Efficiency Analysis in Hospital Management

1. Efficiency Analysis in Hospital Management Hervé Leleu CNRS Research Director IÉSEG School of Management LEM Lille Economics Management

2. Introduction Hospital is a complex human organization Also a complex research topic at the crossroads of many sciences and disciplines : medicine, social sciences and engineering Efficiency analysis developed here is the contribution of economics to hospital management. It is only one facet of a global performance analysis. Economists are interested by allocation problems and try to answer to a basic question: what is the best allocation of resources to produce goods and services? In the hospital sector, economists are mostly interested by: • Efficient use of resources within an hospital • Scale (dis)economies and the optimal size of an hospital • Scope (dis)economies and the optimal specialization/diversification • Efficient use of resources within the industry and optimal allocation of financial resources among hospitals

3. Whatisefficiencyanalysis? Performance analysis is based on benchmarking. The simple idea is to compare among Decision Making Units (DMUs) the use of resources (inputs) in the production of activities (outcomes, outputs). DMUs (Decision Making Units) define the level of analysis. DMUs can be doctors, wards, hospitals, groups of hospitals, sectors… Efficiency analysis in hospital management just answers to some basic questions: • Is it possible to produce more health outcomes regarding the level of resources used by an hospital? • Is it possible to use less resources by keeping the same level of activity? • What is the optimal size of an hospital that is the size with the best productivity? • Is diversification of activities within the same DMU is better than specialization among different DMUs? • How can we measure technical progress in the hospital industry over time?

4. Main economic concepts for efficiencyanalysis Five main concepts are used in performance analysis: • Productivity is defined as the ratio of outputs over inputs. Can be partial or global (TFP). Assumes CRS. • Technical Efficiency is defined as the maximal level of outputs for a given level of inputs or alternatively, the minimal level of inputs required to produce a given level of outputs. Assumes VRS. • Technical Progress is defined as the increase of productivity over time (new practices, new treatments, new equipment). Best practices improve over time. • Scale efficiency and Optimal Size is defined as the most efficient scale size for a DMU with the maximal productivity. Assumes CRS. • Scope Efficiency is defined as the increase in efficiency by producing a mix of outputs within the same DMU instead producing specialized outputs in different DMUs. In empirical works, we will seek for the “best practices” among a sample of hospitals and we will compare each hospital to this set of best practices.

5. Performance as productivity Assumptions: 1 output, 1 input or multiple outputs/multiple inputs but all other things being equal (ceteris paribus reasoning) Output: Number of inpatients Productivity = Y/X = slope OA Prod A = 500/20 = 25 inpat./bed Prod B = 500/30 = 17 inpat./bed Prod C = 800/40 = 20 inpat./bed If ALS = 12 days, then: OR A = 500*12/25*360 = 83% OR B = 500*12/30*360 = 56% OR C = 800*12/40*360 = 66% Hospital A has a better productivity, higher OR than hospital B and C, probably because HospB and C have empty beds HospC 800 Hosp A 500 HospB 0 30 40 20 Input : Number of beds Productivity allows comparison of hospitals of different size by assuming Constant Returns to Scale (CRS)

6. Performance as efficiency Output: Number of inpatients Best practice frontier Hosp B • Efficiency = distance to the frontier • Hospitals A and B are efficient and define the BPF • Hospital C is inefficient: • Can reduce its input by 20 beds for the same level of output (empty beds) • Can increase its output by 300 inpatients for the same level of input (inefficiency probably due to a higher ALS) 800 Hosp A Hosp C 500 0 40 20 Input : Number of beds Efficiency compares hospitals of the same size by assuming Variable Returns to Scale (VRS)

7. Performance as technical progress Output: Number of inpatients Technical progress = Move of the BPF frontier over time Hospitals A and B treat more patients in 2015 with the same number of beds compared to 2000 Productivity of Hosp A has increased from 25 patients per bed to 35 patients per bed. Probably, a new treatment or a new equipment leads to a reduce ALS BPF in 2015 Hosp B 1100 BPF in 2000 800 Hosp B Hosp A 700 500 Hosp A 0 40 20 Input : Number of beds

