Opportunities for Bayesian analysis in evaluation of health-care interventions

David Spiegelhalter

MRC Biostatistics Unit Cambridge

david.spiegelhalter@mrc-bsu.cam.ac.uk

Summary

• What is the Bayesian approach?• Example: CHART• Why is it relevant to evaluation in health-care?• Example: HIPS • What areas might benefit most?• Example: ASTIN • What are key challenges?

What is the Bayesian approach?

A possible definition.

‘the explicit quantitative use of external evidence in the design, monitoring, analysis, interpretation and reporting of a health-care evaluation’

But what does this mean?

Basic Bayesian ideas

• Uncertainty about unknown quantities expressed as a probability distribution

• This ‘prior’ distribution is a judgement based on all available evidence

• Bayes theorem provides a formal way of revising this distribution as more evidence accumulates

“Posterior prior x likelihood”

CHART trial in non small-cell lung cancer

The Data Monitoring Committee met annually and was presented with full data.

Date No patients

No deaths

Observed hazard

ratio 

95% CI 2-sidedP-value

1992 256 78 0.55 (0.35 to 0.86)

0.007

1993 380 192 0.63 (0.47 to 0.83)

0.001

1994 460 275 0.70 (0.55 to 0.90)

0.003

1995 563 379 0.75 (0.61 to 0.93)

0.004

1996 563 444 0.76 (0.63 to 0.90)

0.003

CHART Lung trial results

Why is it relevant to evaluation in health-care?

• Can incorporate all relevant evidence in an incremental way

• Can model potential biases in studies• Answers question: how should new evidence

change our opinions?• Directly make statements such as:

“Probability that X is cost-effective is 92%”• Inference feeds naturally into decision-

making and planning further studies• Requires explicit, accountable judgments,

recognising context and multiple stakeholders

Comparison of Charnley and Stanmore hip prosthesis (NICE, 2000)

(a) Medium weight to registry

K = acceptable cost per QALY

Pro

b(c

ost-

effective)

0 5000 15000

0.0

0.2

0.4

0.6

0.8

1.0

(a) Medium weight to registry

K = acceptable cost per QALY

Pro

b(c

ost-

effective)

0 5000 15000

0.0

0.2

0.4

0.6

0.8

1.0

(a) Medium weight to registry

K = acceptable cost per QALY

Pro

b(c

ost-

effective)

0 5000 15000

0.0

0.2

0.4

0.6

0.8

1.0

0% health discount1.5%6%

(b) Low weight to registry

K = acceptable cost per QALY

0 5000 15000

0.0

0.2

0.4

0.6

0.8

1.0

(b) Low weight to registry

K = acceptable cost per QALY

0 5000 15000

0.0

0.2

0.4

0.6

0.8

1.0

(b) Low weight to registry

K = acceptable cost per QALY

0 5000 15000

0.0

0.2

0.4

0.6

0.8

1.0

(c) Equal weights

K = acceptable cost per QALY

0 5000 15000

0.0

0.2

0.4

0.6

0.8

1.0

(c) Equal weights

K = acceptable cost per QALY

0 5000 15000

0.0

0.2

0.4

0.6

0.8

1.0

(c) Equal weights

K = acceptable cost per QALY

0 5000 15000

0.0

0.2

0.4

0.6

0.8

1.0

What areas might benefit most?

• Planning and monitoring development programmes

• Selection of compounds for further investigation

• Data monitoring within studies• Adaptive designs in proof-of-concept studies• Evidence synthesis• Cost-effectiveness analysis• Value-of-information (payback) models

ASTIN study• Adaptive dose-response study of UK-279,276 in acute ischaemic

stroke (Krams, Lees, Hacke, Grieve, Orgogozo, Ford etc (2003)• 15 doses available: placebo, 10 - 120 mg• Primary outcome: increase in Scandinavian Stroke Scale (SSS)

at 90 days (adjusted for baseline) • Next dose suggested is that which minimises the expected

variance of the response at the ED95 (minimal dose near maximal efficacy)

• Randomisation: 15\% to placebo, 85\% `near' suggested dose• Fits smoothly flexible curve: no imposed shape• IDMC examined data every week• Stop for efficacy when 90% probability that effect at ED95 > 2• Stop for futility when 90% probability that effect at ED95 < 1• Design approved by FDA (based on simulation studies)• Stopped by IDMC for futility after 966 patients randomised

Changing dosing pattern

Final dose-effect curve

Doses finally given

Monitoring changing probabilities

What are key challenges?

• Marshalling appropriate evidence• Robust, rigorous modeling with appropriate

sensitivity analysis• Presentation in persuasive way to decision-

makers in companies and regulatory authorities

• Integration of cost-effectiveness ideas into product-development programmes

BUTCannot make silk purse …., so need good

studies and good data

References

Berry DA, Mueller P, Grieve AP, Smith M, Parke T, Blazek R, Mitchard N and Krams M (2001) Adaptive Bayesian designs for dose-ranging drug trials. Case Studies in Bayesian Statistics, Volume V. Eds Gatsonis C, Carlin B and Carriquiry A. Springer-Verlag, New York. p 99-181

O'Hagan A Luce BR (2003) A Primer on Bayesian Statistics in Health Economics. Centre for Bayesian Statistics in Health Economics, Sheffield

Parmar MKB, Griffiths GO, Spiegelhalter DJ, Souhami RL, Altman DG and van der Scheuren E (2001) Monitoring large randomised clinical trials - a new approach using Bayesian methods, Lancet, 358, 375—381

Spiegelhalter DJ, Abrams K, and Myles JP. Bayesian Approaches to Clinical Trials and Health Care Evaluation. Wiley, Chichester, 2004.

Spiegelhalter DJ and Best NG (2003) Bayesian methods for evidence synthesis and complex cost-effectiveness models: an example in hip prostheses. Statistics in Medicine, 22, 000-000