Effective matrix designs for COVID-19 group testing.

Area of Science:

• Infectious Disease Epidemiology
• Biostatistics
• Combinatorial Mathematics

Background:

• Group testing strategies, such as pooling samples, can significantly reduce resource expenditure for COVID-19 testing compared to individual testing, particularly when disease prevalence is low.
• Existing pooling matrices and decoding algorithms have limitations, creating a need for more efficient and flexible designs.
• Review of published pooling matrices and decoding algorithms highlights gaps in current combinatorial methods for constructing effective group testing designs.

Approach:

• Developed a novel algorithm, Polynomial Pools (PP), utilizing polynomial constructions on a sample grid to generate pooling assignments.
• Derived direct formulas for creating pooling designs that guarantee accurate decoding of individual samples.
• Expanded the parameter space for constructing pooling matrices beyond current methodologies.

Key Points:

• The Polynomial Pools (PP) algorithm enables the creation of one-round pooling designs with high compression ratios.
• PP designs ensure correct decoding of all samples, accommodating a specified number of positive cases.
• This approach integrates and generalizes recent combinatorial methods for COVID-19 testing, offering enhanced design capabilities.

Conclusions:

• Group testing remains a resource-efficient strategy for COVID-19 surveillance, especially at low prevalence levels.
• The Polynomial Pools (PP) method addresses existing gaps in combinatorial group testing constructions.
• PP facilitates the development of new, advantageous pooling designs applicable to various testing scenarios.