Partitioning and subsampling statistics in compartment-based quantification methods

The precision of compartment-based quantification methods is subject to multiple effects, of which partitioning and subsampling play a major role. Partitioning is the process of aliquoting the sample liquid and consequently the contained target molecules, whereas subsampling denotes the fact that usually only a portion of a sample is analyzed. In this work, we present a detailed statistical description comprising the effects of partitioning and subsampling on the relative uncertainty of the test result. We show that the state-of-the-art binomial model does not provide accurate results for the level of subsampling present when analyzing the nucleic acid content of single specific cells. Hence, in this work we address partitioning and subsampling effects separately and subsequently combine them to derive the relative uncertainty of a test system and compare it for single cell content analysis and body fluid analysis. In point-of-care test systems the area for partitioning and detection is usually limited, which means that a trade-off between the number of partitions (related to a partitioning uncertainty) and the amount of analyzed volume (related to a subsampling uncertainty) might be inevitable. In case of low target concentration, the subsampling uncertainty is dominant whereas for high target concentration, the partitioning uncertainty increases, and a larger number of partitions is beneficial to minimize the combined uncertainty. We show, that by minimizing the subsampling uncertainty in the test system, the quantification uncertainty of low target concentrations in single cell content analysis is much smaller than in body fluid analysis. In summary, the work provides the methodological basis for a profound statistical evaluation of partitioning and subsampling effects in compartment-based quantification methods and paves the way towards an improved design of future digital quantification devices for highly accurate molecular diagnostic analysis at the point-of-care.