Dela An, Shtylla Blerta, de Pillis Lisette
Institute of Mathematical Sciences, Claremont Graduate University, Claremont, CA 91711, USA.
Mathematics Department, Pomona College, Claremont, CA 91711, USA.
J Theor Biol. 2022 Aug 7;546:111159. doi: 10.1016/j.jtbi.2022.111159. Epub 2022 May 14.
Increasingly-sophisticated parameter-sensitivity analysis techniques continue to be developed, and each technique comes with its own set of advantages and disadvantages. Selecting which parameter-sensitivity method to use for a particular model, however, is not a straightforward task. In this work, we present a multi-method framework that incorporates three global sensitivity analysis methods: two variance-based methods and one derivative-based method. The two variance-based methods are Sobol's method and MeFAST. The derivative-based method is known as DGSM (Derivative-based Global Sensitivity Measures). MeFAST (Multi test eFAST) is a new parameter sensitivity analysis implementation we built upon the eFAST (Extended Fourier Amplitude Sensitivity Test) algorithm. The improvements incorporated into MeFAST address some important aspects of prior eFAST implementations. We present an intuitive description of each implemented algorithm along with MATLAB codes and a guide to tuning algorithm hyper-parameters for better efficiency. We demonstrate the full methodology and workflow using two example mathematical models of different complexity: the first is a model of HIV disease progression and the second is a model of tumor growth. The computational framework we provide generates graphics for visualizing and comparing the results of all three sensitivity analysis algorithms (DGSM, Sobol, and MeFAST). This algorithm output comparison tool allows one to make a more informed decision when assessing which parameters most importantly influence model outcomes.
日益复杂的参数敏感性分析技术不断涌现，每种技术都有其自身的优缺点。然而，为特定模型选择使用哪种参数敏感性方法并非易事。在这项工作中，我们提出了一个多方法框架，该框架纳入了三种全局敏感性分析方法：两种基于方差的方法和一种基于导数的方法。两种基于方差的方法是索博尔方法和MeFAST。基于导数的方法称为DGSM（基于导数的全局敏感性度量）。MeFAST（多重测试eFAST）是我们在eFAST（扩展傅里叶幅度敏感性测试）算法基础上构建的一种新的参数敏感性分析方法。纳入MeFAST的改进解决了先前eFAST方法的一些重要方面。我们对每种实现的算法进行了直观描述，并提供了MATLAB代码以及调整算法超参数以提高效率的指南。我们使用两个不同复杂度的示例数学模型展示了完整的方法和工作流程：第一个是HIV疾病进展模型，第二个是肿瘤生长模型。我们提供的计算框架生成图形，用于可视化和比较所有三种敏感性分析算法（DGSM、索博尔方法和MeFAST）的结果。这种算法输出比较工具使人们在评估哪些参数对模型结果影响最为重要时能够做出更明智的决策。
