Tony O'Hagan - Academic pages - Abstracts

## Calculating Partial Expected Value of Perfect Information in Cost-Effectiveness Models

Alan Brennan, Samer Kharroubi, Anthony O’Hagan and Jim Chilcott

*School of Health and Related Research* and
*Department of Probability and Statistics, University of Sheffield, Sheffield, England*

**Publication details: **
*Medical Decision Making* **27**, 448-470, 2007.

### Abstract

Partial EVPI calculations can quantify the value of learning about particular
subsets of uncertain parameters in decision models. Published case studies
have used different computational approaches. This paper aims to clarify
computation of partial EVPI and encourage its use. Our mathematical description
efining partial EVPI shows two nested expectations, which must be evaluated
separately because of the need to compute a maximum between them. We set out
a generalised Monte Carlo sampling algorithm using two nested simulation loops,
firstly an outer loop to sample parameters of interest and only then an inner
loop to sample the remaining uncertain parameters, given the sampled parameters
of interest. Alternative computation methods and ‘shortcut’ algorithms are
assessed and mathematical conditions for their use are considered.
Maxima of Monte Carlo estimates of expectations are always biased upwards,
and we demonstrate the effect of small samples on bias in computing partial EVPI.
A series of case studies demonstrates the accuracy or otherwise of using
‘short-cut’ algorithm approximations in simple decision trees, models with
increasingly correlated parameters, and many period Markov models with
increasing non-linearity. The results show that even if relatively small
correlation or non-linearity is present, then the ‘shortcut’ algorithm
can be substantially inaccurate. The case studies also suggest that fewer
samples on the outer level and larger numbers of samples on the inner level
could be the most efficient approach to gaining accurate partial EVPI estimates.
Remaining areas for methodological development are set out.

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Updated: 22 August 2007
Maintained by: Tony O'Hagan