Some methodological issues in Some methodological issues in value of information analysis: value of information analysis: an application of partial EVPI an application of partial EVPI and EVSI to an economic model and EVSI to an economic model of Zanamivir of Zanamivir Karl Claxton and Tony Ades Karl Claxton and Tony Ades
Some methodological issues in value of information analysis: an application of partial EVPI and EVSI to an economic model of Zanamivir. Karl Claxton and Tony Ades. Partial EVPIs. Light at the end of the tunnel……. ……..maybe it’s a train. A simple model of Zanamivir. Distribution of inb. - PowerPoint PPT Presentation
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Some methodological issues in value of Some methodological issues in value of information analysis: information analysis:
an application of partial EVPI and EVSI to an application of partial EVPI and EVSI to an economic model of Zanamiviran economic model of Zanamivir
Karl Claxton and Tony AdesKarl Claxton and Tony Ades
Partial EVPIsPartial EVPIs
Light at the end of the tunnel……Light at the end of the tunnel……
…………..maybe it’s a train..maybe it’s a train
A simple model of ZanamivirA simple model of Zanamivirphz 0.018
EVPIEVPIpippip = EV(perfect information about pip) - EV(current information) = EV(perfect information about pip) - EV(current information)
EV(optimal decision for a EV(optimal decision for a particular resolution of pip)particular resolution of pip)
Expectation of this difference over all resolutions of pipExpectation of this difference over all resolutions of pip
EV(prior decision for the EV(prior decision for the same resolution of pip)same resolution of pip)
--
Partial EVPIPartial EVPI
Some implications:Some implications: information about an input is only valuable if it changes information about an input is only valuable if it changes
our decision our decision information is only valuable if pip information is only valuable if pip does notdoes not resolve at its resolve at its
expected value expected value
General solution:General solution: linear and non linear modelslinear and non linear models inputs can be (spuriously) correlatedinputs can be (spuriously) correlated
Felli and Hazen (98) “short cut”Felli and Hazen (98) “short cut”EVPIEVPIpippip = EVPI when resolve all other inputs at their expected value = EVPI when resolve all other inputs at their expected value
Appears counter intuitive:Appears counter intuitive: we resolve all other uncertainties then ask what is the value of pip ie we resolve all other uncertainties then ask what is the value of pip ie
“residual” EVPIpip ?“residual” EVPIpip ?
But:But: resolving at EV does not give us any informationresolving at EV does not give us any information
Correct if:Correct if: linear relationship between inputs and net benefitlinear relationship between inputs and net benefit inputs are not correlatedinputs are not correlated
wrong current information position for partial EVPIwrong current information position for partial EVPI what is the value of resolving pip when we already have perfect what is the value of resolving pip when we already have perfect
information about all other inputs?information about all other inputs? Expect residual EVPIExpect residual EVPIpippip < partial EVPI < partial EVPIpippip
EVPI when resolve all other inputs at each realisation ?EVPI when resolve all other inputs at each realisation ?
Thompson and Evans (96) and Thompson and Graham (96)Thompson and Evans (96) and Thompson and Graham (96)
inb simplifies to:inb simplifies to:
inb = inb =
Rearrange: Rearrange:
pip: inb = pip: inb =
pcz: inb = pcz: inb =
phz: inb = phz: inb =
rsd: inb = rsd: inb =
upd: inb = upd: inb =
phs: inb = phs: inb =
pcs: inb = pcs: inb =
Felli and Hazen (98) used a similar approachFelli and Hazen (98) used a similar approach Thompson and Evans (96) is a linear modelThompson and Evans (96) is a linear model emphasis on EVPI when set others to joint expected valueemphasis on EVPI when set others to joint expected value requires payoffs as a function of the input of interest requires payoffs as a function of the input of interest
Reduction in cost of uncertaintyReduction in cost of uncertainty
intuitive appealintuitive appeal consistent with conditional probabilistic analysisconsistent with conditional probabilistic analysis
RCURCUE(pip)E(pip) = EVPI - EVPI(pip resolved at expected value) = EVPI - EVPI(pip resolved at expected value)
ButBut pip may not resolve at E(pip) and prior decisions may changepip may not resolve at E(pip) and prior decisions may change value of perfect information if forced to stick to the prior value of perfect information if forced to stick to the prior
decision ie the value of a reduction in variancedecision ie the value of a reduction in variance Expect RCUExpect RCUE(pip)E(pip) < partial EVPI < partial EVPI
Value of including a strategy?Value of including a strategy?
EVPI with and without the strategy includedEVPI with and without the strategy included demonstrates biasdemonstrates bias difference = EVPI associated with the strategy?difference = EVPI associated with the strategy?
EV(perfect information, all included) – EV(perfect information, all included) –
generate a predictive distribution for sample of ngenerate a predictive distribution for sample of n sample from the predictive and prior distributions to sample from the predictive and prior distributions to
form a preposteriorform a preposterior propagate the preposterior through the modelpropagate the preposterior through the model value of information for sample of nvalue of information for sample of n find n* that maximises EVSI-cost sampling find n* that maximises EVSI-cost sampling
as n increases var(rip*n) falls towards var(pip)as n increases var(rip*n) falls towards var(pip) var(pip’) < var(pip) and falls with nvar(pip’) < var(pip) and falls with n pip’ are the possible posterior meanspip’ are the possible posterior means
EVSIpipEVSIpip
= reduction in the cost of uncertainty due to n obs on pip= reduction in the cost of uncertainty due to n obs on pip
= difference in partials (EVPIpip – EVPIpip’)= difference in partials (EVPIpip – EVPIpip’)
EEpippip[Max[Maxd d EEotherother(NB(NBdd||other, pipother, pip)] = E)] = Epip’pip’[Max[Maxd d EEotherother(NB(NBdd||other, pip’other, pip’)] )]
Expected Value of Sample Information (EVSIpip)
0.00
0.20
0.40
0.60
0.80
1.00
0 200 400 600 800 1000 1200 1400 1600
Sample size (n)
Val
ue
of
info
rmat
ion
Posterior Partial EVPI
EVSIpip
Prior Partial EVPI
EVSIpipEVSIpip
Why not the difference in prior and preposterior EVPI?Why not the difference in prior and preposterior EVPI? effect of pip’ only through var(NB)effect of pip’ only through var(NB) change decision for the realisation of pip’ once study is change decision for the realisation of pip’ once study is
completedcompleted difference in prior and preposterior EVPI will difference in prior and preposterior EVPI will
EVSI for any input that is conjugateEVSI for any input that is conjugate generate preposterior for log odds ratio for complication and generate preposterior for log odds ratio for complication and
hospitalisation etc hospitalisation etc trial design for individual endpoint (rsd)trial design for individual endpoint (rsd) trial designs with a number of endpoints (pcz, phz, upd, rsd)trial designs with a number of endpoints (pcz, phz, upd, rsd)
n for an endpoint will be uncertain (n_pcz = n*pip, etc)n for an endpoint will be uncertain (n_pcz = n*pip, etc) consider optimal n and allocation (search for n*)consider optimal n and allocation (search for n*)
combine different designs eg: combine different designs eg: obs study (pip) and trial (upd, rsd) or obs study (pip, upd), obs study (pip) and trial (upd, rsd) or obs study (pip, upd),