Strong Orthogonal Arrays and Orthogonal Array-Based Latin Hypercube Designs for Planning Experiments: A Method for Improving Study Design in Biomedical Research

Abstract

Orthogonal Array-based Latin Hypercube Designs (OALHDs) have not only become popular in practice among techniques used in the development of computer experiments but also helpful whenever interest is on designing some traditional experiments. Design construction for computer experiments has become a novel area especially in Nigeria and Africa at large since it is more about experimental planning rather than modelling aspect in which some progress has been made. The Bush Construction Type II method was used in this study to construct a strong Orthogonal Array (OA) of strength three, using Galois Fields (GF) of order s which gave rise to the constructed Orthogonal Array-Based Latin Hypercube Designs (OALHDs) for planning experiments. The OALHD was used in this research as a Latin hypercube design constructed based on orthogonal arrays in order to achieve better space-filling properties that would otherwise not be accomplished by a random Latin hypercube design (LHD). Orthogonal Array (N, k) LHD were constructed at parameter values of OA (N, k) = (216, 8) and (343, 9). This study aims at applying the OALHDs constructed to improve the study design or conducted in biomedical research. The health related quality of health data of HIV patients was used in the application. This is a novel approach in the medical setting. The method of construction employed the maximin criterion in the k- Nearest Neighbour with Euclidean distance for constructing strong the Orthogonal Array-Based Latin Hypercube Designs (OALHDs). The OA (216, 8) LHD and OA (343, 9) LHD constructed possessed better space-filling properties and they achieve uniformity in each dimension of the designed variables. This study concludes that the OALHDs can be used to improve the study design in biomedical research. A MATLAB 2016 computer package was used for program implementation and analysis. Keywords: Computer experiments, Bush construction type II method, Galois fields, Latin hypercube designs, Orthogonal array