8. Performance as optimal size Output: Number of inpatients BPF CRS BPF VRS 750 Hosp B Optimal size is defined by hospital A with the best productivity (5 patients per bed). HospA is at the MPSS Hospitals B is technically efficient but too big (productivity of 3 patients per bed). It suffers from diseconomies of scale. Hospitals C is technically efficient but too small (productivity of 3 patients per bed). It could benefit from economies of scale. Hosp A: MPSS 500 150 Hosp C 0 250 100 50 Input : Number of beds

9. Performance as scope efficiency Input 1: Number of hours BPF DRG 1 and 2 Hosp A produces only DRG 1 Hosp B produces only DRG 2 Hosp C produces both DRG 1 and 2 Hosp A and Hosp B are technically efficient but Hosp C uses less input to produce DRG 1 and 2 that the sum of inputs used by Hosp A and Hosp B Diversification of activities can lead to scope efficiency BPF DRG 1 250 A+B 225 Hosp A Hosp C 200 Hosp C Hosp B 50 BPF DRG 2 0 250 50 225 200 Input : Number of equipment

10. Performance: based on Quantity or Value? Note that all the previous concepts of performance are based on volume measured in physical units (number of beds, doctors, nurses, hours, number of patients, days…). We don’t need prices at this stage. Therefore these concepts of economic performance are well suited for the hospital industry. Health is a non-market good and even hospital inputs are often non-market resources. In most countries the hospital industry is a highly regulated market with budgets and tariffs instead of market prices. The only assumption for economic behavior requested for all analyses is avoiding waste in input uses.

11. Goingfurther in economic performance By assuming stronger assumptions of cost-minimisation or profit-maximisation and the availability of prices, we can enrich the performance analysis with the concepts of allocative efficiency. Allocative efficiency is defined as the right choice of inputs or outputs given their prices that is choosing the best mix of inputs leading to the minimum cost of production and choosing the best mix of outputs leading to the maximum profit. Cost efficiency and profit efficiency can probably be useful for a for-profit hospital sector but even in this case regulation is often a barrier to fully apply these concepts.

12. Data EnvelopmentAnalysis:An efficient tool to measureefficiency The main challenge in efficiency analysis for hospital management is the effective measure of efficiency taking into account the specificity of the hospital industry. The hospital production function or more broadly the hospital technology is characterized by: A complex production process involving multiple inputs and multiple outputs production technology. Ex: DRGs as the measure of activity. Minimal assumptions on economic behaviour: in general no profit maximisation, no cost minimization Datasets based on quantities (inputs, outputs)

13. DEA as a tool to measureefficiency Traditional econometric approaches are difficult to implement in the hospital industry: • Multiple outputs require duality and estimation of cost function for which input prices are needed • Assumption on the functional form of the production function • Assumption on the functional form of the inefficiency Alternatively, activity analysis like the DEA approach is well-suited: • Allows for multiple outputs and multiple inputs • Envelops the data and requires no specific assumptions • Allows to estimate all types of efficiency defined above • Uses duality to estimate shadow prices of inputs and outputs (a shadow price is the relative value of two outputs or two inputs)

14. DEA as a tool to measureefficiency The production possibility set(PPS) is defined by observed hospitals in a sample The PPS can be generalized in any dimensions Only the availability of data limits the analysis Number of inpatients Hosp B 800 Hosp A 500 40 25 Number of beds

15. DEA as a tool to measureefficiency Number of inpatients Hosp B 800 The production frontier (BPF) envelops the observed data It is based on minimal assumption of free disposability and convexity It is easy to compute in any dimensions by a linear program Hosp A 500 40 25 Number of beds

16. DEA as a tool to measureefficiency The technical inefficiency is measured as the distance to the frontier Generally expressed as a % Output inefficiency = (600-500)/500 = 20% Input inefficiency = (30-25)/40 = 17% Technical efficiency is computed by a LP. Could be computed in any dimensions Number of inpatients Hosp B 600 Output inefficiency is the distance to the BPF Hosp A 500 Hosp C Input inefficiency is the distance to the BPF 25 30 Number of beds

