The Contrast and Convergence of Bayesian and Frequentist Statistical Approaches in Pharmacoeconomic Analysis

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.

[1]  A O'Hagan,et al.  Bayesian methods for design and analysis of cost-effectiveness trials in the evaluation of health care technologies , 2002, Statistical methods in medical research.

[2]  L B Sheiner,et al.  Bayesian individualization of pharmacokinetics: simple implementation and comparison with non-Bayesian methods. , 1982, Journal of pharmaceutical sciences.

[3]  B. Bloom,et al.  Classic or Bayesian research design and analysis. Does it make a difference? , 2002, International journal of technology assessment in health care.

[4]  R. Klein,et al.  A Bayesian approach to modelling the natural history of a chronic condition from observations with intervention. , 1999, Statistics in medicine.

[5]  S. Sheingold CAN BAYESIAN METHODS MAKE DATA AND ANALYSES MORE RELEVANT TO DECISION MAKERS? , 2001, International Journal of Technology Assessment in Health Care.

[6]  J. Ware Investigating Therapies of Potentially Great Benefit: ECMO , 1989 .

[7]  D. Spiegelhalter,et al.  Disease Mapping With WinBUGS and MLwiN, Bayesian Approaches to Clinical Trials and Health Care Evaluation , 2004 .

[8]  J Lipscomb,et al.  Performing cost-effectiveness analysis by integrating randomized trial data with a comprehensive decision model: application to treatment of acute ischemic stroke. , 1999, Journal of clinical epidemiology.

[9]  E. J. PubMed Citation,et al.  An International Randomized Trial Comparing Four Thrombolytic Strategies for Acute Myocardial Infarction , 2009 .

[10]  S J Pocock,et al.  The combination of randomized and historical controls in clinical trials. , 1976, Journal of chronic diseases.

[11]  K Claxton,et al.  An economic approach to clinical trial design and research priority-setting. , 1996, Health economics.

[12]  David Lindley,et al.  A Class of Utility Functions , 1976 .

[13]  R J Lilford,et al.  For Debate: The statistical basis of public policy: a paradigm shift is overdue , 1996, BMJ.

[14]  Andrew H. Briggs,et al.  Handling Uncertainty in Cost-Effectiveness Models , 2000, PharmacoEconomics.

[15]  W Ray Kim,et al.  Bayesian estimation, simulation and uncertainty analysis: the cost-effectiveness of ganciclovir prophylaxis in liver transplantation. , 2002, Health economics.

[16]  G. N. Wilkinson On Resolving the Controversy in Statistical Inference , 1977 .

[17]  Stephen P. Brooks,et al.  Markov chain Monte Carlo method and its application , 1998 .

[18]  J. Berger,et al.  Testing a Point Null Hypothesis: The Irreconcilability of P Values and Evidence , 1987 .

[19]  Gerry Leversha,et al.  Statistical inference (2nd edn), by Paul H. Garthwaite, Ian T. Jolliffe and Byron Jones. Pp.328. £40 (hbk). 2002. ISBN 0 19 857226 3 (Oxford University Press). , 2003, The Mathematical Gazette.

[20]  J. Lewis,et al.  Statistical principles for clinical trials (ICH E9): an introductory note on an international guideline. , 1999, Statistics in medicine.

[21]  P. van den Broek,et al.  Policy relevance of Bayesian statistics overestimated? , 2004, International Journal of Technology Assessment in Health Care.

[22]  David M. Eddy,et al.  Meta-analysis by the confidence profile method , 1992 .

[23]  Adrian F. M. Smith,et al.  Evidence-based medicine as Bayesian decision-making. , 2000, Statistics in medicine.

[24]  John N. Tsitsiklis,et al.  Introduction to Probability , 2002 .

[25]  Eric R. Ziegel,et al.  Statistical Issues in Drug Development , 1997 .

[26]  M C Weinstein,et al.  Bayesian value-of-information analysis. An application to a policy model of Alzheimer's disease. , 2001, International journal of technology assessment in health care.

[27]  M. Stone,et al.  Marginalization Paradoxes in Bayesian and Structural Inference , 1973 .

