Designing Efficient Designs under Model Uncertainty for Biological Studies

描述（由申请人提供）：疾病具有复杂的病因和模型，经常用于提供对生物过程的见解。实验数据的有用性取决于用于收集数据的设计。该项目的总体目标是利用优化设计理论中的最新工具，以最小的成本和最大的统计效率构建新的和现实的生物现象建模设计。最优设计的一个主要困难是其性能取决于模型，这在实践中是未知的。由于在错误的模型下开发的优化设计可能非常低效，因此实现的设计在模型不确定性下提供足够的推理是至关重要的。我们的重点是非线性回归模型，通常作为微分方程系统的解获得，例子包括研究肿瘤生长速率或抑制的数学模型或研究酶动力学反应的s型回归模型。目前的设计判别技术总是集中在两个非线性模型之间的判别，不切实际地假设只有一个目标，误差是独立的和均方差的。我们的创新之处在于，我们基于理论的设计能够有效地区分具有相关和异方差响应的多个模型，同时能够为不同的目标提供用户指定的效率，更重要的目标具有更高的效率。我们还实现了现代的元启发式算法，用于为任何模型和任何标准生成潜在的量身定制的最佳设计，并使用它们来评估我们的设计，相对于毒理学家在实验中使用紫色海胆的当前设计，这是加州理工学院基因调控网络更大研究的一部分。

DESCRIPTION (provided by applicant): Diseases have complex etiology and models are frequently used to provide insights into the biological processes. The usefulness of the data from the experiments depends on the design used to collect the data. The overall goal in this project is to use the latest tools in optimal design theory to construct new and realistic designs for modeling biological phenomena at minimal cost and maximal statistical efficiency. A main difficulty is that performance of the optimal design depends on the model, which is unknown in practice. Because an optimal design developed under a wrong model can be very inefficient, it is of paramount importance that the implemented design provides adequate inference under model uncertainty. Our focus is on nonlinear regression models typically obtained as solutions to systems of differential equations and examples include mathematical models for studying tumor growth rates or inhibition or sigmoidal regression models for studying enzyme-kinetic reactions. Current design discrimination techniques invariably focus on discriminating between two nonlinear models and unrealistically assume there is only one goal and errors are independent and homoscedastic. Our innovation is that our theory-based designs are able to efficiently discriminate among multiple models with correlated and heteroscedastic responses, and at the same time, able to provide user- specified efficiencies for different objectives, with higher efficiencies for the more important objectives. We also implement modern metaheuristic algorithms for generating potentially tailor-made optimal designs for any model and any criterion and use them to evaluate our designs relative to current designs used by toxicologists using purple sea urchins in experiments as part of a larger study in gene-regulatory network at Caltech.