Bayesian Health Technology Assessment: An Industry Statistician's Perspective

John StevensAstraZeneca R&D Charnwood

Bayesian Statistics Focus Team Leader

Overview• Some history• Why Bayesian statistics?• Summary

Some History

“something could be done”

Why is Bayesian statistics appropriate for health technology assessment?

Incremental Cost-Effectiveness Plane

c

e

K

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!

Cost-Effectiveness Acceptability Curve

Exch

Nonpar

Weak

1 10 100 1000 10000 100000

0.4

0.5

0.6

0.7

0.8

0.9

1.0

K

QCEACs for three different prior structures

Why is Bayesian statistics appropriate for health technology assessment?

More intuitive and meaningful inferences.

Why is Bayesian statistics appropriate for health technology assessment?

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

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

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)

Incorporates prior information in addition to the trial data.

Why is Bayesian statistics appropriate for health technology assessment?

Why is Bayesian statistics appropriate for health technology assessment?

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

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.

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.

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.

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.

Why is Bayesian statistics appropriate for health technology assessment?

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

Why is Bayesian statistics appropriate for health technology assessment?

The ability to tackle more complex problems.

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! Win!

– More intuitive and meaningful inference– The ability to incorporate prior information– The ability to tackle more complex problems