[28]  D. Berry Bayesian Statistics and the Efficiency and Ethics of Clinical Trials , 2004 .

[29]  R J Lilford,et al.  Who's afraid Of Thomas Bayes? , 2000, Journal of epidemiology and community health.

[30]  J B Kadane,et al.  Prime time for Bayes. , 1995, Controlled clinical trials.

[31]  James O. Berger,et al.  The interplay of Bayesian and frequentist analysis , 2004 .

[32]  Charles M. Grinstead,et al.  Introduction to probability , 1999, Statistics for the Behavioural Sciences.

[33]  William E. Griffiths,et al.  Bayesian Econometrics and How to Get Rid of Those Wrong Signs , 1988 .

[34]  M. A. Best Bayesian Approaches to Clinical Trials and Health‐Care Evaluation , 2005 .

[35]  R. L. Winkler,et al.  WHY BAYESIAN ANALYSIS HASN'T CAUGHT ON IN HEALTHCARE DECISION MAKING , 2001, International Journal of Technology Assessment in Health Care.

[36]  A Gafni,et al.  Cost-effectiveness of azithromycin for preventing Mycobacterium avium complex infection in HIV-positive patients in the era of highly active antiretroviral therapy. The Swiss HIV Cohort Study. , 1999, The Journal of antimicrobial chemotherapy.

[37]  David R. Jones,et al.  An introduction to bayesian methods in health technology assessment , 1999, BMJ.

[38]  Daniel F Heitjan,et al.  Bayesian estimation of cost-effectiveness: an importance-sampling approach. , 2004, Health economics.

[39]  T. Bayes An essay towards solving a problem in the doctrine of chances , 2003 .

[40]  K Claxton,et al.  Redefining the analytical approach to pharmacoeconomics. , 1999, Health economics.

[41]  R. Chisin Cost-Effectiveness Analysis , 2009, Journal of Nuclear Medicine.

[42]  H. Jeffreys,et al.  Theory of probability , 1896 .

[43]  S. Goodman Toward Evidence-Based Medical Statistics. 1: The P Value Fallacy , 1999, Annals of Internal Medicine.

[44]  M C Weinstein,et al.  The FDA's regulation of health economic information. , 2000, Health affairs.

[45]  S. Holm A Simple Sequentially Rejective Multiple Test Procedure , 1979 .

[46]  Y. Shih Bayesian approach in pharmacoeconomics: relevance to decision-makers , 2003, Expert review of pharmacoeconomics & outcomes research.

[47]  M. Degroot Optimal Statistical Decisions , 1970 .

[48]  M. Bala,et al.  ESTIMATING THE BAYESIAN LOSS FUNCTION , 2001, International Journal of Technology Assessment in Health Care.

[49]  David Lindley,et al.  Statistical Decision Functions , 1951, Nature.

[50]  N. Zethraeus,et al.  Definition, interpretation and calculation of cost-effectiveness acceptability curves. , 2000, Health economics.

[51]  M. Drummond,et al.  A rational framework for decision making by the National Institute For Clinical Excellence (NICE) , 2002, The Lancet.

[52]  Christian P. Robert,et al.  The Bayesian choice , 1994 .

[53]  A Simple Problem with Strikingly Different Frequentist and Bayesian Solutions , 1970 .

[54]  L D Fisher,et al.  Comments on Bayesian and frequentist analysis and interpretation of clinical trials. , 1996, Controlled clinical trials.

[55]  Daniel L Gillen,et al.  Bayesian evaluation of group sequential clinical trial designs , 2007, Statistics in medicine.

[56]  David Papineau,et al.  The Virtues of Randomization , 1994, The British Journal for the Philosophy of Science.

[57]  J O Chinnis,et al.  BAYESIAN COST-EFFECTIVENESS ANALYSIS , 2001, International Journal of Technology Assessment in Health Care.

[58]  Ronald A. Howard,et al.  Information Value Theory , 1966, IEEE Trans. Syst. Sci. Cybern..

[59]  Sander Greenland,et al.  Bayesian perspectives for epidemiological research: I. Foundations and basic methods. , 2006, International journal of epidemiology.

[60]  D. Spiegelhalter Incorporating Bayesian Ideas into Health-Care Evaluation , 2004 .

