Optimization Models for Calculation of Personalized Strategies

Optimization Models for Calculation of Personalized Strategies

Ievgen Arnoldovich Nastenko (Igor Sikorsky Kyiv Polytechnic Institute, Ukraine), Volodymyr Anatolevich Pavlov (Igor Sikorsky Kyiv Polytechnic Institute, Ukraine), Olena Konstantinovna Nosovets (Igor Sikorsky Kyiv Polytechnic Institute, Ukraine), Oleksandr Davydko (Igor Sikorsky Kyiv Polytechnic Institute, Ukraine) and Oleksander Pavlov (Igor Sikorsky Kyiv Polytechnic Institute, Ukraine)
DOI: 10.4018/978-1-5225-8933-4.ch015

Abstract

The chapter considers the problem of calculating the best individual strategy based on models obtained from observations of a given sample object's reaction to the applied control actions. In order to improve the calculation efficiency, the construction of the optimization problem with line dependence on the control variables is offered. To ensure the calculation adequacy, the object state models of optimal complexity, nonlinear with respect to the initial conditions and parameters, are considered. Examples of optimal personalized treatment strategies calculation are given. The proposed approach can be extended to other practical areas to solve the decision making, provided the development of adequate the object state models in the optimization field.
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Background

Almost any formalized problem can be assigned to one of the three problem classes: design, control, and modeling. And each of these tasks is always dominated by the requirement to solve it in the best way within a definition given area. It would seem that any practical task would have to be formulated and solved as a kind of optimization problem. However, now the optimization statements in the problems of decision making or control actions calculation are usually used only in case when the constraints and the object state models can be obtained analytically. Researchers often avoid statistical estimates of parameters or statistical models due to the introduction of uncertainty related to the modeling error. Nevertheless, the use of stochastic programming methods, the creation of statistical models with an appropriate level of adequacy in the problem variables study area allows us to count on obtaining solutions suitable, at least for expert evaluation of specialists and application in practice. However, the first report of the ISPOR dedicated to best practices in the optimization techniques implementation in medicine marked an extremely rare their application in optimization of therapeutic intervention for individual patients (Crown et al., 2017). One of the few examples of personalized strategies calculation for a particular dynamic programming model is given by Denton, Kurt, Shah, Bryant & Smith (2009). The calculation involves determining the optimal start time for statin treatment of patients with type 2 diabetes. The strategy is personalized depending on the presence in the history of coronary artery disease and cholesterol levels. However, the work does not offer a broader view of the problem as a whole, which leaves the need for common approaches to the task of personalizing strategies. Thus, it can be considered expedient the development and study of this optimization problems class, the development of tools for studying the solutions obtained.

Key Terms in this Chapter

Learning Sample: The whole sample of objects for which is known the class accordance.

External Criterion: A suitably chosen criterion for model structure evaluating.

Generalized Variable: Member of a complete polynomial of a given degree.

Model of the Optimal Structure: Is understood in a sense of achieving an extremum of the algorithm external criterion.

Testing Sample: A sample of objects that using in GMDH algorithms mainly for selection of model structure.

GMDH: Group method of data handling; the structural-parametric synthesis method with an implicit fine for the model complexity.

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