GLMMs for nucleic acid concentration estimation in digital droplet PCR

Digital droplet polymerase chain reaction (ddPCR) is a recently developed alternative for nucleic acids quantification that allows for more accurate and precise estimation of nucleic acids concentrations. By splitting up a sample into about 14000 droplets using microfluidic technology and subsequently counting the numbers of negative (no nucleic acid was initially present) and positive (nucleic acid was initially present) droplets, the concentration of the nucleic acid can be determined by using a Poisson distribution. Often, the procedure is repeated (technical replication) to further increase the accuracy and precision of the concentration estimate.To estimate a copy number variation (CNV), the quantification process is conducted in parallel: the presence or absence for two nucleic acids is measured simultaneously by using two different fluorescent dyes, thus resulting in two concentration estimates. Taking a ratio of these estimates finally results in an estimate for the CNV. We show how the concentration estimation follows from using the generalized linear mixed model (GLMM) framework and how it extends to the CNV case. Furthermore, the GLMM framework also allows for estimation of the concentration and CNV by making use of the technical replicates of the samples through introduction of a random effect. We illustrate the importance of this increased accuracy and precision for applications in a medical diagnostic setting.