IS THERE EMPIRICAL EVIDENCE FOR DECREASING RETURNS TO SCALE IN A HEALTH CAPITAL MODEL?

We estimate a health investment equation, derived from a health capital model that is an extension of the well-known Grossman model. Of particular interest is whether the health production function has constant returns to scale, as in the standard Grossman model, or decreasing returns to scale, as in the Ehrlich-Chuma model and extensions thereof. The model with decreasing returns to scale has a number of theoretically and empirically desirable characteristics that the constant returns model does not have. Although our empirical equation does not point-identify the decreasing returns to scale curvature parameter, it does allow us to test for constant versus decreasing returns to scale. The results are suggestive of decreasing returns and in line with prior estimates from the literature. But when we attempt to control for the endogeneity of health by using instrumental variables, the results become inconclusive. This brings into question the robustness of prior estimates in this literature.     

Non-linearity in the cost-effectiveness frontier

Conventional cost-effectiveness decision rules rely on the assumptions that all health care programmes are divisible and exhibit constant returns to scale for a homogeneous population; hence, the path between adjacent programmes on a cost-effectiveness frontier must be linear. In this paper we build a framework to analyse non-linear 'expansion' paths. We model the impact of two key sources of non-linearity: economies of scale or scope in the production of health care; and prioritisation of patients who are most likely to benefit from more expensive and more effective treatments. We conclude that the expansion path might be linear, convex or concave, depending on the situation. The path might also exhibit vertical discontinuity due to fixed costs or horizontal discontinuity due to indivisibility. The efficiency of resource allocation might be improved by empirical estimation of expansion paths. We discuss the advantages and disadvantages of this approach compared with a standard stratified analysis.     

Health care resource allocation: is the threshold rule good enough?

We review the foundations of resource allocation rules based on cost-effectiveness information. Comprehensive approaches, where a total budget is allocated in one go, require estimation of the costs and effects of all available health care programmes, which is unlikely to be practical. A common alternative is to assess individual programmes against a cost-effectiveness threshold. This has been shown to be efficient if the threshold is well calibrated and all programmes can be wholly or partially implemented with constant returns to scale. We discuss the feasibility of these assumptions, and the effects of relaxing them, concluding that programme indivisibility is unlikely to be a serious problem at a national level, but that miscalibration of the threshold and non-constant returns to scale might be. A rule that avoids these difficulties has been proposed previously: a new programme should only be implemented if it can be funded by cancelling another less effective programme. This could never reduce efficiency, unlike the threshold rule, though we show that it might sometimes fail to recommend an efficiency-improving change. We suggest a refinement of this reallocation rule based on explicit estimation of the costs and effects of partial implementation of the programmes under review. Research is required to assess the practicality of this option.     

Is there an association between economic performance and public satisfaction in health care?

Earlier studies on the association between health systems’ economic performance and public satisfaction were based on between-countries comparisons. This approach can be challenged as it ignores the fact that subjective measures like ‘satisfaction’ might be relative. Cohort analysis is a way of dealing with this issue as it focuses on within-countries comparisons. The association between change in satisfaction with health care systems and change in economic performance, determined by an output-orientated constant returns to scale DEA Malmquist model over the period 1995 to 2000/2002 using OECD data, is explored. The results show that a health care systems’ economic performance is not associated with public satisfaction.     

The cost and efficiency of public and private health care facilities in Ogun state,Nigeria

During the 1980s, Nigeria faced difficult economic conditions resulting in a severely constrained budget for public health services. To assess more carefully the costs and efficiency of the public and private health sectors, the Federal Ministry of Health in Nigeria undertook a comprehensive survey of health care facilities in Ogun State in 1987, the analysis of which is presented in this study. The findings suggest that there is potential to increase service delivery within existing budgets by more cost-effective allocation of inputs. Many public and private providers are not operating at full technical capacity. It also appears that public facilities are not using cost-minimizing combinations of high and low-level health workers, in particular, too many low-level staff are being used to support high-level workers. The cost analysis indicates that there are short-run increasing returns to scale for inpatient and nearly constant returns to scale for outpatient services. Economies of scope for joint production of inpatient and outpatient services are not being realized. A major implication of such analysis is that improved resource allocation decisions heavily depend on the existence of information systems at the health facility level which carefully integrate financial information with other appropriate and adequate measures of service inputs, health care quality, facility utilization and ultimately health status.     

