Comparing the Technical Efficiency of Hospitals in Italy and Germany: Non-parametric Conditional Approach

Transcription

1 Comparing the Technical Efficiency of Hospitals in Italy and Germany: Non-parametric Conditional Approach TRACKING REGIONAL VARIATION IN HEALTH CARE Berlin, 4th June 2015 Yauheniya Varabyova, University of Hamburg Rudolf Blankart, University of Hamburg Aleksandra Torbica, University of Bocconi Jonas Schreyögg, University of Hamburg

2 Agenda Introduction Methods Data Results Conclusion Yauheniya Varabyova Universität Hamburg 2

3 Introduction: Literature Huge amount of publications on hospital efficiency: about 300 until2006 (Hollingsworth, 2008) + about 170 after2006 (database research) International comparisons of hospital efficiency NordDRG in Denmark, Finnland, Norway und Sweden 6 studies in Scandinavian countries review by Medin et al. (2013) similar organization of health care Different DRG-systems OUTPUT Dervaux et al. (2004): 1080 hospitals Patient in France und und procedure 903 in the classifications USA Mobley & Magnussen (1998): 178 INPUT hospitals in California and 52 in Norway Steinmann et al. (2004): 105 hospitals Personnel in Sachsen, classification Germany und 251 in Switzerland Mateus et al. (2015): 163 English ( ), 56 Portuguese ( ), 276 Spanish Currency systems and prices ( ) und 19 Slovenian ( ) hospitals Yauheniya Varabyova Universität Hamburg 3

4 Methods: Conceptual Framework Conditional approach INPUTS LABOR Physicians Nurses CAPITAL Hospital beds Hospital background Bed size category Ownership type Specialization Environmental characteristics Competition Urbanization Income Age structure OUTPUTS INDIRECT Adj. inpatient discharges Day cases Yauheniya Varabyova Universität Hamburg 4

5 Data: hospital characteristics (calendar year 2010) Variable Italy: 920 Germany: Mean SD Mean SD INPUTS Beds Physicians Nurses OUTPUTS Adj. inpatient discharges Day cases *Discharges are adjusted on the basis of length of stay Herr (2008) using the weights across 130 diagnoses (International Shortlist for Hospital Morbidity Tabulation), OECD Health Data Italy ICD ISHMT Germany ICD-10 Yauheniya Varabyova Universität Hamburg 5

6 Regional data: urbanization, income, age structure OECD Regional Data Territorial Level 3 (Germany: 96 spatial planning regions, Italy: 110 provinces) Yauheniya Varabyova Universität Hamburg 6

7 Results: Efficiency values Obs. Mean SD Min 1st Qu. Mdn 3rd Qu. Max Unconditional efficiency Total sample Italy 19% inefficiency Italy 920 Germany % 0.74 inefficiency Germany Bandwidths for hospital characteristics Bed size category Ownership Specialization E E E+06 Bandwidths for regional characteristics Competition E E E E+06 Urbanization Income Age structure E E E E+07 Country dummy Conditional efficiency Total sample 2301 Italy % inefficiency Italy 920 Germany % 0.70 inefficiency Germany Yauheniya Varabyova Universität Hamburg 7

8 Results: Regional variation in hospital efficiency (median values) Yauheniya Varabyova Universität Hamburg 8

9 Results: Non-parametric regression The ratios of conditional to unconditional efficiencies were non-parametrically regressed on the environmental variables (Racine & Li, 2004): R i z = f z i R z x, y z + ε i, where = λ m,n x, y z λ m,n x, y Variable Conditional efficiency Unconditional efficiency Value Hospital characteristics Bed size category <2e-16 *** Ownership <2e-16 *** Specialization <2e-16 *** Regional characteristics Competition Urbanization Income Age structure Country dummy <2e-16 *** Yauheniya Varabyova Universität Hamburg 9

10 Results: Partial regression plots R z x, y z = λ m,n x,y z λ m,n x,y = Conditional efficiency Unconditional efficiency <50 <150 <400 <650 <3213 Bed size category public for-profit non-profit Ownership Specialization Country Yauheniya Varabyova Universität Hamburg 10

11 Conclusion Methods Non-parametric conditional efficiency method allows to consider external factors Case-mix adjustment based on length of stay in different diagnostic groups is easily applicable to hospital data in different countries Regional variation German hospitals are on average more efficient than Italian hospitals New states of Germany and states in the North are more efficient than Southern Germany No clear geographical pattern emerged in Italy Factors associated with efficiency Hospital size (55% of Italian hospitals have up to 150 beds) Ownership (72% of Italian beds are in public ownership) Specialization (economies of scope) Further research In order to explore the role of institutions the analysis should be expanded to include more countries Yauheniya Varabyova Universität Hamburg 11

12 Thank you for your attention! Yauheniya Varabyova Hamburg Center for Health Economics Universität Hamburg Esplanade Hamburg Tel: Yauheniya Varabyova Universität Hamburg 12

