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In Silico Clinical Trials for Cardiovascular Disease

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Comparison of Optimal Design Methods in Inverse Problems.

H T Banks¹, Kathleen Holm, Franz Kappel

¹Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695-8213.

Inverse Problems

|August 23, 2011

Summary

This study introduces a new framework for optimal experimental design, focusing on minimizing parameter estimation errors. The novel SE-optimal design is presented and compared to existing methods, offering improved accuracy for parameter estimation in scientific models.

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Area of Science:

* Mathematical Optimization
* Statistical Inference
* Computational Modeling

Background:

* Optimal design methods aim to improve parameter estimation accuracy by selecting optimal sampling distributions.
* Existing methods often rely on minimizing specific cost functions related to parameter estimate errors.
* The Fisher Information Matrix (FIM) is a key component in many optimal design criteria.

Purpose of the Study:

* To develop a unified theoretical framework for optimal design criteria based on the Fisher Information Matrix.
* To introduce a new optimal design criterion: SE-optimal design (standard error optimal design).
* To compare the performance of SE-optimal design against traditional D-optimal and E-optimal designs.

Main Methods:

* Formulation of the optimal design problem within a general optimization framework for sampling time distributions.
* Development of a Prohorov metric-based theoretical framework to handle FIM-based design criteria.
* Introduction of an approximation theory within the new framework.
* Computation and comparison of standard errors using asymptotic theory or bootstrapping on optimal meshes.

Main Results:

* A novel theoretical framework for optimal design criteria based on the FIM has been established.
* The SE-optimal design criterion was introduced and demonstrated to be effective.
* Comparisons showed that optimal sampling distributions derived from different criteria yield varying standard errors for parameter estimates.

Conclusions:

* The proposed Prohorov metric-based framework provides a rigorous approach to optimal design problems.
* SE-optimal design offers a valuable alternative for improving parameter estimation accuracy.
* The study illustrates the practical application of these optimal design methods using diverse scientific models.