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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计算部分完美信息期望值的多级和准蒙特卡罗方法
DOI：
10.1101/2021.03.30.21254626
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Fang W
中科院分区：
文献类型：
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作者：
Fang W
部分完全信息的期望值（EVPPI）提供了一个上限的价值收集进一步的证据，一组输入的成本效益决策模型。EVPPI的标准Monte Carlo估计在计算上是昂贵的，因为它需要嵌套模拟。已经开发了基于回归近似模型的替代方法，但当感兴趣的不确定参数数量很大且参数估计值高度相关时，这些方法并不实用。与回归近似相关的误差难以确定，而MC允许控制偏差和精度。在这篇文章中，我们探讨了潜在的准蒙特卡罗（QMC）和多级蒙特卡罗（MLMC）估计，以减少估计EVPPI的计算成本，减少方差与MC相比，同时保持精度。我们还开发的方法，应用QMC和MLMC EVPPI，解决特定的挑战，出现马尔可夫链蒙特卡罗（MCMC）已被用来估计输入参数分布。我们使用2个示例来说明这些方法：用于抑郁症治疗的简化决策树模型和用于预防房颤中风治疗的复杂马尔科夫模型，这两个模型都使用MCMC输入。我们比较的性能QMC和MLMC与MC和近似技术的广义加性模型（GAM）回归，高斯过程（GP）回归，集成嵌套拉普拉斯近似（INLA-GP）。我们发现QMC和MLMC提供大量的计算节省时，参数集是大的，相关的，当EVPPI是大的。我们还发现，GP和INLA-GP在这些情况下是有偏见的，而GAM不能估计大参数集的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.