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.

Keywords:

• approximate design
• dose-response
• particle swarm optimization
• qualitative factors
• quantitative factors

Acknowledgments

The content of this paper is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

Additional information

Funding

The research of Dr. Wong was partially supported by a grant from the National Institute of General Medical Sciences of the National Institutes of Health under Award Number R01GM107639.

Notes on contributors

Joshua Lukemire

Joshua Lukemire is a Ph.D. candidate in Biostatistics at Emory University. He received his bachelor's in Statistics from the University of Georgia, and his master's degree in Biostatistics from Emory University. His research interests include design of experiments and neuroimaging statistics.

Abhyuday Mandal

Abhyuday Mandal is a Professor and the Undergraduate Coordinator of the University of Georgia, Department of Statistics. He received his bachelor's and master's degrees from Indian Statistical Institute, Kolkata, another master's degree from University of Michigan and Ph.D. in 2005 from Georgia Institute of Technology. His research interests include design of experiments, optimization techniques and survey sampling. Currently he is an Associate Editor of Sankhya - Series B, Statistics and Probability Letters and Journal of Statistical Theory and Practice.

Weng Kee Wong

Weng Kee Wong is a Professor of Biostatistics at UCLA Fielding School of Public Health. He is a Fellow of the Institute of Mathematical Statistics, a Fellow of the American Statistical Association, a Fellow of the American Association for the Advancement of Science and an elected member of the International Statistical Institute. He received his Ph.D. in Statistics from the University of Minnesota in 1990 and has served as Principal Investigator on multiple R01 grants from NIH. He is currently associate editor for multiple statistics journals and his current research area is in use of metaheuristics to find various types of optimal designs for challenging and high-dimensional problems in the biomedical and industrial areas.