Skip to main content
Erschienen in: The European Journal of Health Economics 8/2016

07.10.2015 | Original Paper

Choice of statistical model for cost-effectiveness analysis and covariate adjustment: empirical application of prominent models and assessment of their results

verfasst von: Theodoros Mantopoulos, Paul M. Mitchell, Nicky J. Welton, Richard McManus, Lazaros Andronis

Erschienen in: The European Journal of Health Economics | Ausgabe 8/2016

Einloggen, um Zugang zu erhalten

Abstract

Context

Statistical models employed in analysing patient-level cost and effectiveness data need to be flexible enough to adjust for any imbalanced covariates, account for correlations between key parameters, and accommodate potential skewed distributions of costs and/or effects. We compare prominent statistical models for cost-effectiveness analysis alongside randomised controlled trials (RCTs) and covariate adjustment to assess their performance and accuracy using data from a large RCT.

Method

Seemingly unrelated regressions, linear regression of net monetary benefits, and Bayesian generalized linear models with various distributional assumptions were used to analyse data from the TASMINH2 trial. Each model adjusted for covariates prognostic of costs and outcomes.

Results

Cost-effectiveness results were notably sensitive to model choice. Models assuming normally distributed costs and effects provided a poor fit to the data, and potentially misleading inference. Allowing for a beta distribution captured the true incremental difference in effects and changed the decision as to which treatment is preferable.

Conclusions

Our findings suggest that Bayesian generalized linear models which allow for non-normality in estimation offer an attractive tool for researchers undertaking cost-effectiveness analyses. The flexibility provided by such methods allows the researcher to analyse patient-level data which are not necessarily normally distributed, while at the same time it enables assessing the effect of various baseline covariates on cost-effectiveness results.
Anhänge
Nur mit Berechtigung zugänglich
Fußnoten
1
The formula for calculating the SMD for a continuous covariate (x) is: \(SMD_{x} = \frac{{\mu_{x1} - \mu_{x2} }}{{\sqrt {(var_{x1} + var_{x2} )/2} }}\), where \(\mu_{x1} , \mu_{x2}\) and \(var_{x1} , var_{x2}\) are the means and variances for each group [40].
 
