Finding optimal design in nonlinear mixed effect models using multiplicative algorithms

Abstract

Background and objectives: To optimize designs for longitudinal studies analyzed by nonlinear mixed effect models (NLMEMs), the Fisher information matrix (FIM) can be used. In this work, we focused on the multiplicative algorithms, previously applied in standard individual regression, to find optimal designs for NLMEMs.

Methods: We extended multiplicative algorithms to mixed models and implemented the algorithm both in R and in C. Then, we applied the algorithm to find D-optimal designs in two longitudinal data examples, one with continuous and one with binary outcome.

Results: For these examples, we quantified the improved speed when C is used instead of R. Design optimization using the multiplicative algorithm led to designs with D-efficiency gains between 13% and 25% compared to non-optimized designs.

Conclusion: We found that the multiplicative algorithm can be used efficiently to design longitudinal studies.

Keywords: D-optimality; Fisher information matrix; Longitudinal studies; Multiplicative algorithm; Nonlinear mixed effect model; Optimal design.