Abstract
The application of Bayesian statistical analyses has been facilitated in recent years by methodological advances and an increasing complexity necessitated within research. Substantial debate has historically accompanied this analytic approach relative to the frequentist method, which is the predominant statistical ideology employed in clinical studies. While the essence of the debate between the two branches of statistics centres on differences in the use of prior information and the definition of probability, the ramifications involve the breadth of research design, analysis and interpretation. The purpose of this paper is to discuss the application of frequentist and Bayesian statistics in the pharmacoeconomic assessment of healthcare technology. A description of both paradigms is offered in the context of potential advantages and disadvantages, and applications within pharmacoeconomics are briefly addressed. Additional considerations are presented to stimulate further development and to direct appropriate applications of each method such that the integrity and robustness of scientific inference be strengthened.
Similar content being viewed by others
References
Bayes RT. An essay toward solving a problem in the doctrine of chances. Phil Trans Royal Soc London 1763; 53: 370–418
Efron B. Controversies in the foundation of statistics. Am Math Month 1978; 85: 231–246
Edwards A. A history of likelihood. Internat Stat Rev 1974; 42: 9–15
Kennedy P. A guide to econometrics. 5th ed. Cambridge (MA): MIT Press, 2003
Spiegelhalter DJ, Myles JP, Jones DR, et al. An introduction to Bayesian methods in health technology assessment. BMJ 1999; 319: 508–512
Speigelhalter DJ, Abrams KR, Myles JP. Bayesian approaches to clinical trials and health-care evaluation. West Sussex (UK): John Wiley & Sons, 2004
Lilford RJ, Braunholtz D. Who’s afraid of Thomas Bayes? J Epidem Community Health 2000; 54: 731–739
Shih YCT. Bayesian approach in pharmacoeconomics: relevance to decision-makers. Expert Rev Pharmacoeconomics Outcomes Res 2003; 3: 237–250
Dunson DB. Practical advantages of Bayesian analysis of epidemiologic data. Am J Epidem 2001; 153: 1222–1226
Spiegelhalter DJ. Incorporating Bayesian ideas into health-care evaluation. Stat Sci 2004; 19: 156–174
Stangl DK, Berry DA. Bayesian statistics in medicine: where are we and where should we be going? Sankhya: Indian J Stat 1998; 60: 176–195
Lilford RJ. The statistical basis of public policy: a paradigm shift is overdue. BMJ 1996; 313: 603–607
Wilson G. Tides of change: is Bayesianism the new paradigm in statistics? J Stat Plan Inference 2003; 113: 371–374
Bayarri MJ, Berger JO. The interplay of Bayesian and frequentist analysis. Stat Sci 2004; 19: 58–80
Wilkinson GN. On resolving the controversy in statistical inference [with discussion]. J Royal Stat Soc Series B (Methodology) 1977; 39: 119–171
Goodman SN. Toward evidence-based medical statistics: 1. The p-value fallacy. Ann Intern Med 1999; 130: 995–1004
Emerson SS, Kittelson JM, Gillen DL. Bayesian evaluation of group sequential clinical trial designs. University of Washington Biostatistics Working Papers Series: paper 242 [online]. Available from URL: http://www.bepress.com/uwbiostat/paper242 [Accessed 2005 Jul 4]
Bland JM, Altman DG. Bayesians and frequentists. BMJ 1998; 317: 1151
Freund JE. Mathematical statistics. 2nd ed. Englewood Cliffs (NJ): Prentice Hall, 1971
Grinstead CM, Snell JL. Introduction to probability. 2nd ed. Washington, DC: American Mathematical Society, 1997
Dorfman JH. Bayesian economics through numerical methods: a guide to decision-making with prior information. New York (NY): Springer, 1997
Jeffreys H. Theory of probability. 3rd ed. Oxford (UK): Clarendon, 1961
O’Hagan A, Luce B. A primer on Bayesian analysis in health economics and outcomes research. Sheffield (UK): Centre for Bayesian Statistics in Health Economics, 2003
Skrepnek GH. Regression methods in the empirical analysis of health care data. J Manag Care Pharm 2005; 11: 240–251
Casella G, Berger RL. Statistical inference. 2nd ed. Belmont (CA): Duxbury, 2001
Woolridge JM. Introductory econometrics: a modern approach. 2nd ed. Mason (OH): Thomson Southwestern, 2003
Neyman J. Frequentist probability and frequentist statistics. Synthese 1977; 36: 97–131
Skrepnek GH. Cost-effectiveness analysis. In: Bootman JL, Townsend RJ, McGhan WF, editors. Principles of pharmacoeconomics. 3rd ed. Cincinnati (OH): W Harvey Whitney, 2005
