Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand.
School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand.
Bull Math Biol. 2024 May 8;86(6):70. doi: 10.1007/s11538-024-01304-1.
Practical limitations of quality and quantity of data can limit the precision of parameter identification in mathematical models. Model-based experimental design approaches have been developed to minimise parameter uncertainty, but the majority of these approaches have relied on first-order approximations of model sensitivity at a local point in parameter space. Practical identifiability approaches such as profile-likelihood have shown potential for quantifying parameter uncertainty beyond linear approximations. This research presents a genetic algorithm approach to optimise sample timing across various parameterisations of a demonstrative PK-PD model with the goal of aiding experimental design. The optimisation relies on a chosen metric of parameter uncertainty that is based on the profile-likelihood method. Additionally, the approach considers cases where multiple parameter scenarios may require simultaneous optimisation. The genetic algorithm approach was able to locate near-optimal sampling protocols for a wide range of sample number (n = 3-20), and it reduced the parameter variance metric by 33-37% on average. The profile-likelihood metric also correlated well with an existing Monte Carlo-based metric (with a worst-case r > 0.89), while reducing computational cost by an order of magnitude. The combination of the new profile-likelihood metric and the genetic algorithm demonstrate the feasibility of considering the nonlinear nature of models in optimal experimental design at a reasonable computational cost. The outputs of such a process could allow for experimenters to either improve parameter certainty given a fixed number of samples, or reduce sample quantity while retaining the same level of parameter certainty.
数据的质量和数量的实际限制可能会限制数学模型中参数识别的精度。已经开发了基于模型的实验设计方法来最小化参数不确定性，但这些方法中的大多数都依赖于模型灵敏度在参数空间中局部点的一阶近似。实用的可识别性方法，如似然轮廓法，已经显示出在超越线性近似的情况下量化参数不确定性的潜力。本研究提出了一种遗传算法方法，以优化具有展示性 PK-PD 模型的各种参数化的样本时间，以辅助实验设计。该优化依赖于基于似然轮廓法的所选参数不确定性度量。此外，该方法还考虑了可能需要同时优化多个参数方案的情况。遗传算法方法能够为广泛的样本数量（n=3-20）找到接近最优的采样方案，并平均降低参数方差度量 33-37%。似然轮廓法度量也与现有的基于蒙特卡罗的度量很好地相关（最差情况 r>0.89），同时将计算成本降低了一个数量级。新的似然轮廓法度量和遗传算法的结合证明了在合理的计算成本下，在最优实验设计中考虑模型非线性性质的可行性。这样一个过程的输出可以让实验者在给定固定样本数量的情况下提高参数确定性，或者在保持相同参数确定性的情况下减少样本数量。