Literatur
1.
Zurück zum Zitat Fuchs, V.R., Garber, A.M.: The new technology assessment. N. Engl. J. Med. 323(10), 673 (1990)CrossRefPubMed Fuchs, V.R., Garber, A.M.: The new technology assessment. N. Engl. J. Med. 323(10), 673 (1990)CrossRefPubMed
2.
Zurück zum Zitat Drummond, M.F., Sculpher, M.J., Torrance, G.W., O’Brien, B.J., Stoddart, G.L.: Methods for the economic evaluation of health care programmes (3rd edn). Oxford University Press, Oxford (2005) Drummond, M.F., Sculpher, M.J., Torrance, G.W., O’Brien, B.J., Stoddart, G.L.: Methods for the economic evaluation of health care programmes (3rd edn). Oxford University Press, Oxford (2005)
3.
Zurück zum Zitat Senn, S.J.: Covariate imbalance and random allocation in clinical trials. J. Stat. Med. 8, 467–475 (1989)CrossRef Senn, S.J.: Covariate imbalance and random allocation in clinical trials. J. Stat. Med. 8, 467–475 (1989)CrossRef
4.
Zurück zum Zitat Moher, D., Hopewell, S., Schulz, K.F., Montori, V., Gøtzsche, P.C., Devereaux, P.J., Elbourne, P.J., Egger, D.G., Altman, M.: CONSORT 2010 explanation and elaboration: updated guidelines for reporting parallel group randomised trials. Br. Med. J. 340, 869–897 (2010)CrossRef Moher, D., Hopewell, S., Schulz, K.F., Montori, V., Gøtzsche, P.C., Devereaux, P.J., Elbourne, P.J., Egger, D.G., Altman, M.: CONSORT 2010 explanation and elaboration: updated guidelines for reporting parallel group randomised trials. Br. Med. J. 340, 869–897 (2010)CrossRef
6.
Zurück zum Zitat Taves, D.R.: Minimization: a new method of assigning patients to treatment and control groups. Clin. Pharmacol. Ther. 15(5), 443–453 (1974)CrossRefPubMed Taves, D.R.: Minimization: a new method of assigning patients to treatment and control groups. Clin. Pharmacol. Ther. 15(5), 443–453 (1974)CrossRefPubMed
7.
Zurück zum Zitat Pocock, S.J., Simon, R.: Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial. Biometrics 31(1), 103–115 (1975)CrossRefPubMed Pocock, S.J., Simon, R.: Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial. Biometrics 31(1), 103–115 (1975)CrossRefPubMed
8.
Zurück zum Zitat Senn, S.J.: Testing for baseline balance in clinical trials. J. Stat. Med. 13, 1715–1726 (1994)CrossRef Senn, S.J.: Testing for baseline balance in clinical trials. J. Stat. Med. 13, 1715–1726 (1994)CrossRef
9.
Zurück zum Zitat Hoch, J., Briggs, A., Willan, A.: Something old, something new, something borrowed, something blue: a framework for the marriage of health econometrics and cost-effectiveness analysis. Health Econ. 11, 415–430 (2002)CrossRefPubMed Hoch, J., Briggs, A., Willan, A.: Something old, something new, something borrowed, something blue: a framework for the marriage of health econometrics and cost-effectiveness analysis. Health Econ. 11, 415–430 (2002)CrossRefPubMed
10.
Zurück zum Zitat Manca, A., Hawkins, N., Sculpher, M.: Estimating mean QALYs in trial-based cost-effectiveness analysis: the importance of controlling for baseline utility. Health Econ. 14, 487–496 (2005)CrossRefPubMed Manca, A., Hawkins, N., Sculpher, M.: Estimating mean QALYs in trial-based cost-effectiveness analysis: the importance of controlling for baseline utility. Health Econ. 14, 487–496 (2005)CrossRefPubMed
11.
Zurück zum Zitat Willan, A., Briggs, A.: Statistical analysis of cost-effectiveness data. Wiley, Chichester (2006)CrossRef Willan, A., Briggs, A.: Statistical analysis of cost-effectiveness data. Wiley, Chichester (2006)CrossRef
13.
Zurück zum Zitat Nixon, R.M., Thompson, S.G.: Methods for incorporating covariate adjustment, subgroup analysis and between-centre differences into cost-effectiveness evaluations. Health Econ. 14, 1217–1229 (2005)CrossRefPubMed Nixon, R.M., Thompson, S.G.: Methods for incorporating covariate adjustment, subgroup analysis and between-centre differences into cost-effectiveness evaluations. Health Econ. 14, 1217–1229 (2005)CrossRefPubMed
14.
