Optimal Design in Hierarchical Models with application in Multi-center Trials

TL;DR

This paper investigates optimal experimental designs for individual predictions in hierarchical models, especially in multi-center trials, revealing that balanced designs are often suboptimal when treatment effects vary significantly.

Contribution

It introduces methods to determine optimal designs for individual predictions in hierarchical models and compares them to traditional balanced designs in multi-center trials.

Findings

Balanced designs are suboptimal with high treatment effect variability.

More subjects should be allocated to the active treatment in such cases.

Efficiency loss with balanced designs may be limited, leading to moderate sample size increases.

Abstract

Hierarchical random effect models are used for different purposes in clinical research and other areas. In general, the main focus is on population parameters related to the expected treatment effects or group differences among all units of an upper level (e.g. subjects in many settings). Optimal design for estimation of population parameters are well established for many models. However, optimal designs for the prediction for the individual units may be different. Several settings are identiffed in which individual prediction may be of interest. In this paper we determine optimal designs for the individual predictions, e.g. in multi-center trials, and compare them to a conventional balanced design with respect to treatment allocation. Our investigations show, that balanced designs are far from optimal if the treatment effects vary strongly as compared to the residual error and more subjects should be recruited to the active (new) treatment in multi-center trials. Nevertheless, effciency loss may be limited resulting in a moderate sample size increase when individual predictions are foreseen with a balanced allocation.