Non-parametric Bayesian value of information analysis

Aim: •To inform the efficient allocation of research resources

Objectives:•To use all the available information regarding the alternative sources of funding•To be sufficiently simple to apply to enable widespread adoption

Requirements

•A fully populated stochastic decision model (preferably one that facilitates analyses of 1st order uncertainty)

•A method for generating a set of hypothetical data describing the most likely outcome of any future research

The stochastic decision model

Comparing adjuvant therapies for early breast cancer

Discrete event simulation (DES) model

4 categories of input parameters, 2 forms of probability distribution

Beta: proportions and utility values

Gamma: Survival times and costs

VOI analysis components

•Expected value of perfect information (EVPI)

•Expected value of sample information

•(EVSI)

•Expected net benefits of sampling (ENBS)

EVPI process

If T1 is the mean cost-effective intervention, the EVPI(episode) is the sum

of the incremental net benefits in the proportion of iterations in which T0

displays positive incremental net benefits

EVPI(population) =

P

p

pepisode r

IEVPI

1 )1(

I: number of episodes in specified periodp: periodP: number of periods relevant to decisionR: discount rate

EVSI definition

Difference in net benefits between the baseline EVPI and the EVPI estimated using updated probability distributions.

EVSI assumptions

Additional data will yield the same mean values as the observed data

- if additional data is sampled from prior distribution is there a potential for EVSI decreasing with increased sample?

The additional data will reduce the variance of the baseline probability distributions

EVSI process

Estimate the proportion of patients informing each input parameter.

Update original probability distributions using the properties of the conjugate

families of the beta and gamma distributions.

EVSI process

Estimate the optimal sample allocation between the interventions.

Analyse the model and the EVPI.

Compare the baseline and updated EVPI.

ENBS definition

The EVSI minus the cost of obtaining the additional data

)( 011

var TTT

iablefixedpopulation CCn

nCCEVSI

Appropriateness of…

• Beta and Gamma distributions

• Assumption regarding values of additional data

• Neyman’s formula for sample allocation

Further research required…

• Methods for estimation of ‘length of application of research’

• Impact of time required to obtain additional data– Estimate ENBS on basis of length of research?

• Accounting for relevant data collected in parallel trials

• Influence on the structure of the model