Watson Samuel I, Pan Yi
Insitute of Applied Health Research, University of Birmingham, Birmingham, UK.
Stat Comput. 2023;33(5):112. doi: 10.1007/s11222-023-10280-w. Epub 2023 Jul 29.
We show how combinatorial optimisation algorithms can be applied to the problem of identifying c-optimal experimental designs when there may be correlation between and within experimental units and evaluate the performance of relevant algorithms. We assume the data generating process is a generalised linear mixed model and show that the c-optimal design criterion is a monotone supermodular function amenable to a set of simple minimisation algorithms. We evaluate the performance of three relevant algorithms: the local search, the greedy search, and the reverse greedy search. We show that the local and reverse greedy searches provide comparable performance with the worst design outputs having variance greater than the best design, across a range of covariance structures. We show that these algorithms perform as well or better than multiplicative methods that generate weights to place on experimental units. We extend these algorithms to identifying modle-robust c-optimal designs.
The online version contains supplementary material available at 10.1007/s11222-023-10280-w.
我们展示了组合优化算法如何应用于在实验单元之间和内部可能存在相关性的情况下识别c最优实验设计的问题，并评估相关算法的性能。我们假设数据生成过程是一个广义线性混合模型，并表明c最优设计准则是一个单调超模函数，适用于一组简单的最小化算法。我们评估了三种相关算法的性能：局部搜索、贪婪搜索和反向贪婪搜索。我们表明，在一系列协方差结构中，局部搜索和反向贪婪搜索提供了可比的性能，最差设计输出的方差大于最佳设计。我们表明，这些算法的性能与为实验单元生成权重的乘法方法一样好或更好。我们将这些算法扩展到识别模型稳健的c最优设计。
在线版本包含可在10.1007/s11222-023-10280-w获取的补充材料。
