1. Bayesian Health Technology Assessment: An Industry Statistician's Perspective John Stevens AstraZeneca R&D Charnwood Bayesian Statistics Focus Team Leader

2. Overview Some history Why Bayesian statistics? Summary

3. Some History “something could be done”

4. Why is Bayesian statistics appropriate for health technology assessment?

5. Incremental Cost-Effectiveness Plane cc ee K

6. Inferences about Cost-Effectiveness Net (Monetary) Benefit,  (K) = K  e -  c > 0 Objective to make inferences : Q(K) = P( K  e -  c > 0 ) –Q(K) is the posterior probability that NB > 0 –Q(K) is the C/E-acceptability curve This is intrinsically Bayesian!

7. Cost-Effectiveness Acceptability Curve

8. Why is Bayesian statistics appropriate for health technology assessment? More intuitive and meaningful inferences.

9. Why is Bayesian statistics appropriate for health technology assessment?

10. Prior Information A fundamental feature of Bayesian statistics Represents information that is available in addition to observing the data Prior information almost always exists and this should be used to strengthen inferences –Does not mean that inferences are necessarily more favourable –Particularly important where the design objectives of a clinical trial may not relate to the effectiveness measure –Can be structural information as well as numerical information Prior information should always be used for internal planning

11. Subjectivity Prior information is intrinsically subjective An unscrupulous analyst can concoct any desired result The potential for manipulation is not unique to Bayesian statistics But ….. –nowhere is the discipline of statistics carried out with more discipline than in the pharmaceutical industry, and –nowhere will Bayesian statistics be carried out with greater discipline than in the pharmaceutical industry Synthesis of evidence should follow a formal process for justifying the prior information

12. Synthesis of Evidence “The elicitation and description of prior information should be given at least as much care and attention as the planning, execution and data scrutiny of the trial itself.” O’Hagan, Stevens and Montmartin (2001)

13. Incorporates prior information in addition to the trial data. Why is Bayesian statistics appropriate for health technology assessment?

15. Sensitivity Analysis Economic models are necessary in support of arguments of cost-effectiveness Parameter estimates are typically drawn from a variety of sources Univariate sensitivity analysis is still common Uncertainty and inaccuracy in parameter estimates should be acknowledged Correlations between input parameters should also be acknowledged Bayesian probabilistic sensitivity analysis has advantages to both sponsors and decision makers

16. Guidance (1) HTBS: Guidance for manufacturers on submission of evidence relating to clinical and cost-effectiveness in Health Technology Assessments 2002 It may be appropriate in some cases to combine the cost-effectiveness evaluation with one or more meta analyses of the clinical data. This may be done most naturally in a Bayesian framework.

17. Guidance (2) HTBS: Guidance for manufacturers on submission of evidence relating to clinical and cost-effectiveness in Health Technology Assessments 2002 Comprehensive sensitivity analyses should be conducted. For parameters with substantial uncertainty, sensitivity analysis using probability distributions in a Bayesian framework is preferred.

18. Guidance (3) NICE: Guidance for manufacturers and sponsors 2001 When data are drawn from a variety of sources and used in a modelling framework, probabilistic sensitivity analysis is recommended in order to take account of the uncertainty around data values.

19. Why is Bayesian statistics appropriate for health technology assessment? Bayesian PSA allows the output uncertainty to be analysed, with a range of diagnostics to identify the most influential model inputs that are driving the output uncertainty.

20. Why is Bayesian statistics appropriate for health technology assessment?

21. Answering More Complex Questions Frequentist theory relies on large sample approximations Sample means are not necessarily good estimators of population means when data are skew in relatively small samples Bayesian inferences can be computed exactly in highly complex models

22. Why is Bayesian statistics appropriate for health technology assessment? The ability to tackle more complex problems.

23. Summary Bayesian statistics provides: Bayesian PSA allows the output uncertainty to be analysed, with a range of diagnostics to identify the most influential model inputs that are driving the output uncertainty. Win! –More intuitive and meaningful inference –The ability to incorporate prior information –The ability to tackle more complex problems