Sterne JAC, Smith GD. Sifting the evidence: what’s wrong with significance tests. BMJ 2001; 322: 226–231
Berger JO, Sellke T. Testing a point null hypothesis: the irreconcilability of p-values and evidence (with discussion). J Am Stat Assoc 1987; 82: 112–139
Cowles M, Davis C. On the origins of the.05 level of statistical significance. Am Psychol 1982; 37: 553–558
Holm S. A simple sequentially rejective multiple test procedure. Scand J Stat 1979; 6: 65–70
Rothman KJ. No adjustments needed for multiple comparisons. Epidem 1990; 1: 43–46
Theil H, Goldberger AS. On pure and mixed statistical estimation in economics. Internat Econ Rev 1961; 2: 65–78
Goodman SN. Toward evidence-based medical statistics: 2. The Bayes Factor. Ann Intern Med 1999; 130: 1005–1013
Good I. Probability and the weighing of evidence. New York (NY): Charles Griffin, 1950
Berry DA. A case for Bayesianism in clinical trials. Stat Med 1993; 12: 1377–1393
DeGroot MH. Optimal statistical decisions. New York (NY): McGraw-Hill, 1970
Cornfield J. Recent methodological contributions to clinical trials. Am J Epidem 1976; 104: 408–421
Bala MV, Mauskopf J. Estimating the Bayesian loss function: a conjoint analysis approach. Intern J Technol Assess Health Care 2001; 17: 27–37
Briggs AH. A Bayesian approach to stochastic cost-effectiveness analysis. Health Econ 1999; 8: 257–261
Luce BR, Claxton K. Redefining the analytic approach to pharmacoeconomics. Health Econ 1999; 8: 187–189
Ades AE, Sculpher M, Sutton A, et al. Bayesian methods for evidence synthesis in cost-effectiveness analysis. Pharmacoeconomics 2006; 24: 1–19
Qin D. Bayesian econometrics: the first twenty years. Econ Theory 1996; 12: 500–516
Geman S, Geman D. Stochastic relaxation, Gibbs distributions, and Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell 1984; 6: 721–741
Brooks SP. Markov Chain Monte Carlo method and its application. Statistician 1998; 47: 69–100
Andrieu C, Doucet A, Robert CP. Computational advances for and from Bayesian analysis. Stat Sci 2004; 19: 118–127
Winkler RL. Why Bayesian analysis hasn’t caught on in health-care decision making. Internat J Tech Assess Health Care 2001; 17: 56–66
Gill CJ, Sabin L, Schmid CH. Why clinicians are natural Bayesians. BMJ 2005; 330: 1080–1083
Sheiner LB, Beal SL. Bayesian individualization of pharmacokinetics: simple implementation and comparison with non-Bayesian methods. J Pharm Sci 1982; 71: 1344–1348
Ashby D, Smith AFM. Evidence-based medicine as Bayesian decision-making. Stat Med 2000; 19: 3291–3305
Bernardo JM, Smith AFM. Bayesian theory. New York (NY): Wiley, 1994
The GUSTO Investigators. An international randomized trial comparing four thrombolytic strategies for acute myocardial infarction. N Engl J Med 1993; 329: 673–682
Brophy JM, Joseph L. Placing trials in context using Bayesian analysis. JAMA 1995; 273: 871–875
Troiani JS, Carlin BP. Comparison of Bayesian, classical, and heuristic approaches in identifying acute disease events in lung transplant recipients. Stat Med 2004; 23: 803–824
Delaney BC, Holder RL, Allan TF, et al. A comparison of Bayesian and maximum likelihood methods to determine the performance of a point of care test for Heliobacter pylori in the office setting. Med Decis Making 2003; 23: 21–30
Bloom BS, de Pouvourville N, Libert S. Classic or Bayesian research design and analysis: does it make a difference? Intern J Technol Assess Health Care 2002; 18: 120–126
Spiegelhalter D, Myles J, Jones D, et al. Bayesian methods in health technology assessment: a review. Health Technol Assess 2000; 4: 1–130
Kadane JB. Prime time for Bayes. Control Clin Trial 1995; 16: 313–318
Fisher LD. Comments on Bayesian and frequentist analysis and interpretation of clinical trials. Control Clin Trial 1996; 17: 423–434
Urbach P. The value of randomization and control in clinical trials. Stat Med 1993; 12: 1421–1431
Papineau D. The virtues of randomization. Brit J Phil Sci 1994; 455: 437–450
Berry DA. Bayesian statistics and the efficiency and ethics of clinical trials. Stat Sci 2004; 19: 175–187
Breslow N. Biostatistics and Bayes. Stat Sci 1990; 5: 269–284
Pocock S. The combination of randomized and historical controls in clinical trials. J Chron Dis 1976; 29: 175–188
International Conference on Harmonization E9 Expert Working Group. Statistical principles for clinical trials: ICH harmonized tripartite guideline. Stat Med 1999; 18: 1905–1942
