Multilevel and Quasi Monte Carlo Methods for the Calculation of the Expected Value of Partial Perfect Information

Wei Fang, Zhenru Wang, Michael B. Giles, Chris H. Jackson, Nicky J. Welton, Christophe Andrieu and Howard Thom
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Wei Fang: Mathematical Institute, University of Oxford, Oxford, Oxfordshire, UK
Zhenru Wang: Mathematical Institute, University of Oxford, Oxford, Oxfordshire, UK
Michael B. Giles: Mathematical Institute, University of Oxford, Oxford, Oxfordshire, UK
Chris H. Jackson: MRC Biostatistics Unit, University of Cambridge, Cambridge, Cambridgeshire, UK
Nicky J. Welton: Population Health Science, Bristol Medical School, University of Bristol, Bristol, UK
Christophe Andrieu: School of Mathematics, University of Bristol, Bristol, UK
Howard Thom: Population Health Science, Bristol Medical School, University of Bristol, Bristol, UK

Medical Decision Making, 2022, vol. 42, issue 2, 168-181

Abstract: The expected value of partial perfect information (EVPPI) provides an upper bound on the value of collecting further evidence on a set of inputs to a cost-effectiveness decision model. Standard Monte Carlo estimation of EVPPI is computationally expensive as it requires nested simulation. Alternatives based on regression approximations to the model have been developed but are not practicable when the number of uncertain parameters of interest is large and when parameter estimates are highly correlated. The error associated with the regression approximation is difficult to determine, while MC allows the bias and precision to be controlled. In this article, we explore the potential of quasi Monte Carlo (QMC) and multilevel Monte Carlo (MLMC) estimation to reduce the computational cost of estimating EVPPI by reducing the variance compared with MC while preserving accuracy. We also develop methods to apply QMC and MLMC to EVPPI, addressing particular challenges that arise where Markov chain Monte Carlo (MCMC) has been used to estimate input parameter distributions. We illustrate the methods using 2 examples: a simplified decision tree model for treatments for depression and a complex Markov model for treatments to prevent stroke in atrial fibrillation, both of which use MCMC inputs. We compare the performance of QMC and MLMC with MC and the approximation techniques of generalized additive model (GAM) regression, Gaussian process (GP) regression, and integrated nested Laplace approximations (INLA-GP). We found QMC and MLMC to offer substantial computational savings when parameter sets are large and correlated and when the EVPPI is large. We also found that GP and INLA-GP were biased in those situations, whereas GAM cannot estimate EVPPI for large parameter sets.

Keywords: expected value of partial perfect information; nested expectations; multilevel Monte Carlo; quasi Monte Carlo (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:sae:medema:v:42:y:2022:i:2:p:168-181

DOI: 10.1177/0272989X211026305

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