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, Howard Thom

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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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 (MC) 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 paper, we explore the potential of Quasi Monte-Carlo (QMC) and Multilevel Monte-Carlo (MLMC) estimation to reduce computational cost of estimating EVPPI by reducing the variance compared with MC, while preserving accuracy. In this paper, we 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 a two 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 Generalised Additive Model regression (GAM), Gaussian process regression (GP), 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 find GP and INLA-GP to be biased in those situations, while GAM cannot estimate EVPPI for large parameter sets.
Original languageEnglish
Pages (from-to)168-181
Number of pages14
JournalMedical Decision Making
Volume42
Issue number2
Early online date7 Jul 2021
DOIs
Publication statusPublished - 1 Feb 2022

Bibliographical note

Funding Information:
The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: WF, ZW, and HT were supported by the Hubs for Trials Methodology Research (HTMR) network grant N79 for this work. HT and NJW were supported by the HTMR Collaboration and innovation in Difficult and Complex randomised controlled Trials In Invasive procedures (ConDuCT-II). HT and NJW were also supported by the National Institute for Health Research (NIHR) Bristol Biomedical Research Centre (BRC) for part of this work. HT was furthermore supported by MRC grant MR/S036709/1. CA would like to thank the support of EPSRC EP/R018561/1 Bayes4Health. CJ was funded by the UK Medical Research Council programme MC_UU_00002/11. The directly acting oral anticoagulants for prevention of stroke in atrial fibrillation model was funded by NIHR Health Technology Assessment programme project number 11/92/17 and NIHR Senior Investigator award NF-SI-0611-10168.

Funding Information:
We are grateful to Mark Strong at the University of Sheffield for providing his R code to estimate EVPPI, plus its standard error and upward bias, using GAM and GP. The mlmc.R and mlmc.test.R files used to run multilevel Monte Carlo were developed by Louis Aslett, Mike Giles, and Tigran Nagapetyan. 39 This code has been used previously for published MLMC applications. 40 The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: WF, ZW, and HT were supported by the Hubs for Trials Methodology Research (HTMR) network grant N79 for this work. HT and NJW were supported by the HTMR Collaboration and innovation in Difficult and Complex randomised controlled Trials In Invasive procedures (ConDuCT-II). HT and NJW were also supported by the National Institute for Health Research (NIHR) Bristol Biomedical Research Centre (BRC) for part of this work. HT was furthermore supported by MRC grant MR/S036709/1. CA would like to thank the support of EPSRC EP/R018561/1 Bayes4Health. CJ was funded by the UK Medical Research Council programme MC_UU_00002/11. The directly acting oral anticoagulants for prevention of stroke in atrial fibrillation model was funded by NIHR Health Technology Assessment programme project number 11/92/17 and NIHR Senior Investigator award NF-SI-0611-10168.

Publisher Copyright:
© The Author(s) 2021.

Structured keywords

  • HEB
  • HEB (Health Economics Bristol)

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