Evaluation of Combinatorial Optimisation Algorithms for c-Optimal Experimental Designs with Correlated Observations

TL;DR

This paper evaluates combinatorial optimisation algorithms for finding c-optimal experimental designs in correlated data, demonstrating their effectiveness and robustness compared to other methods.

Contribution

It introduces the application of simple minimisation algorithms to c-optimal design with correlated observations and compares their performance.

Findings

Local and reverse greedy searches perform similarly, with worst designs within 10% variance of the best.

Algorithms outperform multiplicative weight methods in design quality.

Extended algorithms can identify model-robust c-optimal designs.

Abstract

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 $<10\%$ 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 moole-robust c-optimal designs.