical education and further generated higher CMI. Beyond the impacts of medical education on hospital CMI, we see that the next two reasons as confounding factors.  We further run a regression based on only physician human capital variable to examine this relationship between medical education and hospital case-mix complexity. To eliminate the rst confounding factor, we further controlled prefecture-level city xed effects, because it is likely that the difference in patient need and choices will not account for variation in hospital CMI. In order to examine impacts of physicians' ability, we include experience variable that used age subtracted years of medical schooling to test contribution of a part of personal ability. The experience variable represent returns of learning-bydoing and of patient volume. We correct the standard errors for clustering on city-level because a prefecture-level city is often seen the hospital referral region in China. We nd no signi cant differences in common hospital characteristics between sample and the universe, and therefore conclude that this sample hospital can represent all tertiary and secondary hospitals. Table 3 displayed hospital case-mix index decomposition by selected hospital characteristics. In terms of government-owned, specialty hospital, and TCM services, CMI differences do not appear large. Both hospital teaching status and hospital level seems have larger impacts on the hospital case-mix complexity. The hospital CMI is distributed from 0.567 to 0.826 across cities, among them two cities -Aba and Ganzi -appears smaller as they are located in remote areas. To examine the sources of variation in hospital CMI, we cannot be satis ed with descriptive results and further use linear regression analysis to explore human capital impacts on hospital case-mix.   Table 3. Hospital case-mix index by selected hospital characteristics Table 4 reports results from ordinary least squares regressions. The rst regression uses only physician human capital as independent variable. In with our expectation, one additional year of physicians' medical training in a hospital is associated with 0.088 increase in hospital case-mix index. This is consistent with primary ndings in descriptive results. The second model includes prefectural-level city xed effects to estimate impacts of physician. The main coe cient of interest is 0.70 (S.E. = 0.006), showing that the estimation of physician human capital is very similar with the model without any additional controls. One difference with previous model is that the R square signi cantly increased from 0.218 to 0.333, which implies relative contributions of more independent variables regarding local areas greatly augmented. This improves performance of our model speci cation, because local area xedeffects is used to control patients sorting across hospitals that is expected to be a major confounding factor to estimates of human capital effects. The last column for dependent variable of hospital case-mix index includes all controls in Table 3 and city-level xed effects. In this model speci cation, we considered that two confounding factors regarding to patients' sorting and physician ability have been controlled. The parameter estimated show that hospitals have higher level of physician human capital signi cantly have more serious case mix. In speci c, when average medical school years increased by one, the hospital CMI increased by nearly 0.05.

Results
Meanwhile, there is little relationship with physicians' experience that is used to proxy their ability. By controlling two potential confounding factors, we therefore obtained the robust positive effects of physician human capital on hospital case-mix.  Fig. 3, we can draw a positive relationship between hospital case-mix index and physician human capital within a hospital measured by average year of medical training without controlling for any covariates. These patterns could arise through channels other than a causal effect of medical training on patients' case-mix complexity. As we have mentioned in the Methods, both patients' sorting across hospitals and physicians' ability instead of their schooling could be confounding factors. Therefore, the ndings from Fig. 3 are strongly suggestive but not de nitive evidence that human capital on case-mix index. Figure 4 further displays a binscatter plot of the relationship estimated in model 4 of Table 4.
Speci cally following Cattaneo (2019), we present binned scatterplots of physician human capital/hospital CMI using regression model with covariates set to mean values [7]. The gure still shows that an increase in physician human capital level corresponding to a signi cant rise in hospital case-mix complexity after controlling for hospital, patients, and local community characteristics. The effect size of human capital is particularly high at tertiary hospital level, suggesting that physicians in larger hospitals are even more important in determining hospitals' case-mix complexity.

Discussion
The objectives of this study is to investigate the relationship between hospital case-mix and physician education mix, by exploiting a speci c phenomenon of substantial variation in physician education mix in hospital that is originated from a multi-tiered medical education system. Based on results from our extended model, we nd out a positive relationship between physician human capital and patient casemix. In speci c, the hospital CMI increased by nearly 0.05 when average years of medical training for physicians increased by one. In order to focus on the issues of medical staff and their patients, we will discuss its theoretical and practical implications from three dimensions as below.