13 References Cazals, C., J.-P. Florens, et al. (2002). "Nonparametric frontier estimation: a robust approach." Journal of econometrics 106(1): Daraio, C. and L. Simar (2005). "Introducing environmental variables in nonparametric frontier models: a probabilistic approach." Journal of productivity analysis 24(1): Dervaux, B., G. D. Ferrier, et al. (2004). "Comparing French and US hospital technologies: a directional input distance function approach." Applied Economics 36(10): Herr, A. (2008). "Cost and technical efficiency of German hospitals: does ownership matter?" Health Economics 17(9): Hollingsworth, B., The measurement of efficiency and productivity of health care delivery. Health Economics 17, Mateus, C., et al. (2015). "Measuring hospital efficiency comparing four European countries." The European Journal of Public Health 25(suppl 1): Medin, E., U. Häkkinen, et al. (2013). "International hospital productivity comparison: Experiences from the Nordic countries." Health Policy 112(1): Mobley IV, L. R. and J. Magnussen (1998). "An international comparison of hospital efficiency: does institutional environment matter?" Applied Economics 30(8): OECD (2014) Health Data Organisation for Economic Co-operation and Development (OECD) DOI: /health-data-en Racine, J. and Q. Li (2004). "Nonparametric estimation of regression functions with both categorical and continuous data." Journal of econometrics 119(1): Steinmann, L., G. Dittrich, et al. (2004). "Measuring and comparing the (in) efficiency of German and Swiss hospitals." The European Journal of Health Economics 5(3): Yauheniya Varabyova Universität Hamburg 13

14 BACK-UP Yauheniya Varabyova Universität Hamburg 14

15 Country facts Characteristic Italy Germany Health system National Health Service Social Health Insurance type Financing of health expenditure 1 80% taxes 18% out-of-pocket 1% private health insurance 70% social security contributions 13% out-of-pocket 9% private health insurance 7% taxes DRG adoption Acute care beds 2.93 (-48%) 5.33 (-20%) per 1,000 pop. 1 Average LOS days (-27%) 8.1 days (-35%) Discharges per 100,000 pop. 1 13,130 (-22%) 24,000 (19%) Hospital ownership, % beds 2 72% public 20% private for-profit 8% private non-profit 46% public 17% private for-profit 37% private non-profit Source: 1 Data for 2010, source: OECD Regional Statistics 2010, the values in parentheses represent the percentage change from Estimates for 2010 from our dataset. Yauheniya Varabyova Universität Hamburg 15

16 METHODS Yauheniya Varabyova Universität Hamburg 16

17 Non-parametric methodology Most frequently used non-parametric methods (Hollingsworth, 2008): Data Envelopment Analysis (DEA) Free Disposal Hull (FDH) Technology Disposability Convexity Scale DEA CRS DEA VRS FDH constant variable Graphical illustration Input = Physicians Output = Adj. inpatient discharges technically efficient observations technically inefficient observations Yauheniya Varabyova Universität Hamburg 17

18 Outlier problem Yauheniya Varabyova Universität Hamburg 18

19 Outlier problem Yauheniya Varabyova Universität Hamburg 19

20 Order-m frontier (Cazals et al. 2002, Daraio & Simar 2005) Yauheniya Varabyova Universität Hamburg 20

21 Order-m frontier Limitations of the conventional non-parametric analysis(dea, FDH): Sensitive to outliers The curse of dimensionality Difficulty to incorporate environmental variables Interpretation of the environmental variables Partial order-m frontier Robust to outliers Conditional methodology Takes into consideration environmental factors Cinzia Dario: only one environmental variable Kristof De Witte: multiple environmental factors Yauheniya Varabyova Universität Hamburg 21

22 The methodology of partial frontier analysis Conventional assumption: all observations belong to the production set: prob x, y Ψ = 1. The FDH estimator for a given DMU (x, y): λ FDH,n x, y = max i x i x j y min i j=1,,q y j Order-m: compare a unit (x, y) to m randomly selected with replacement peers from the population of units producing more output than y The probabilistic formulation of the production process, output-oriented efficiency of order-m: where S Y,n y x = n i=1 n i=1 λ m,n x, y = (1 (1 S Y,n (uy x)) m )du I(x i x,y i y) I(x i x) 0 is the conditional survivor function. Output-oriented efficiency conditional on the set of environmental variables Z r : where S Y,n y x, z = n i=1 n λ m,n x, y z = (1 (1 S Y,n (uy x, z)) m )du 0 I x i x,y i y K h (z,z i ) i=1 I(x i x) K h (z,z i ) Non-parametric assessment of environmental influences: R i z = f z i + ε i, where R z x, y z = λ m,n x,y z λ m,n x,y, K( ) is a kernel function, h hat is the bandwidth. is the ratio of conditional to unconditional efficiency measures Yauheniya Varabyova Universität Hamburg 22

