Logical analysis of sample pooling for qualitative analytical testing

Abstract

When the prevalence of positive samples in a whole population is low, the pooling of samples to detect them has been widely used for epidemic control. However, its usefulness for applying analytical screening procedures in food safety (microbiological or allergen control), fraud detection or environmental monitoring is also evident.

The expected number of tests per individual sample that is necessary to identify all ‘positives’ is a measure of the efficiency of a sample pooling strategy. Reducing this figure is key to an effective use of available resources in environmental control and food safety. This reduction becomes critical when the availability of analytical tests is limited, as the SARS-CoV-2 pandemic showed.

The outcome of the qualitative analytical test is binary. Therefore, the operation governing the outcome of the pooled samples is not an algebraic sum of the individual results but the logical operator (‘or’ in natural language). Consequently, the problem of using pooled samples to identify positive samples naturally leads to proposing a system of logical equations. Therefore, this work suggests a new strategy of sample pooling based on: i) A half-fraction of a Placket-Burman design to make the pooled samples and ii) The logical resolution, not numerical, to identify the positive samples from the outcomes of the analysis of the pooled samples.

For a prevalence of ‘positive’ equal to 0.05 and 10 original samples to be pooled, the algorithm presented here results in an expected value per individual equal to 0.37, meaning a 63% reduction in the expected number of tests per individual sample.

With sensitivities and specificities of the analytical test ranging from 0.90 to 0.99, the expected number of tests per individual ranges from 0.332 to 0.416, always higher than other pooled testing algorithms. In addition, the accuracy of the algorithm proposed is better or similar to that of other published algorithms, with an expected number of hits ranging from 99.16 to 99.90%.

The procedure is applied to the detection of food samples contaminated with a pathogen (Listeria monocytogenes) and others contaminated with an allergen (Pistachio) by means of Polymerase Chain Reaction, PCR, test.