Senn S. Consensus and controversy in pharmaceutical statistics (with discussion). Statistician 2000; 49: 135–176
Campbell G. A regulatory perspective for Bayesian clinical trials. Washington, DC: US FDA, 1999
Briggs AH. A Bayesian approach to stochastic cost-effectiveness analysis: an illustration and application to blood pressure control in type 2 diabetes. Internat J Technol Assess Health Care 2001; 17: 69–82
Fryback DC, Chinnis JOP, Ulvila JW. Bayesian cost-effectiveness analysis: an example using the GUSTO trial. Internat J Technol Assess Health Care 2001; 17: 83–97
Heitjan DF, Moskowitz AJ, Whang W. Bayesian estimation of cost-effectiveness ratios from clinical trials. Health Econ 1999; 8: 191–201
O’Hagan A, Stevens JW, Montmartin J. Inference for the cost-effectiveness acceptability curve and cost-effectiveness ratio. Pharmacoeconomics 2000; 17: 339–349
O’Hagan A, Stevens JW, Montmartin J. Bayesian cost-effectiveness analysis from clinical trial data. Stat Med 2001; 20: 733–753
O’Hagan A, Stevens JW. A framework for cost-effectiveness analysis from clinical trial data. Health Econ 2001; 10: 303–305
O’Hagan A, Stevens JW. Bayesian methods for design and analysis of cost-effectiveness trials in the evaluation of healthcare technologies. Stat Meth Med Res 2002; 11: 469–490
van Hout BA, Al MJ, Gordon GS, et al. Costs, effects, and C/E ratios alongside a clinical trial. Health Econ 1994; 3: 309–319
Stinnett AA, Mullahy J. A new framework for the analysis of uncertainty in cost-effectiveness analysis. Med Decis Making 1998; 18: 68s–80s
Lothgren M, Zethraeus N. Definition, interpretation and calculation of cost-effectiveness acceptability curves. Health Econ 2000; 9: 623–630
Berger J, Phillipe A, Robert C. Estimation of quadratic functions: noninformative priors for non-centrality parameters. Statist Sinica 1998; 8: 359–376
Berger J. Statistical decision theory and Bayesian analysis. 2nd ed. New York (NY): Springer, 1985
Eaton ML. Group invariance applications in statistics. Hayward (CA): IMS, 1989
Robert CP. The Bayesian choice. 2nd ed. New York (NY): Springer, 2001
Chambers ML. A simple problem with strikingly different frequentist and Bayesian solutions. J Royal Stat Soc Series B (Methodological) 1970; 32: 278–282
Bartholomew DJ. A comparison of some Bayesian and frequentist inferences. Biometrika 1965; 52: 19–35
Bartholomew DJ. A comparison of frequentist and Bayesian approaches to inference with prior knowledge: foundations of statistical inference (Proc Sympos, Univ Waterloo, Waterloo, Ont, 1970). Toronto (ON): Holt, Rinehart, and Winston, 1970: 34
Briggs AH, Wonderling DE, Mooney CZ. Pulling cost-effectiveness analysis up by its bootstraps: a non-parametric approach to confidence interval estimation. Health Econ 1997; 6: 327–340
Spiegelhalter DJ, Best NG. Bayesian approaches to multiple sources of evidence and uncertainty in complex cost-effectiveness analyses. Stat Med 2003; 22: 3687–3709
Cooper NJ, Abrams KR, Sutton AJ, et al. Use of Bayesian methods for Markov modeling in cost-effectiveness analysis: an application to taxane use in advanced breast cancer [technical report, 02-02]. Leicester (UK): University of Leicester, 2002
Sendi PP, Craig BA, Meier G, et al. Cost-effectiveness of azithromycin for preventing Mycobacterium avium complex infection in HIV-positive patients in the era of highly active antiretroviral therapy. J Antimicrob Chemo 1999; 44: 811–817
Matchar DB, Samsa GP, Matthews JR, et al. The stroke prevention policy model: linking evidence and clinical decisions. Ann Intern Med 1997; 127: 704–711
Al MJ, van Hout BA. A Bayesian approach to economic analyses of clinical trials: the case of stenting versus balloon angioplasty. Health Econ 2000; 9: 599–609
Samsa GP, Reutter RA, Parmigiani G, et al. Performing cost-effectiveness analysis by integrating randomised trial data with a comprehensive decision model: application to treatment of acute ischemic stroke. Clin Epidem 1999; 52: 259–271
Heitjan DF, Li H. Bayesian estimation of cost-effectiveness: an importance-sampling approach. Health Econ 2004; 13: 191–198
Craig BA, Fryback DG, Klein R, et al. A Bayesian approach to modeling the natural history of a chronic condition from observations with intervention. Stat Med 1999; 18: 1355–1371
Howard RA. Information value theory. IEEE Trans System Sci Cybernetics 1966; SCC2: 22–26