[61]  J. Berger Statistical Decision Theory and Bayesian Analysis , 1988 .

[62]  Roger L Holder,et al.  A Comparison of Bayesian and Maximum Likelihood Methods to Determine the Performance of a Point of Care Test for Helicobacter pylori in the Office Setting , 2003, Medical decision making : an international journal of the Society for Medical Decision Making.

[63]  Dalene K Stangl,et al.  Bridging the gap between statistical analysis and decision making in public health research , 2005, Statistics in medicine.

[64]  Jeffrey H. Dorfman Bayesian Economics Through Numerical Methods: A Guide to Econometrics and Decision-Making with Prior Information , 1997 .

[65]  James O. Berger,et al.  ESTIMATION OF QUADRATIC FUNCTIONS: NONINFORMATIVE PRIORS FOR NON-CENTRALITY PARAMETERS , 1998 .

[66]  Jonathan A C Sterne,et al.  Sifting the evidence—what's wrong with significance tests? , 2001, BMJ : British Medical Journal.

[67]  A H Briggs,et al.  A Bayesian approach to stochastic cost-effectiveness analysis. , 1999, Health economics.

[68]  D B Dunson,et al.  Commentary: practical advantages of Bayesian analysis of epidemiologic data. , 2001, American journal of epidemiology.

[69]  R. Robinson Economic Evaluation and Health Care Cost-effectiveness analysis , 2006 .

[70]  J. Neyman,et al.  Frequentist probability and frequentist statistics , 1977, Synthese.

[71]  A H Briggs,et al.  Pulling cost-effectiveness analysis up by its bootstraps: a non-parametric approach to confidence interval estimation. , 1997, Health economics.

[72]  F. Harrell,et al.  USING FULL PROBABILITY MODELS TO COMPUTE PROBABILITIES OF ACTUAL INTEREST TO DECISION MAKERS , 2001, International Journal of Technology Assessment in Health Care.

[73]  Sj Senn Consensus and controversy in pharmaceutical statistics. (With discussion) , 2000 .

[74]  M. L. Eaton Group invariance applications in statistics , 1989 .

[75]  A. Goldberger,et al.  On Pure and Mixed Statistical Estimation in Economics , 1961 .

[76]  K J Rothman,et al.  No Adjustments Are Needed for Multiple Comparisons , 1990, Epidemiology.

[77]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[78]  L. Joseph,et al.  Placing trials in context using Bayesian analysis. GUSTO revisited by Reverend Bayes. , 1995, JAMA.

[79]  A A Stinnett,et al.  Net Health Benefits , 1998, Medical decision making : an international journal of the Society for Medical Decision Making.

[80]  Norman E. Breslow,et al.  Biostatistics and Bayes , 1990 .

[81]  W. Mcghan,et al.  Principles of Pharmacoeconomics , 1990 .

[82]  A H Briggs,et al.  A BAYESIAN APPROACH TO STOCHASTIC COST-EFFECTIVENESS ANALYSIS , 2001, International Journal of Technology Assessment in Health Care.

[83]  Ronald A. Howard,et al.  Value of Information Lotteries , 1967, IEEE Trans. Syst. Sci. Cybern..

[84]  A J Moskowitz,et al.  Bayesian estimation of cost-effectiveness ratios from clinical trials. , 1999, Health economics.

[85]  M J Al,et al.  A Bayesian approach to economic analyses of clinical trials: the case of stenting versus balloon angioplasty. , 2000, Health economics.

[86]  Sander Greenland Response: Bayesian perspectives for epidemiological research , 2006 .

[87]  Lawrence Joseph,et al.  Placing Trials in Context Using Bayesian Analysis , 2009 .

[88]  David J Spiegelhalter,et al.  Bayesian approaches to multiple sources of evidence and uncertainty in complex cost‐effectiveness modelling , 2003, Statistics in medicine.

[89]  L. Stein,et al.  Probability and the Weighing of Evidence , 1950 .

[90]  Bradley Efron Controversies in the Foundations of Statistics , 1978 .

[91]  A. W. F. Edwards,et al.  A History of Likelihood , 1974 .