Zurück zum Zitat O’Hagan, A., Stevens, J.W.: A framework for cost-effectiveness analysis from clinical trial data. Health Econ. 10, 303–315 (2001)CrossRefPubMed O’Hagan, A., Stevens, J.W.: A framework for cost-effectiveness analysis from clinical trial data. Health Econ. 10, 303–315 (2001)CrossRefPubMed
15.
Zurück zum Zitat Briggs, A., Gray, A.: The distribution of health care costs and their statistical analysis for economic evaluation. J. Health Serv. Res. Policy 3, 233–245 (1998)PubMed Briggs, A., Gray, A.: The distribution of health care costs and their statistical analysis for economic evaluation. J. Health Serv. Res. Policy 3, 233–245 (1998)PubMed
16.
Zurück zum Zitat Tambour, M., Zethraeus, N., Johannesson, M.: A note on confidence intervals in cost-effectiveness analysis. Int. J. Technol. Assess. Health Care 14(3), 467–471 (1998)CrossRefPubMed Tambour, M., Zethraeus, N., Johannesson, M.: A note on confidence intervals in cost-effectiveness analysis. Int. J. Technol. Assess. Health Care 14(3), 467–471 (1998)CrossRefPubMed
17.
Zurück zum Zitat Willan, A.R., Briggs, A.H., Hoch, J.S.: Regression methods for covariate adjustment and subgroup analysis for non-censored cost-effectiveness data. Health Econ. 13, 461–475 (2004)CrossRefPubMed Willan, A.R., Briggs, A.H., Hoch, J.S.: Regression methods for covariate adjustment and subgroup analysis for non-censored cost-effectiveness data. Health Econ. 13, 461–475 (2004)CrossRefPubMed
18.
Zurück zum Zitat Greene, W.H.: (2002) Econometric analysis (5th ed.). Prentice Hall, New Jersey (2002) Greene, W.H.: (2002) Econometric analysis (5th ed.). Prentice Hall, New Jersey (2002)
19.
Zurück zum Zitat Vazquez-Polo, F.J., Negrin, M., Gonzalez, B.: Using covariates to reduce uncertainty in the economic evaluation of clinical trial data. Health Econ. 14, 545–557 (2005)CrossRefPubMed Vazquez-Polo, F.J., Negrin, M., Gonzalez, B.: Using covariates to reduce uncertainty in the economic evaluation of clinical trial data. Health Econ. 14, 545–557 (2005)CrossRefPubMed
20.
Zurück zum Zitat Briggs, A.H.: A Bayesian approach to stochastic cost-effectiveness analysis. Health Econ. 8, 257–261 (1999)CrossRefPubMed Briggs, A.H.: A Bayesian approach to stochastic cost-effectiveness analysis. Health Econ. 8, 257–261 (1999)CrossRefPubMed
21.
Zurück zum Zitat Chaloner, K., Rhame, F.S.: Quantifying and documenting prior beliefs in clinical trials. Stat. Med. 20, 581–600 (2001)CrossRefPubMed Chaloner, K., Rhame, F.S.: Quantifying and documenting prior beliefs in clinical trials. Stat. Med. 20, 581–600 (2001)CrossRefPubMed
22.
Zurück zum Zitat O’Hagan, A., Stevens, J.W.: Bayesian assessment of sample size for clinical trials of cost-effectiveness. Med. Decis. Making 21, 219–230 (2001)CrossRefPubMed O’Hagan, A., Stevens, J.W.: Bayesian assessment of sample size for clinical trials of cost-effectiveness. Med. Decis. Making 21, 219–230 (2001)CrossRefPubMed
23.
Zurück zum Zitat Thompson, S.G., Barber, J.A.: How should cost data in pragmatic randomised trials be analysed? Br. Med. J. 320(7243), 1197–1200 (2000)CrossRef Thompson, S.G., Barber, J.A.: How should cost data in pragmatic randomised trials be analysed? Br. Med. J. 320(7243), 1197–1200 (2000)CrossRef
24.
Zurück zum Zitat Nixon, R.M., Wonderling, D., Grieve, R.D.: Non-parametric methods for cost-effectiveness analysis: the central limit theorem and the bootstrap compared. Health Econ. 19(3), 316–333 (2010)CrossRefPubMed Nixon, R.M., Wonderling, D., Grieve, R.D.: Non-parametric methods for cost-effectiveness analysis: the central limit theorem and the bootstrap compared. Health Econ. 19(3), 316–333 (2010)CrossRefPubMed
25.
Zurück zum Zitat Manning, W.G., Mullahy, J.: Estimating log models: to transform or not to transform? J. Health Econ. 20(4), 461–494 (2001)CrossRefPubMed Manning, W.G., Mullahy, J.: Estimating log models: to transform or not to transform? J. Health Econ. 20(4), 461–494 (2001)CrossRefPubMed
26.
