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.
The choice of an experimental design is extremely important because it can drastically affect the (i) number of animals required, (ii) amount of labor, (iii) amount of time, (iv) financial cost, and (v) the quality of the statistical inference. The latter pint was emphatically made in a foreword entitled Animal experiments under fire for poor design on page 981 in NATURE, 2006, Vol. 444, where the editor commented in red print that Small- scale studies are pointless if they do not produce results that people have confidence in followed by a figure caption that read Are animals being wasted in badly thought through experiments? This project develops innovative and realistic designs using state-of-the art statistical techniques to enable bench scientists conduct more efficient experiments so that their results are more reliable and more likely to translate to useful findings in clinical trials.
|Dette, Holger; Schorning, Kirsten (2016) Optimal designs for comparing curves. Ann Stat 44:1103-1130|
|Duarte, Belmiro P M; Wong, Weng Kee; Oliveira, Nuno M C (2016) Model-based optimal design of experiments - semidefinite and nonlinear programming formulations. Chemometr Intell Lab Syst 151:153-163|
|Dette, Holger; Pepelyshev, Andrey; Zhigljavsky, Anatoly (2016) Optimal designs in regression with correlated errors. Ann Stat 44:113-152|
|Jaynes, Jessica; Wong, Weng-Kee; Xu, Hongquan (2016) Using blocked fractional factorial designs to construct discrete choice experiments for healthcare studies. Stat Med 35:2543-60|
|Phoa, Frederick Kin Hing; Chen, Ray-Bing; Wang, Weichung et al. (2016) Optimizing Two-level Supersaturated Designs using Swarm Intelligence Techniques. Technometrics 58:43-49|
|Chen, Hsiu-Wen; Wong, Weng Kee; Xu, Hongquan (2016) Data-driven desirability function to measure patients' disease progression in a longitudinal study. J Appl Stat 43:783-795|
|Duarte, Belmiro P M; Wong, Weng Kee (2015) Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach. Int Stat Rev 83:239-262|
|Dette, Holger; Titoff, Stefanie; Volgushev, Stanislav et al. (2015) Dose response signal detection under model uncertainty. Biometrics 71:996-1008|
|Dette, Holger; Melas, Viatcheslav B; Guchenko, Roman (2015) Bayesian T-optimal discriminating designs. Ann Stat 43:1959-1985|
|Wong, Weng Kee; Chen, Ray-Bing; Huang, Chien-Chih et al. (2015) A Modified Particle Swarm Optimization Technique for Finding Optimal Designs for Mixture Models. PLoS One 10:e0124720|
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