23 m selection Source: Hammerschimdt et al. (2009) Methoden zur Lösung grundlegender Probleme der Datenqualität in DEA-basierten Effizienzanalysen. DBW 69 Yauheniya Varabyova Universität Hamburg 23

24 The influence of m on the partial frontier Yauheniya Varabyova Universität Hamburg 24

25 Alpha selection Source: Tauchmann (2011) orderalpha: non-parametric order-alpha Efficiency Analysis for Stata Yauheniya Varabyova Universität Hamburg 25

26 Main assumptions of conventional non-parametric analyses Yauheniya Varabyova Universität Hamburg 26

27 Outlier problem The non-parametric approach presents several limitations: the difficulty in carrying out statistical inference; the curse of dimensionality; sensitivity to extreme values and outliers Wrong record: 7.8 instead of 78 FTE physicians Such extreme values can have a heavy impact on the upper boundary of the frontier All DMUs would be benchmarked according to this one erroneous record Yauheniya Varabyova Universität Hamburg 27

28 Outlier detection Wilson (1993) proposed a method employing an influence function based on the geometric volume spanned by the sample observations, and the sensitivity of this volume with respect to deletions of singletons, pairs, triplets, etc. from the sample. Stopping point: i=1 Observations: 7 Yauheniya Varabyova Universität Hamburg 28

29 Outlier detection Wilson (1993) proposed a method employing an influence function based on the geometric volume spanned by the sample observations, and the sensitivity of this volume with respect to deletions of singletons, pairs, triplets, etc. from the sample. Stopping point: i=2 Observations: 7, 19 Yauheniya Varabyova Universität Hamburg 29

30 Outlier detection Wilson (1993) proposed a method employing an influence function based on the geometric volume spanned by the sample observations, and the sensitivity of this volume with respect to deletions of singletons, pairs, triplets, etc. from the sample. Stopping point: i=3 Observations: 7, 19, 23 Yauheniya Varabyova Universität Hamburg 30

31 Outlier detection Problems The stopping point, i, for the outlier analysis is arbitrary Should be large enough to allow for masking produced by several observations in the data Extremely slow for i larger than 3 or 4 Becomes intractable for larger data sets (samples larger than a few hundred observations) Rarely implemented empirically Yauheniya Varabyova Universität Hamburg 31

32 RESULTS Yauheniya Varabyova Universität Hamburg 32

33 Descriptive Statistics Variable Italy Germany Mean SD Min Max Mean SD Min Max Input variables Beds , ,213 Physicians , ,712 Nurses , ,694 Output variables Inpatient adjusted 8,324 9, ,319 12,198 12, ,675 Day cases 3,220 5, ,485 1,800 2, ,999 Hospital background characteristics Bed size category 1: (24,50] 98 (11%) 60 (4%) 2: (50,150] 404 (44%) 373 (27%) 3: (150,400] 257 (28%) 606 (44%) 4: (400, 650] 76 (8%) 207 (15%) 5: (650, 3213] 85 (9%) 135 (10%) Specialization Ownership type 1: Public 500 (54%) 456 (33%) 2: Private for-profit 357 (39%) 313 (23%) 3: Private non-profit 63 (7%) 612 (44%) Environmental variables Market concentration Degree of urbanization 1: Rural remote 36 (4%) 0 (0%) 2: Rural close to a city 68 (7%) 258 (19%) 3: Intermediate 422 (46%) 383 (28%) 4: Urban 394 (43%) 740 (54%) Quartile of income 1: 1st quartile 432 (47%) 152 (11%) 2: 2nd quartile 173 (19%) 402 (29%) 3: 3rd quartile 175 (19%) 393 (28%) 4: 4th quartile 140 (15%) 434 (31%) Population age 65+, % Observations 920 (100%) 1381 (100%) Yauheniya Varabyova Universität Hamburg 33

34 0.5 Efficiency Boxplot conditional efficiency Italy excludes outside values Germany Yauheniya Varabyova Universität Hamburg 34

35 Partial regression plots Notes: Efficiency.ratio = the ratio of conditional efficiency estimates to unconditional efficiency estimates. In the output-oriented framework, increasing line (for continuous variables) or higher bar (for categorical variables) imply a favorable effect on production efficiency. Bed size category: 1=[25,50], 2=(50,150], 3=(150,400], 4=(400,650], 5=(650,3213]; ownership: 1=public, 2=private for-profit, 3=private non-profit; degree of urbanization: 1=rural remote, 2=rural close to a city, 3=intermediate, 4=urban; quartile of income: 1=1 st quartile, 2=2 nd quartile, 3=3 rd quartile, 4=4 th quartile. Yauheniya Varabyova Universität Hamburg 35

36 Limitations Complexity of data collection: language barrier, data protection Further variables to describe the production process INPUTS: Other personnel categories, medical equipment, expenses OUTPUTS: Outpatient visits, research and teaching Quality Conditional methodology does not examine causal effects Computational burden Yauheniya Varabyova Universität Hamburg 36