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Calculating Partial Expected Value of Perfect Information via Monte Carlo Sampling Algorithms

School of Health and Related Research, The University of Sheffield, Sheffield, England, a.brennan{at}sheffield.ac.uk

Samer Kharroubi, PhD

Department of Mathematics, University of York, Heslington, York, England

Anthony O'Hagan, PhD

Department of Probability and Statistics, The University of Sheffield, Sheffield, England

Jim Chilcott, MSc

School of Health and Related Research, The University of Sheffield, Sheffield, England

Partial expected value of perfect information (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 article examines the computation of partial EVPI estimates via Monte Carlo sampling algorithms. The mathematical definition shows 2 nested expectations, which must be evaluated separately because of the need to compute a maximum between them. A generalized Monte Carlo sampling algorithm uses nested simulation with an outer loop to sample parameters of interest and, conditional upon these, an inner loop to sample remaining uncertain parameters. Alternative computation methods and shortcut algorithms are discussed and mathematical conditions for their use considered. Maxima of Monte Carlo estimates of expectations are biased upward, and the authors show that the use of small samples results in biased EVPI estimates. Three case studies illustrate 1) the bias due to maximization and also the inaccuracy of shortcut algorithms 2) when correlated variables are present and 3) when there is nonlinearity in net benefit functions. If relatively small correlation or nonlinearity is present, then the shortcut algorithm can be substantially inaccurate. Empirical investigation of the numbers of Monte Carlo samples suggests that fewer samples on the outer level and more on the inner level could be efficient and that relatively small numbers of samples can sometimes be used. Several remaining areas for methodological development are set out. A wider application of partial EVPI is recommended both for greater understanding of decision uncertainty and for analyzing research priorities.

Key Words: Key words: partial expected value of perfect information • Monte Carlo sampling • decision modeling. (Med Decis Making 2007:27:448—470)

Medical Decision Making, Vol. 27, No. 4, 448-470 (2007)
DOI: 10.1177/0272989X07302555


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