Multilevel and Quasi Monte Carlo Methods for the Calculation of the Expected Value of Partial Perfect Information.
Multilevel and Quasi Monte Carlo Methods for the Calculation of the Expected Value of Partial Perfect Information.
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DOI：
10.1177/0272989x211026305
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发表时间：
2022-03
期刊：
影响因子：
--
通讯作者：
Thom H
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文献类型：
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作者：
Fang W;Wang Z;Giles MB;Jackson CH;Welton NJ;Andrieu C;Thom H
部分完全信息的期望值（EVPPI）为成本效益决策模型的一组输入值提供了收集进一步证据的价值上限。对 EVPPI 进行标准蒙特卡罗估算需要嵌套模拟，因此计算成本很高。目前已开发出基于模型回归近似的替代方法，但在相关不确定参数数量较多且参数估计高度相关时，这种方法并不可行。与回归近似相关的误差难以确定，而 MC 可以控制偏差和精度。在本文中，我们探讨了准蒙特卡罗（QMC）和多级蒙特卡罗（MLMC）估计的潜力，与 MC 相比，它们能在保持精度的同时减少方差，从而降低 EVPPI 估计的计算成本。我们还开发了将 QMC 和 MLMC 应用于 EVPPI 的方法，以解决在使用马尔可夫链蒙特卡罗（MCMC）估计输入参数分布时出现的特殊挑战。我们用两个例子来说明这些方法：一个是治疗抑郁症的简化决策树模型，另一个是预防心房颤动中风的复杂马尔可夫模型，这两个模型都使用了 MCMC 输入。我们将 QMC 和 MLMC 的性能与 MC 以及广义加法模型 (GAM) 回归、高斯过程 (GP) 回归和嵌套拉普拉斯近似 (INLA-GP) 等近似技术进行了比较。我们发现，当参数集较大且相互关联时，以及当 EVPPI 较大时，QMC 和 MLMC 可大大节省计算量。我们还发现，GP 和 INLA-GP 在这些情况下存在偏差，而 GAM 则无法估计大型参数集的 EVPPI。
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.