Zurück zum Zitat O’Hagan, A., Stevens, J.W.: Assessing and comparing costs: how robust are the bootstrap and methods based on asymptotic normality? Health Econ. 12, 33–49 (2003)CrossRefPubMed O’Hagan, A., Stevens, J.W.: Assessing and comparing costs: how robust are the bootstrap and methods based on asymptotic normality? Health Econ. 12, 33–49 (2003)CrossRefPubMed
27.
Zurück zum Zitat Basu, A.: Extended generalised linear models: simultaneous estimation of flexible link and variance functions. Stata J. 5(4), 501–516 (2005) Basu, A.: Extended generalised linear models: simultaneous estimation of flexible link and variance functions. Stata J. 5(4), 501–516 (2005)
28.
Zurück zum Zitat Mihaylova, B., Briggs, A., O’Hagan, A., Thompson, S.G.: Review of statistical methods for analysing healthcare resources and costs. Health Econ. 20(8), 897–916 (2011)CrossRefPubMed Mihaylova, B., Briggs, A., O’Hagan, A., Thompson, S.G.: Review of statistical methods for analysing healthcare resources and costs. Health Econ. 20(8), 897–916 (2011)CrossRefPubMed
29.
Zurück zum Zitat Moreno, E., Giron, F.J., Vazquez-Polo, F.J., Negrin, M.A.: Optimal healthcare decisions: the importance of the covariates in cost-effectiveness analysis. Eur. J. Oper. Res. 218, 512–522 (2012)CrossRef Moreno, E., Giron, F.J., Vazquez-Polo, F.J., Negrin, M.A.: Optimal healthcare decisions: the importance of the covariates in cost-effectiveness analysis. Eur. J. Oper. Res. 218, 512–522 (2012)CrossRef
30.
Zurück zum Zitat McManus, R.J., Mant, J., Bray, E.P., Holder, R., Jones, M.I., Greenfield, S., Kaambwa, B., Banting, M., Bryan, S., Little, P., Williams, B., Hobbs, F.D.R.: Telemonitoring and self-management in the control of hypertension (TASMINH2): a randomised controlled trial. The Lancet. 376(9736), 163-172 (2010) McManus, R.J., Mant, J., Bray, E.P., Holder, R., Jones, M.I., Greenfield, S., Kaambwa, B., Banting, M., Bryan, S., Little, P., Williams, B., Hobbs, F.D.R.: Telemonitoring and self-management in the control of hypertension (TASMINH2): a randomised controlled trial. The Lancet. 376(9736), 163-172 (2010)
31.
Zurück zum Zitat The EuroQol Group: EuroQol—a new facility for the measurement of health-related quality of life. Health Policy 16(3), 199–208 (1990)CrossRef The EuroQol Group: EuroQol—a new facility for the measurement of health-related quality of life. Health Policy 16(3), 199–208 (1990)CrossRef
32.
33.
Zurück zum Zitat Billingham L.J., Abrams, K.R., Jones, D.R.: Methods for the analysis of quality-of-life and survival data in health technology assessment. Health Technology Assessment. 3(10) (1999) Billingham L.J., Abrams, K.R., Jones, D.R.: Methods for the analysis of quality-of-life and survival data in health technology assessment. Health Technology Assessment. 3(10) (1999)
34.
Zurück zum Zitat Dolan, P.: Modeling valuations for EuroQol health states. Med. Care 35(11), 1095–1108 (1997)CrossRefPubMed Dolan, P.: Modeling valuations for EuroQol health states. Med. Care 35(11), 1095–1108 (1997)CrossRefPubMed
35.
Zurück zum Zitat Zellner, A.: An efficient method of estimating seemingly unrelated regression equations and tests for aggregation bias. J. Am. Stat. Assoc. 57, 348–368 (1962)CrossRef Zellner, A.: An efficient method of estimating seemingly unrelated regression equations and tests for aggregation bias. J. Am. Stat. Assoc. 57, 348–368 (1962)CrossRef
36.
Zurück zum Zitat McCullough, P., Nelder, J.A.: Generalized linear models, 2nd edn. Chapman & Hall, London (1989) McCullough, P., Nelder, J.A.: Generalized linear models, 2nd edn. Chapman & Hall, London (1989)
37.
Zurück zum Zitat Anderson, D.R.: Model based inference in the life sciences. Springer, New York (2008) Anderson, D.R.: Model based inference in the life sciences. Springer, New York (2008)
38.
Zurück zum Zitat Stata: Stata programming reference manual, version 11. StataCorp, Texas (2009) Stata: Stata programming reference manual, version 11. StataCorp, Texas (2009)
39.