[92]  Giovanni Parmigiani,et al.  The Stroke Prevention Policy Model: Linking Evidence and Clinical Decisions , 1997, Annals of Internal Medicine.

[93]  M. Sculpher,et al.  Bayesian methods for evidence synthesis in cost-effectiveness analysis , 2012, PharmacoEconomics (Auckland).

[94]  A. Doucet,et al.  Computational Advances for and from Bayesian Analysis , 2004 .

[95]  D G Altman,et al.  Bayesians and frequentists , 1998, BMJ.

[96]  G. Skrepnek Summary of Functional Forms Involving Logarithms for a Simple Regression Equation , 2005 .

[97]  D. Qin BAYESIAN ECONOMETRICS: The First Twenty Years , 1996, Econometric Theory.

[98]  M. Sculpher,et al.  Representing uncertainty: the role of cost-effectiveness acceptability curves. , 2001, Health economics.

[99]  David R. Jones,et al.  Bayesian methods in health technology assessment: a review. , 2000, Health technology assessment.

[100]  David Lindley,et al.  Theory and Practice of Bayesian Statistics , 1983 .

[101]  G. Casella,et al.  Statistical Inference , 2003, Encyclopedia of Social Network Analysis and Mining.

[102]  D A Berry,et al.  A case for Bayesianism in clinical trials. , 1993, Statistics in medicine.

[103]  Gordon B. Hazen,et al.  A Bayesian approach to sensitivity analysis. , 1999, Health economics.

[104]  D. Bartholomew,et al.  A comparison of some Bayesian and frequentist inferences. II. , 1965, Biometrika.

[105]  P. Urbach,et al.  The value of randomization and control in clinical trials. , 1993, Statistics in medicine.

[106]  A O'Hagan,et al.  A framework for cost-effectiveness analysis from clinical trial data. , 2001, Health economics.

[107]  David Turner,et al.  Comprehensive decision analytical modelling in economic evaluation: a Bayesian approach. , 2004, Health economics.

[108]  C. Schmid,et al.  Why clinicians are natural bayesians , 2005, BMJ : British Medical Journal.

[109]  Anthony O’Hagan,et al.  Inference for the Cost-Effectiveness Acceptability Curve and Cost-Effectiveness Ratio , 2000, PharmacoEconomics (Auckland).

[110]  L Leblond,et al.  Some comments on misspecification of priors in Bayesian modelling of measurement error problems. , 1997, Statistics in medicine.

[111]  Peter E. Kennedy A Guide to Econometrics , 1979 .

[112]  Joel B. Greenhouse,et al.  [Investigating Therapies of Potentially Great Benefit: ECMO]: Comment: A Bayesian Perspective , 1989 .

[113]  Stephen Senn Consensus and Controversy in Pharmaceutical Statistics , 2000 .

[114]  M. Cowles,et al.  On the Origins of the . 05 Level of Statistical Significance , 2005 .

[115]  Bradley P Carlin,et al.  Comparison of Bayesian, classical, and heuristic approaches in identifying acute disease events in lung transplant recipients , 2004, Statistics in medicine.

[116]  Chih-Hsiang Ho Some Frequentist Properties of a Bayesian Method in Clinical Trials , 1991 .

[117]  M J Al,et al.  Costs, effects and C/E-ratios alongside a clinical trial. , 1994, Health economics.

[118]  John C. Hershey,et al.  Carrier Screening for Cystic Fibrosis , 1998, Medical decision making : an international journal of the Society for Medical Decision Making.

[119]  Jeffrey M. Wooldridge,et al.  Introductory Econometrics: A Modern Approach , 1999 .

[120]  K Claxton,et al.  Bayesian approaches to the value of information: implications for the regulation of new pharmaceuticals. , 1999, Health economics.

[121]  J. Cornfield Recent methodological contributions to clinical trials. , 1976, American journal of epidemiology.

[122]  S. Goodman,et al.  Toward Evidence-Based Medical Statistics. 2: The Bayes Factor , 1999, Annals of Internal Medicine.

[123]  A O'Hagan,et al.  Bayesian cost‐effectiveness analysis from clinical trial data , 2001, Statistics in medicine.