Optimal investment in HIV prevention programs: more is not always better

This paper develops a mathematical/economic framework to address the following question: Given a particular population, a specific HIV prevention program, and a fixed amount of funds that could be invested in the program, how much money should be invested? We consider the impact of investment in a prevention program on the HIV sufficient contact rate (defined via production functions that describe the change in the sufficient contact rate as a function of expenditure on a prevention program), and the impact of changes in the sufficient contact rate on the spread of HIV (via an epidemic model). In general, the cost per HIV infection averted is not constant as the level of investment changes, so the fact that some investment in a program is cost effective does not mean that more investment in the program is cost effective. Our framework provides a formal means for determining how the cost per infection averted changes with the level of expenditure. We can use this information as follows: When the program has decreasing marginal cost per infection averted (which occurs, for example, with a growing epidemic and a prevention program with increasing returns to scale), it is optimal either to spend nothing on the program or to spend the entire budget. When the program has increasing marginal cost per infection averted (which occurs, for example, with a shrinking epidemic and a prevention program with decreasing returns to scale), it may be optimal to spend some but not all of the budget. The amount that should be spent depends on both the rate of disease spread and the production function for the prevention program. We illustrate our ideas with two examples: that of a needle exchange program, and that of a methadone maintenance program.     

Health care in the CIS countries

The study analyses the technical efficiency of community hospitals in Ukraine during 1997–2001. Hospital cost amount to two-thirds of Ukrainian spending on health care. Data are available on the number of beds, physicians and nurses employed, surgical procedures performed, and admissions and patient days. We employ data envelopment analysis to calculate the efficiency of hospitals and to assess productivity changes over time. The scores calculated with an output-oriented model assuming constant returns to scale range from 150% to 110%. Average relative inefficiency of the hospitals is initially above 30% and later drops to 15% or below. The average productivity change is positive but below 1%; a Malmquist index decomposition reveals that negative technological progress is overcompensated by positive catching-up.     

Assessing the efficiency of rural health centres in Burkina Faso: an application of Data Envelopment Analysis

Background  Effective health care provision benefits from the support of measurement techniques. Contrary to the situation in industrialised countries efficiency analyses in the health care sector in Africa are a very recent phenomenon. Hardly any of the existing studies was conducted at the level of primary care. Aim  The purpose of this study was twofold: (1) to evaluate the relative efficiency of health centres in rural Burkina Faso and (2) to investigate reasons for inefficient performance. Methods  Data Envelopment Analysis (DEA) was applied. To account for the situation in that country, the output-oriented approach was used in connection with different returns to scale assumptions. To identify the spatial effect of the catchment area on efficiency the Tobit model was applied. Results  According to constant returns to scale, 14 health centres were relatively efficient. The DEA projections suggest that the inefficient units were too big to be efficient. Tobit regression showed that the relatively efficient health centres are located close to villages in their catchment area. Conclusions  For ethical reasons it is not appropriate to try to improve the efficiency of health centres by closing some of them. Their efficiency can be improved and lives can be saved if access to health centres is enhanced. Funding: This study was supported by a research grant of the German Research Foundation (Deutsche Forschungsgemeinschaft).     

基于数据包络法的江苏省卫生资源配置效率研究*

目的通过对江苏省2016年13市卫生资源配置效率的横向分析和2007—2016年江苏省卫生资源配置效率的纵向分析,提出相应的建议及改进措施,以提高卫生资源配置的利用效率。方法使用数据包络方法(DEA),通过MaxDEA 7软件中的CCR模型进行分析,投入指标选择床位数和卫生技术人员数,产出指标选择诊疗总人次和出院总人次。结果 2016年南京市、徐州市、镇江市和宿迁市达到DEA有效,苏州市、扬州市DEA弱有效,其余均无效,并且苏州市呈现规模收益递减;2010年、2013年、2014年和2016年江苏省卫生资源配置达到DEA有效,2007—2009年、2011年和2015年DEA弱有效,2012年DEA无效。2015年规模报酬递减,其余非DEA有效年份规模报酬均递增。结论建议因地制宜调整卫生资源投入,控制规模,建立合理的卫生资源评价指标体系,加强医院内部管理,通过政府和市场良好的配合提高卫生资源的利用效率。     

卫生体系效率评价的概念框架与测量方法——兼论应用数据包络分析的方法学问题

提高效率与促进公平是医药卫生体制改革的目的,卫生体系效率评价是医药卫生体制改革评价的重要方面。本文构建了可操作性更强的卫生体系效率测量的概念框架及其测量指标,在此基础上讨论了应用数据包络分析测量卫生体系效率时需要注意的一些方法学问题,包括模型导向和规模报酬的选择、样本大小与默认有效、外部不可控因素、效率值的可比性、率或比值数据的处理和负向指标的处理等方法学问题。     

Are vaccination sites in Bangladesh scale efficient?