Zurück zum Zitat Spiegelhalter, D.J., Thomas, A., Best, N.: WinBUGS, version 1.2. MRC Biostatistics Unit, Cambridge (1999) Spiegelhalter, D.J., Thomas, A., Best, N.: WinBUGS, version 1.2. MRC Biostatistics Unit, Cambridge (1999)
40.
Zurück zum Zitat Gomes, M., Grieve, R., Nixon, R., Edmond, S., Carpenter, J., Thompson, S.G.: Methods for covariate adjustment in cost-effectiveness analysis that use cluster randomised trials. Health Econ. 21, 1101–1118 (2012)CrossRefPubMed Gomes, M., Grieve, R., Nixon, R., Edmond, S., Carpenter, J., Thompson, S.G.: Methods for covariate adjustment in cost-effectiveness analysis that use cluster randomised trials. Health Econ. 21, 1101–1118 (2012)CrossRefPubMed
41.
Zurück zum Zitat Austin, P.C.: Balance diagnostics for comparing the distribution of baseline covariates between treatment groups in propensity-score matched samples. Stat. Med. 28, 3083–3107 (2009)CrossRefPubMedPubMedCentral Austin, P.C.: Balance diagnostics for comparing the distribution of baseline covariates between treatment groups in propensity-score matched samples. Stat. Med. 28, 3083–3107 (2009)CrossRefPubMedPubMedCentral
42.
Zurück zum Zitat Rosenbaum, P.R., Rubin, D.B.: Constructing a control-group using multivariate matched sampling methods that incorporate the propensity score. Am. Stat. 39, 33–38 (1985) Rosenbaum, P.R., Rubin, D.B.: Constructing a control-group using multivariate matched sampling methods that incorporate the propensity score. Am. Stat. 39, 33–38 (1985)
43.
Zurück zum Zitat Altman, D.G.: Comparability of randomised groups. Statistician 34(1), 125–136 (1985)CrossRef Altman, D.G.: Comparability of randomised groups. Statistician 34(1), 125–136 (1985)CrossRef
44.
Zurück zum Zitat Zhou, X.H.: Inferences about population means of health care costs. Stat. Methods Med. Res. 11, 327–339 (2002)CrossRefPubMed Zhou, X.H.: Inferences about population means of health care costs. Stat. Methods Med. Res. 11, 327–339 (2002)CrossRefPubMed
45.
Zurück zum Zitat Nixon, R.M., Thompson, S.G.: Parametric modelling of cost data in medical studies. Stat. Med. 23, 1311–1331 (2004)CrossRefPubMed Nixon, R.M., Thompson, S.G.: Parametric modelling of cost data in medical studies. Stat. Med. 23, 1311–1331 (2004)CrossRefPubMed
46.
Zurück zum Zitat Nixon, R.M., Wonderling, D., Grieve, R.D.: Non-parametric methods for cost-effectiveness analysis: the central limit theorem and the bootstrap compared. Health Econ. 19, 316–333 (2010)CrossRefPubMed Nixon, R.M., Wonderling, D., Grieve, R.D.: Non-parametric methods for cost-effectiveness analysis: the central limit theorem and the bootstrap compared. Health Econ. 19, 316–333 (2010)CrossRefPubMed
47.
Zurück zum Zitat Cantoni, E., Ronchetti, E.: A robust approach for skewed and heavy-tailed outcomes in the analysis of health care expenditures. J. Health Econ. 25(2), 198–213 (2006)CrossRefPubMed Cantoni, E., Ronchetti, E.: A robust approach for skewed and heavy-tailed outcomes in the analysis of health care expenditures. J. Health Econ. 25(2), 198–213 (2006)CrossRefPubMed
48.
Zurück zum Zitat Basu, A., Manca, A.: Regression estimators for generic health-related quality of life and quality-adjusted life years. Med. Decis. Making 32, 56–69 (2012)CrossRefPubMed Basu, A., Manca, A.: Regression estimators for generic health-related quality of life and quality-adjusted life years. Med. Decis. Making 32, 56–69 (2012)CrossRefPubMed
49.
Zurück zum Zitat Kieschnick, R., McCullough, B.D.: Regression analysis of variates observed on (0,1): percentages, proportions and fractions. Stat. Model. 3, 193–213 (2003)CrossRef Kieschnick, R., McCullough, B.D.: Regression analysis of variates observed on (0,1): percentages, proportions and fractions. Stat. Model. 3, 193–213 (2003)CrossRef
50.
Zurück zum Zitat Smithson, M., Verkuilen, J.: A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables. Psychol. Methods 11(1), 54–71 (2006)CrossRefPubMed Smithson, M., Verkuilen, J.: A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables. Psychol. Methods 11(1), 54–71 (2006)CrossRefPubMed
