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.

背景和目标：为了优化非线性混合效应模型 (NLMEM) 分析的纵向研究设计，可以使用 Fisher 信息矩阵 (FIM)。在这项工作中，我们专注于先前应用于标准个体回归的乘法算法，以寻找 NLMEM 的最佳设计。

方法：我们将乘法算法扩展到混合模型，并在 R 和 C 中实现了该算法。然后，我们应用该算法在两个纵向数据示例中找到 D 最优设计，一个是连续的，一个是二元结果。

结果：对于这些示例，我们量化了使用 C 而不是 R 时提高的速度。与非优化设计相比，使用乘法算法的设计优化导致设计的 D 效率增益介于 13% 和 25% 之间。

结论：我们发现乘法算法可以有效地用于设计纵向研究。