Constructions and Comparisons of Pooling Matrices for Pooled Testing of COVID-19

Area of Science:

• Biostatistics
• Combinatorial Mathematics
• Computational Biology

Background:

• Group testing offers cost-effective alternatives to individual testing by pooling samples.
• Effective group testing relies on optimal pooling matrices and decoding algorithms.
• Existing pooling matrices have limitations in adapting to varying prevalence rates.

Purpose of the Study:

• To introduce a novel family of pooling matrices derived from packing the pencil of lines (PPoL) in finite projective planes.
• To evaluate the performance of PPoL matrices against established methods like 2D-pooling, P-BEST, and Tapestry.
• To assess the impact of prevalence rates on the efficiency and cost-effectiveness of different group testing strategies.

Main Methods:

• Development of a new family of pooling matrices based on packing the pencil of lines (PPoL).
• Performance comparison using the two-stage definite defectives (DD) decoding algorithm.
• Extensive simulations across a range of prevalence rates (up to 5%) to evaluate relative costs.

Main Results:

• No single pooling matrix demonstrated optimal performance across all tested prevalence rates.
• The proposed PPoL matrices showed adaptable performance, with construction parameters adjustable to prevalence rates.
• PPoL matrices emerged as a potentially superior alternative to fixed pooling matrices for dynamic optimization.

Conclusions:

• The choice of pooling matrix significantly impacts the efficiency and cost of group testing.
• The PPoL matrix family provides a flexible and potentially more cost-effective solution for group testing by adapting to prevalence rates.
• Dynamic adjustment of pooling matrix parameters is crucial for optimizing group testing performance.