51.
Zurück zum Zitat Higgins, J.P.T., Green, S. (eds.) Cochrane handbook for systematic reviews of interventions version 5.1.0 [updated March 2011]. The Cochrane Collaboration, 2011. Available from www.cochrane-handbook.org Higgins, J.P.T., Green, S. (eds.) Cochrane handbook for systematic reviews of interventions version 5.1.0 [updated March 2011]. The Cochrane Collaboration, 2011. Available from www.​cochrane-handbook.​org
52.
Zurück zum Zitat Welton, N.J., Sutton, A.J., Cooper, N.J., Abrams, K.R., Ades, A.E.: Evidence synthesis for decision making in healthcare. John Wiley: Chichester, UK (2012) Welton, N.J., Sutton, A.J., Cooper, N.J., Abrams, K.R., Ades, A.E.: Evidence synthesis for decision making in healthcare. John Wiley: Chichester, UK (2012)
53.
Zurück zum Zitat Bernardo, J., Smith, A.F.M.: Bayesian theory. John Wiley: New York. (1994) Bernardo, J., Smith, A.F.M.: Bayesian theory. John Wiley: New York. (1994)
55.
Zurück zum Zitat Cook, T.D., DeMets, D.L.: Introduction to statistical methods for clinical trials. Chapman & Hall/CRC, Boca Raton (2008) Cook, T.D., DeMets, D.L.: Introduction to statistical methods for clinical trials. Chapman & Hall/CRC, Boca Raton (2008)
56.
Zurück zum Zitat Pocock, S.J., Assmann, S.E., Enos, L.E., Kasten, L.E.: Subgroup analysis, covariate adjustment and baseline comparisons in clinical trial reporting: current practice and problems. Stat. Med. 21, 2917–2930 (2002)CrossRefPubMed Pocock, S.J., Assmann, S.E., Enos, L.E., Kasten, L.E.: Subgroup analysis, covariate adjustment and baseline comparisons in clinical trial reporting: current practice and problems. Stat. Med. 21, 2917–2930 (2002)CrossRefPubMed
57.
Zurück zum Zitat Sun, X., Ioannidis, J.P., Agoritsas, A., Alba, A.C., Guyatt, G.: How to use a subgroup analysis. Users’ guides to the medical literature. JAMA 311(4), 405–411 (2014)CrossRefPubMed Sun, X., Ioannidis, J.P., Agoritsas, A., Alba, A.C., Guyatt, G.: How to use a subgroup analysis. Users’ guides to the medical literature. JAMA 311(4), 405–411 (2014)CrossRefPubMed
58.
Zurück zum Zitat Sculpher, M.J.: Heterogeneity in cost-effectiveness analysis. Pharmacoeconomics 26(9), 799–806 (2008)CrossRefPubMed Sculpher, M.J.: Heterogeneity in cost-effectiveness analysis. Pharmacoeconomics 26(9), 799–806 (2008)CrossRefPubMed
59.
Zurück zum Zitat Kaambwa, B., Bryan, S., Jowett, S., Mant, J., Bray, E., P., Hobbs, R.F.D., Holder, R., Jones, M.I., Little, P., Williams, B., McManus, R.J.: Telemonitoring and self-management in the control of hypertension (TASMINH2): a cost-effectiveness analysis. European Journal of Preventive Cardiology. 0(00), 1–14 (2013) Kaambwa, B., Bryan, S., Jowett, S., Mant, J., Bray, E., P., Hobbs, R.F.D., Holder, R., Jones, M.I., Little, P., Williams, B., McManus, R.J.: Telemonitoring and self-management in the control of hypertension (TASMINH2): a cost-effectiveness analysis. European Journal of Preventive Cardiology. 0(00), 1–14 (2013)
60.
Zurück zum Zitat Herdman, M., Gudex, C., Lloyd, A.: Development and preliminary testing of the new five level version of EQ-5D (EQ-5D-5L). Qual. Life Res. 20(10), 1727–1736 (2011)CrossRefPubMedPubMedCentral Herdman, M., Gudex, C., Lloyd, A.: Development and preliminary testing of the new five level version of EQ-5D (EQ-5D-5L). Qual. Life Res. 20(10), 1727–1736 (2011)CrossRefPubMedPubMedCentral
Metadaten
Titel
Choice of statistical model for cost-effectiveness analysis and covariate adjustment: empirical application of prominent models and assessment of their results
verfasst von
Theodoros Mantopoulos
Paul M. Mitchell
Nicky J. Welton
Richard McManus
Lazaros Andronis
Publikationsdatum
07.10.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
The European Journal of Health Economics / Ausgabe 8/2016
Print ISSN: 1618-7598
Elektronische ISSN: 1618-7601
DOI
https://doi.org/10.1007/s10198-015-0731-8

Weitere Artikel der Ausgabe 8/2016

The European Journal of Health Economics 8/2016 Zur Ausgabe