OBJECTIVES: The overall aim of this study is to discern whether and to what degree vaccination sites exhibit constant returns to scale. METHODS: Data Envelopment Analysis is used to compare all the facilities in the sample in terms of input costs used to produce multiple outputs. The application considers the Expanded Program on Immunization (EPI), which operated in Dhaka City, Bangladesh, during 1999. RESULTS: A preponderance of EPI sites were determined to be operating at increasing returns to scale. CONCLUSIONS: Our findings question the applicability of cost-effectiveness analyses that assume constant returns to scale.     

Adapting portfolio theory for the evaluation of multiple investments in health with a multiplicative extension for treatment synergies

Portfolio theory is central to the analysis of risk in many areas of economics but is seldom used appropriately in health economics. This contribution examines the use of portfolio theory in the context of cost-effectiveness analysis (CEA). A number of modifications are needed to apply portfolio analysis to the economic evaluation of health care interventions. First, the method of reporting the results of a CEA, and consequently some of the underlying assumptions, needs to be modified. Second, portfolio theory needs to be expressed in terms of effects on individuals aggregated to a population. Finally, one needs to allow for the possibility of synergy between the various health interventions. This paper derives a general formula for a portfolio of health care interventions that allows for synergies between interventions where the population effects are aggregated from individual effects. A number of special cases are also derived to highlight the nature of the formulation of the modified portfolio theory. We conclude that, while modified portfolio theory adds a theoretical foundation to health care evaluations, it may not be operational until estimates of the correlation between interventions are available, and the question of uncertainty is resolved in health care evaluation. Also, while a synergy may be present at the individual level, when aggregated over a large population it may not be significant given the standard assumption of constant returns to scale.     

The efficiency of the delivery of neonatal care in the UK

BACKGROUND: A recent paper in Journal of Public Health Medicine (O'Neill et al., 2000; 22(1): 108-115) used regression modelling to determine the average costs of neonatal care services for a sample of 49 units in the United Kingdom in 1990-1991, and concluded that economies of scale were present in the sample as a whole. Although this form of modelling is useful, analysis of the efficiency of production for individual units is also important. METHODS: Data envelopment analysis (DEA) was used to analyse the data set published by O'Neil et al., to determine technical efficiency of neonatal units, measuring efficiency compared with a benchmark efficient frontier, and estimating economies of scale for each unit. Potential cost savings if units were to operate efficiently are estimated. RESULTS: There is evidence of substantial levels of technical inefficiency. Economies of scale varied between units, with increasing returns in the 36 inefficient units, and mainly constant returns in the 13 efficient units. This suggests that the presence of technical inefficiency was as important as scale inefficiencies. Total cost savings, if all units were operating efficiently, are estimated at ?10.4 million, equivalent to 10 extra units producing 57,000 additional days of care. CONCLUSIONS: DEA is a technique of great potential value in analysing the efficiency of health care production. As well as inefficiencies in the production of neonatal care in the United Kingdom due to differences in the scale of production, there appears to have been considerable technical inefficiency, which was not due to differences in case mix. The potential cost savings from efficiency gains are large.     

Health Technology Assessment With Diminishing Returns to Health: The Generalized Risk-Adjusted Cost-Effectiveness (GRACE) Approach

ObjectivesCost-effectiveness analysis (CEA) embeds an assumption at odds with most economic analysis–that of constant returns to health in the creation of happiness (utility). We aim to reconcile it with the bulk of economic theory.MethodsWe generalize the traditional CEA approach, allow diminishing returns to health, and align CEA with the rest of the health economics literature.ResultsThis simple change has far-reaching implications for the practice of CEA. First, optimal cost-effectiveness thresholds should systematically rise for more severe diseases and fall for milder ones. We provide formulae for estimating how these thresholds vary with health-related quality of life (QoL) in the sick state. Practitioners can also use our approach to account for treatment outcome uncertainty. Holding average benefits fixed, risk-averse consumers value interventions more when they reduce outcome uncertainty (‘insurance value’) and/or when they provide a chance at positively skewed outcomes (‘value of hope’). Finally, we provide a coherent way to combine improvements in QoL and life expectancy (LE) when people have diminishing returns to QoL.ConclusionThis new approach obviates the need for increasingly prevalent and ad hoc exceptions to CEA for end-of-life care, rare disease, and very severe disease (eg, cancer). Our methods also show that the value of improving QoL for disabled people is greater than for comparable non-disabled people, thus resolving an ongoing and mathematically legitimate objection to CEA raised by advocates for disabled people. Our Generalized Risk-Adjusted Cost-Effectiveness (GRACE) approach helps align HTA practice with realistic preferences for health and risk.     