Education mix
Hsieh and Tang rst introduced the context and consequences of multi-tiered medical education system, in which one of the most important outcome is an education mix among medical staff [2]. Although the multi-tiered medical education system could launch a mass production of medical students at the same time, it also pays the price of low overall quality of physician and the mixed quality of physician. As we found in this study, the educational level of hospital physicians signi cantly accounts for a substantial part of variation in case-mix of hospital.
From the perspective of hospital, managing human resources for health in a facility often involves how to organise groups of staff with different specialty, skills, grades, quali cations and experience in order to provide better care. Therefore, those de nitions, like staff mix, specialty mix and skill mix are commonly issues discussed in previous literature [8][9][10][11]. For example, there has been a long-term focus on staff mix or sta ng level. These "macro" studies often employ large-scale datasets, usually from multiple sites or even country-level [3,12]. Researchers' interests generally focus on the relationship between human resources and outcomes of health or cost [13]. In addition, the de nition of skill mix is often not so clear, but "micro" in general, and may cover a series of topics of skill mix [8,14]. For instance, these topics may include skill substitution between physicians and nurses, delegation of different professional groups, cost and effectiveness of traditional practitioners (such as doctors who still practice complementary and alternative medicine in inner and remote areas), and some other relevant topics [15].
Studies at least partly regarding education mix are still few and limited, in contrast to other research in this eld, such as specialty mix, skill mix or quali cation mix. First, education mix previously often used in the nursing group [16,17], because it is not common to achieve uniform quality standard in nurses' medical education or training. Second, studies concerning variation in physician education and its in uences on healthcare can only pay attentions on the ranking of medical schools and the ranking of hospitals [18,19], instead of fundamental differences in physicians' medical education, like secondary or tertiary medical education [2]. To the best of our knowledge, the issue of multi-tiered medical education still need more concerns across countries.
Overall, we have identi ed some literature evidences on heterogeneity in features of health workforce and its impacts on health care provision. While for some health care system, they still need to face the problems of physician education mix. Thus one of the most important contribution of our study is to measure the physician education mix across hospitals and further investigate its in uences on health care provision, namely, the case-mix index.
Reasons for case-mix complexity variation Before we discuss that physician group as one of the most important determinants of hospital case-mix, we need to give a view on reasons for case-mix variation. Reasons for patient case-mix in hospital are often complicated, mixed and dynamical, because hospital case-mix is an outcome of interaction between physician group and patient pool and their decision and choices.
Previous literature shows that reasons for CMI changes were attributed to (1) whether the real patients case-mix changed due to changes in patients' medical needs; (2) the completeness of DRGs coding, e.g.
improvements of medical documentation regarding Comorbidity & Complication; (3) the upcoding or "DRG creep" refers to that physician recoding the cases in higher weight of DRG category without changes in hospital resources consumption [20]. Nevertheless, the association between case-mix and hospital accreditation category, hospital ownership, and other hospital features are also documented [21,22]. Becker and Steinwald (1981) explicitly mentioned that they expected the characteristics of hospital's medical staff will affect case-mix complexity, however they had no direct information on medical staff, which is a critical limitation in previous published studies [1]. Our study addressed this literature gap, and rst discussed and examined the association between physician human capital and hospital's case-mix complexity by exploiting variation in hospital physicians' medical education.

Medical staff as a determinant of hospital case-mix
Previous studies regarding hospital case-mix implicitly assume that physicians are homogeneous, which is based on a fact that all developed countries have a uni ed standard medical education system.
However, the medical education system greatly varied across countries that often resulted in heterogeneity in physician human capital. Arrow illustrated four key variables determining the physicians market in a classic health economics paper. Among these four factors, both quality of entering students and medical education programs are concerned with medical education system, and are strongly relevant to physician human capital [23]. As a consequence, both supply quantity and quality of physician human capital are of signi cantly importance in in uencing health care market.
However, it is complicated to linking health workforce characteristics mix to health care dynamics [24].
Because we still need to discuss three causes for this striking relationship: (1) the casual effect of additional medical training; (2) patients' sorting across hospitals (or physicians); (3) physicians' ability bring about higher medical education and further generated higher CMI. For the relationship between these factors, we have presented in the Fig. 5 regarding physician education mix and other factors as determinants of hospital case-mix. According to our model speci cation, we have simply controlled both patient-level variables and physicians' ability or experience in confounding the regression model. Thus we may focus on and interpret the rst reason for association between physician human capital and hospital case-mix.
While there are still two explanations with respect to the casual effect of higher medical education: One of possible explanation is that "good" doctor may have incentives to manage and treat cases with higher relative weights and thus promote CMI. Yet this may not be the case in China as the incentive structure for healthcare providers is inappropriate based on a review of evidences [25]. The other possible explanation is that those physician groups with lower human capital are more likely to manage case volume with lower CMI. Previous literature has shown that the hospitals and their doctors prefer to manage both case volume and case-mix complexity given capacity and budget constraints [26,27].
This is the rst study that investigating the physician human capital as one determinant of hospital casemix. However, our study has at least two potential limitations. First, this is a cross-sectional model and a more rigorous model exploring causality may still be present; second, confounder from other unobservable hospital characteristics still exist. We also have plans to conduct further studies on (1) whether physician education mix or human capital variation in uence health outcomes of patients? (2) what the role of the variation in physician human capital in determining health workers' compensation is? Figure 5. Physician education mix and other factors as determinants of hospital case-mix Conclusion This paper rst investigates the relationship between hospital physician education mix and patient casemix using solid data from DRG system. In particular, we rst present that hospitals with higher level of physician education mix are more likely to treat more serious case mix. Our investigation may inform researchers and policymakers of health workforce in at least two aspects: rst, we need to pay more attention on the role of physician education mix, beyond topics such as staff mix, specialty mix and skill mix that are commonly issues discussed in previous literature; second, it is important to control for physician-level variation in education in future studies that used data from some unstandardized health care system. This study also contributes to current literature in two points: rst, our paper addressed a limitation and extended the classical framework of Becker and Steinwald, in which they rst examined the determinants of hospital case-mix complexity, but they missed the role of educational level of physicians in hospital; second, we further developed an idea about multi-tiered medical education and its impacts on health care market from Hsieh and Tang's paper. Figure 1 CMI distribution across hospitals   Physician education mix and other factors as determinants of hospital case-mix