Uncertainty Quantification of Fluorescence Signals in Flow Cytometry Part I: An Analytical Perspective Beyond Q and B

This manuscript is the first in a series that develops and realizes core ideas from metrology and uncertainty quantification (UQ) as applied to flow cytometry. The work herein is motivated by the problem of estimating the detection efficiency (Q) and background (B) of cytometers. Despite more than 30 years of study, canonical solutions to this problem make approximations that both ignore and amplify various sources of noise, thereby leading to unstable estimators of $Q$ and negative values of $B$. Moreover, it is not always clear how to compare instruments on the basis of such properties. To address these issues, we propose a global data analysis strategy that combines measurements taken with different gains while simultaneously accounting for gain-independent background effects, which are typically ignored but often dominant. Of note, this technique yields stable estimates of $Q$ and $B$ while also quantifying the relative impacts of other noise sources. Conceptually, our analysis also unifies and explains the shortcomings of existing data analysis methods. Most importantly, however, this work allows us to rigorously define concepts such as limits of detection and quantification associated with instrument performance alone and in a way that removes effects associated with sample preparation, operator effects, and so forth. Importantly, this allows for direct comparison of cytometers on the basis of sample-independent uncertainty metrics and yields information for optimizing cytometer performance in terms of instrument-induced uncertainties. Results are experimentally verified using both commercial instruments and a NIST-developed serial cytometer, with extensions considered in companion manuscripts of this series.