Estimating Technical Efficiency in the Hospital Sector with Panel Data

Background: Policy makers are increasingly interested in developing performance indicators that measure hospital efficiency. These indicators may give the purchasers of health services an additional regulatory tool to contain health expenditure. Objective: Using panel data, this study compares different parametric (econometric) and non-parametric (linear programming) techniques for the measurement of a hospital’s technical efficiency. Method: This comparison was made using a sample of 17 Italian hospitals in the years 1996–9. Results: Highest correlations are found in the efficiency scores between the non-parametric data envelopment analysis under the constant returns to scale assumption (DEA-CRS) and several parametric models. Correlation reduces markedly when using more flexible non-parametric specifications such as data envelopment analysis under the variable returns to scale assumption (DEA-VRS) and the free disposal hull (FDH) model. Correlation also generally reduces when moving from one output to two-output specifications. Conclusions: This analysis suggests that there is scope for developing performance indicators at hospital level using panel data, but it is important that extensive sensitivity analysis is carried out if purchasers wish to make use of these indicators in practice.     

Consumer satisfaction and supplier induced demand

This study examines the relationship between supply of primary physicians and consumer satisfaction with access to, and quality of, primary physician services in Norway. The purpose is to throw light on a long-standing controversy in the literature on supplier inducement (SID): the interpretation of the positive association between physician density and per capita utilization of health services. We find that an increase in the number of physicians leads to improved consumer satisfaction, and that the relationship between satisfaction and physician density exhibits diminishing returns to scale. Our results suggest that policy-makers can compute the socially optimal density of physicians without knowledge about whether SID exists, if one accepts the (controversial) assumption that consumer satisfaction is a valid proxy for patient utility.     

Measuring the efficiencies of visiting nurse service agencies using data envelopment analysis

This study develops a measure of the efficiency of visiting nurse (VN) agencies in Japan, examining the issues related to the measurement of efficiency, and identifying the characteristics that influence efficiency. We have employed a data envelopment analysis to measure the efficiency of 108 VN agencies, using the numbers of 5 types of staff as the input variables and the numbers of 3 types of visits as the output variables. The median efficiency scores of the VN agencies were found to be 0.80 and 1.00 according to the constant returns to scale (CRS) and variable returns to scale (VRS) models, respectively, and the median scale efficiency score was 0.95. This study supports using both the CRS and VRS models to measure the scale efficiency of VN service agencies. We also found that relatively efficient VN agencies filled at least 30 % of staff positions with experienced workers, and so concluded that this characteristic has a direct influence on the length of visits.     

Physician productivity and returns to scale.

Cobb-Douglas production functions are used to estimate returns to scale in a sample of solo and group medical practices stratified by size and type of practice. Solo practices and small single-specialty groups are stratified by specialty, and large multispecialty groups are stratified as general practice-general surgery or comprehensive-care groups. Output measures used are gross revenue, total patient visits, and office visits; input measures reflecting practice scale are number of physicians, number of rooms, and number of nonphysician office personnel. Results indicate increasing returns to scale for solo and small group practices but decreasing returns to scale for very large groups. Possible reasons for inefficiency in large practices and the implications of the findings for public policy on health maintenance organizations are discussed.     

Bridging the gap between health and non-health investments: moving from cost-effectiveness analysis to a return on investment approach across sectors of economy

When choosing from a menu of treatment alternatives, the optimal treatment depends on the objective function and the assumptions of the model. The classical decision rule of cost-effectiveness analysis may be formulated via two different objective functions: (i) maximising health outcomes subject to the budget constraint or (ii) maximising the net benefit of the intervention with the budget being determined ex post. We suggest a more general objective function of (iii) maximising return on investment from available resources with consideration of health and non-health investments. The return on investment approach allows to adjust the analysis for the benefits forgone by alternative non-health investments from a societal or subsocietal perspective. We show that in the presence of positive returns on non-health investments the decision-maker’s willingness to pay per unit of effect for a treatment program needs to be higher than its incremental cost-effectiveness ratio to be considered cost-effective.      

Ramsey waits: allocating public health service resources when there is rationing by waiting

The optimal allocation of a public health care budget across treatments must take account of the way in which care is rationed within treatments since this will affect their marginal value. We investigate the optimal allocation rules for public health care systems where user charges are fixed and care is rationed by waiting. The optimal waiting time is higher for treatments with demands more elastic to waiting time, higher costs, lower charges, smaller marginal welfare loss from waiting by treated patients, and smaller marginal welfare losses from under-consumption of care. The results hold for a wide range of welfarist and non-welfarist objective functions and for systems in which there is also a private health care sector. They imply that allocation rules based purely on cost effectiveness ratios are suboptimal because they assume that there is no rationing within treatments.