Howard RA. Value of information lotteries. IEEE Trans System Sci Cybernetics 1967; SCC3: 24–60
Claxton K, Neumann PJ, Araki S, et al. Bayesian value-of-information analysis. Internat J Technol Assess Health Care 2001; 17: 38–55
Claxton K, Posnett J. An economic approach to clinical trial design and research priority-setting. Health Econ 1996; 5: 513–524
Claxton K. Bayesian approaches to the value of information: implications for the regulation of new pharmaceuticals. Health Econ 1999; 8: 269–274
Neumann PJ, Claxton K, Weinstein MC. The FDA’s regulation of health economic information. Health Affairs 2000; 19: 129–137
Claxton K, Schulper M, Drummond M. A rational framework for decision making by the National Institute for Clinical Excellence (NICE). Lancet 2002; 360: 711–715
Fenwick E, Claxton K, Schulper M. Representing uncertainty: the role of cost-effectiveness acceptability curves. Health Econ 2001; 10: 779–787
Felli JC, Hazen GB. A Bayesian approach to sensitivity analyses. Health Econ 1999; 8: 263–268
Parmigiani G. Modeling in medical decision making: a Bayesian approach. Hoboken (NJ): John Wiley & Sons, 2002
Cooper NJ, Sutton AJ, Abrams KR, et al. Comprehensive decision analytic modeling in economic evaluation: a Bayesian approach. Health Economics 2004; 13: 203–226
Harrell F, Shih YCT. Using full probability models to compute probabilities of actual interest to decision makers. Internat J Technol Assess Health Care 2001; 17: 17–26
Stangl DK. Bridging the gap between statistical analysis and decision making in public health research. Stat Med 2005; 24: 503–511
Eddy DM, Hasselblad V, Schachter RD. Meta-analysis by the confidence profile method: the statistical synthesis of evidence. Boston (MA): Academic Press, 1992
Briggs AH. Handling uncertainty in cost-effectiveness models. Pharmacoeconomics 2000; 17: 479–500
Vanness DJ, Kim WR. Bayesian estimation, simulation and uncertainty analysis: the cost-effectiveness of ganciclovir prophylaxis in liver transplantation. Health Econ 2002; 11: 551–566
Brennan P. Statistical basis of public policy: epidemiology does not need Bayesian inference [letter]. BMJ 1997; 314: 72
Kass RE, Greenhouse JB. A Bayesian perspective: comment on’ Investigating therapies of potentially great benefit: ECMO’ by JH Ware. Statist Sci 1989; 4: 310–317
Lindley DV. Theory and practice of Bayesian statistics. Statistician 1983; 32: 1–11
Dawid AP, Stone M, Zidek JV. Marginalization paradoxes in Bayesian and structural inference (with discussion). J Royal Stat Soc Series B (Methodological) 1973; 35: 189–233
O’Neill R. Early stopping rules workshop: conclusions. Stat Med 1994; 13: 1493–1494
Senn S. Statistical issues in drug development. New York (NY): John Wiley & Sons, 2002
van der Wilt GJ, Rovers M, Straatman H, et al. Policy relevance of Bayesian statistics overestimated? Intern J Technol Assess Health Care 2004; 20: 488–492
Richardson S, Leblond L. Some comments on misspecification of priors in Bayesian modeling of measurement error problems. Stat Med 1997; 16: 203–213
Wald A. Statistical decision functions. New York (NY): Wiley, 1950
Ho CH. Some frequentist properties of a Bayesian method in clinical trials. Biom J 1991; 33: 735–740
Griffiths WE. Bayesian econometrics and how to get rid of those wrong signs. Rev Market Agricult Econ 1988; 56: 36–56
Sheingold SH. Can Bayesian methods make data and analyses more relevant to decision makers? Internat J Tech Assess Health Care 2001; 17: 114–122
Lindley DV. Is our view of Bayesian statistics too narrow? (with discussion). Bayesian Stat 1992; 4: 1–15
Greenland S. Response: Bayesian perspectives for epidemiological research [comment]. Int J Epidemiol 2006; 35: 777–778
Greenland S. Bayesian perspectives for epidemiological research: I. Foundations and basic methods. Int J Epidemiol 2006; 35: 765–775
Acknowledgements
No sources of funding were used to assist in the preparation of this article. The author has no conflicts of interest that are directly relevant to the content of this article.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Skrepnek, G.H. The Contrast and Convergence of Bayesian and Frequentist Statistical Approaches in Pharmacoeconomic Analysis. Pharmacoeconomics 25, 649–664 (2007). https://doi.org/10.2165/00019053-200725080-00003
Published:
Issue Date:
DOI: https://doi.org/10.2165/00019053-200725080-00003