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
EVPIepisode  
1
Ip
(1  r )
p
I: number of episodes in specified period
p: period
P: number of periods relevant to decision
R: 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
EVSIpopulation  Cfixed  Cv ar iable
nT 1

(CT 1  CT 0 )
n
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