Algorithmic construction of optimal block designs for two-colour cDNA microarray experiments using the linear mixed effects model

ABSTRACT

In this study, methods for efficient construction of A-, MV-, D- and E-optimal or near-optimal block designs for two-colour cDNA microarray experiments with array as the block effect are considered. Two algorithms, namely the array exchange and treatment exchange algorithms together with the complete enumeration technique are introduced. For large numbers of arrays or treatments or both, the complete enumeration method is highly computer intensive. The treatment exchange algorithm computes the optimal or near-optimal designs faster than the array exchange algorithm. The two methods however produce optimal or near-optimal designs with the same efficiency under the four optimality criteria.

Keywords:

• Array exchange algorithm
• A-, MV-, D- and E-optimal designs
• Complete enumeration
• Microarray experiment
• Treatment exchange algorithm

MATHEMATICS SUBJECT CLASSIFICATION:

• 62K10

Additional information

Funding

This research is supported by grants from the National Research Foundation (NRF) through the Competitive Support for Unrated Researchers Programme (Reference: CSUR14080485666, Grant No: 98717 and Grant holder: Prof L. K. Debusho) and the Incentive Funding for Rated Researchers Programme (Grant No: UID 85456 and Grant holder: L. M. Haines), the University of South Africa and the University of Cape Town. Any opinion, finding and conclusion or recommendation expressed in this material is that of the authors and the NRF does not accept liability in this regard.