17. DEA as a tool to measureefficiency Other efficiency concepts (productivity, technical progress, optimal size and scope efficiency) are measured in the same way. All theses concepts are formally defined in a mathematical framework initiated by Shephard (1953): • Definition of the production possibility as a mathematical set • Definition of minimal economic assumptions as mathematical axioms imposed to the PPS • Definition of efficiency as DMUs on the frontier of the PPS • Definition of a mathematical distance-function to measure distance to the frontier of the PPS Measurement tools based on linear programming proposed by Farrell (1957) and Charnes, Cooper and Rhodes (1978)

18. Methodological overview of the approachfor measuring technical inefficiency Definition of the technology Definition of the distance function Axioms on Y: free disposability, convexity, returns to scale… Operationaldefinition of Ybased on observed data Estimation of the technicalefficiency by the distance function: The problemis a linear program Solved by traditional LP solver (excel, gams, lindo, mathematica, mapple…)

19. Some applications to the hospital sector • Estimation of technicalefficiency of ICUs(DERVAUX B., LELEU H., MINVIELLE E., Valdmanis V., AEGERTER P., GUIDET B. (2009). Assessing Performance of French Intensive Care Units: A Directional Distance Function Approach at the Patient Level, International Journal of Production Economics, 120(2) : 585-594.) • Comparisonof hospitalefficiencyamong countries (DERVAUX B., FERRIER G., LELEU H., Valdmanis V. (2004). Comparing French And US Hospital Technologies: A Directional Input Distance Function Approach, Applied Economics, 36(10) : 1065-1081.) • Estimation of capacityutilization rates and reallocation of capacitiesamonghospitals(FERRIER G., LELEU H., Valdmanis V. (2009). Hospital Capacity in Large Urban Areas: Is There Enough in Times of Need? Journal of Productivity Analysis, 32(10) : 103-117.) • Optimal productive size of ICUs(LELEU H., MOISES J., Valdmanis V. (2012). Optimal productive size of hospital's intensive care units. International Journal of Production Economics, 136(2) : 297-305.) • Estimation of scope efficiency in the US Hospitals(FERRIER G., LELEU H., MOISES J., Valdmanis V. (2013). The Focus Efficiency of U.S. Hospitals, Atlantic Economic Journal, 41(3) : 241–263.)

20. Some applications to the hospital sector • Estimation of shadowprices and reimbursement rates of different types of patient in nursing homes (DERVAUX B., LELEU H., NOGUES H., Valdmanis V. (2006). Assessing French Nursing Home Efficiency: An Indirect Output Distance Approach, Socio-Economic Planning Sciences, 40(1) : 70-91.) • Estimation of shadowprices for health outputs (DERVAUX B., LELEU H., Valdmanis V. (2004). Estimating Tradeoffs Among Health Care System's Objectives, Health Services and Outcomes Research Methodology, 5(1) : 39-58. ) • Shadow pricingof surgicalactivities(DERVAUX B., LELEU H. (2002). Adéquation de la tarification à l’activité chirurgicale des établissements privés français, Journal d’Economie Médicale, 20(3-4) : 201-2) • Structural efficiency implied by Certificate of Needs regulation (FERRIER G., LELEU H., Valdmanis V. (2010). The Impact of CON Regulation on Hospital Efficiency, Health Care Management Science, 13(1) : 84-100) • Regionalreallocation of beds in surgeryunits(DERVAUX B., KERSTENS K., LELEU H. (2000). Remedying Excess Capacities in French Surgery Units by Industry Reallocations: The Scope for Short and Long Term Improvements in Plant Capacity Utilization. In J.L.T Blank (ed.) Public Provision and Performance: Contributions from Efficiency and Productivity Measurement, Elsevier, ISBN 0444504834, 121-147.)

21. Conclusion Concepts for efficiency analysis are well-established and measurement tools are operational. The devil is in the data: • How do we measure health outcomes? • How do we include severity? Can we define a good case-mix index? • How we measure quality of care? Which indicators? • How to implement an efficient information system in hospitals to get homogenous data? Measurement of efficiency is the first step. It is useful for improving allocation of resources among hospitals. Explaining the variability of efficiency is the second step. Understanding the determinants of inefficiency like environmental factors can help for policy decision.