Optimal designs for comparing regression curves -- dependence within and between groups

TL;DR

This paper develops optimal experimental designs for comparing two regression curves with dependent data, utilizing stochastic analysis to improve estimation precision and confidence band width.

Contribution

It introduces a novel approach combining continuous-time models and stochastic analysis to derive efficient designs for dependent data in regression comparison.

Findings

Simultaneous estimation improves precision over separate estimation.

Optimal designs significantly narrow confidence bands.

Simulation confirms efficiency gains with the proposed method.

Abstract

We consider the problem of designing experiments for the comparison of two regression curves describing the relation between a predictor and a response in two groups, where the data between and within the group may be dependent. In order to derive efficient designs we use results from stochastic analysis to identify the best linear unbiased estimator (BLUE) in a corresponding continuous time model. It is demonstrated that in general simultaneous estimation using the data from both groups yields more precise results than estimation of the parameters separately in the two groups. Using the BLUE from simultaneous estimation, we then construct an efficient linear estimator for finite sample size by minimizing the mean squared error between the optimal solution in the continuous time model and its discrete approximation with respect to the weights (of the linear estimator). Finally, the optimal design points are determined by minimizing the maximal width of a simultaneous confidence band for the difference of the two regression functions. The advantages of the new approach are illustrated by means of a simulation study, where it is shown that the use of the optimal designs yields substantially narrower confidence bands than the application of uniform designs.