Optimal experimental designs for ordinal models with mixed factors for industrial and healthcare applications

Abstract

Models with ordinal outcomes are an important part of generalized linear models and design issues for them are less studied, especially when the model has discrete and continuous factors. We propose an effective and flexible Particle Swarm Optimization (PSO) algorithm for finding locally D-optimal approximate designs for experiments with ordinal outcomes modeled using the cumulative logit link. We apply our technique to obtain a locally D-optimal approximate design for an odor removal experiment with both discrete and continuous factors and show that this design is superior to the design obtained by discretizing the continuous factor. Additionally, we find a pseudo-Bayesian D-optimal approximate design for this problem and study the performance of both designs under a range of plausible parameter values. We also (i) demonstrate PSO’s versatility by finding locally D-optimal approximate designs for a manufacturing example with surface defects and multiple continuous factors, and (ii) use PSO to find other optimal designs for estimating percentiles in a dose-response study.