Designing Efficient Designs under Model Uncertainty for Biological Studies

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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.