Optimal designs for comparing regression models with correlated observations

Abstract

We consider the problem of efficient statistical inference for comparing two regression curves estimated from two samples of dependent measurements. Based on a representation of the best pair of linear unbiased estimators in continuous time models as a stochastic integral, an efficient pair of linear unbiased estimators with corresponding optimal designs for finite sample size is constructed. This pair minimises the width of the confidence band for the difference between the estimated curves. We thus extend results readily available in the literature to the case of correlated observations and provide an easily implementable and efficient solution. The advantages of using such pairs of estimators with corresponding optimal designs for the comparison of regression models are illustrated via numerical examples.

Lessons learned from IDeAl — 33 recommendations from the IDeAl-net about design and analysis of small population clinical trials

“…Finally, optimal designs for the comparison of curves have been developed, which minimizes the maximum width of the confidence band for the difference between two regression functions. In particular, it was demonstrated that the application of optimal designs instead of commonly used designs yields a reduction of the width of the confidence band by more than 50% [ 86 , 87 ].…”

“…In summary, we developed a new optimized design and analysis strategy for comparing dose-response profiles to extrapolate clinical trial results from a larger to a smaller population. The comparison of dose response curves should be done by the bootstrap approach [ 47 , 87 ]. If the aim of the study is the extrapolation of efficacy and safety information, we recommend considering and comparing the MEDs of two given populations [ 84 ].…”

“… The derived methodology shows a very robust performance and can be used also in cases where no precise information about the functional form of the regression curves is available [ 88 ]. In case of planning a dose-finding study comparing two populations, we recommend to use optimal designs in order to achieve substantially more precise results [ 86 , 87 ]. …”

Minimax D-optimal designs for multivariate regression models with multi-factors

“…Another body of work investigated optimal designs under continuous time regression models with correlated errors (Dette et al 2016, Dette, Konstantinou & Zhigljavsky 2017, Dette, Schorning & Konstantinou 2017, Dette et al 2018), including continuous time versions of model (1)- (3) Unfortunately, in practice, V is never known, which makes it impossible to use the GLSE with W = V , or the optimal designs for the GLSE with W = V .…”

Optimal experimental design that minimizes the width of simultaneous confidence bands

“…The optimal design problem focusing on the width of the simultaneous confidence bands can be formalized in a different way. When comparing two estimated regression curves, Dette and Schorning (2016) and Dette, et al (2017) proposed to minimize the L por L ∞ -norm of the variance function of the estimator of the difference between the two curves. They demonstrated that their proposal reduces the width substantially compared with the pair of optimized designs for individual regression models.…”