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In immunological studies, the characterization of small, functionallydistinct cell subsets from blood and tissue is crucial to decipher system levelbiological changes. An increasing number of studies rely on assays that providesingle-cell measurements of multiple genes and proteins from bulk cell samples.A common problem in the analysis of such data is to identify biomarkers (orcombinations of thereof) that are differentially expressed between twobiological conditions (e.g., before/after vaccination), where expression isdefined as the proportion of cells expressing the biomarker or combination inthe cell subset of interest.  Here, we present a Bayesian hierarchical framework based on a beta-binomialmixture model for testing for differential biomarker expression usingsingle-cell assays. Our model allows inference to be subject specific, as istypically required when accessing vaccine responses, while borrowing strengthacross subjects through common prior distributions. We propose two approachesfor parameter estimation: an empirical-Bayes approach using anExpectation-Maximization algorithm and a fully Bayesian one based on a Markovchain Monte Carlo algorithm. We compare our method against frequentistapproaches for single-cell assays including Fisher's exact test, a likelihoodratio test, and basic log-fold changes. Using several experimental assaysmeasuring proteins or genes at the single-cell level and simulated data, weshow that our method has higher sensitivity and specificity than alternativemethods. Additional simulations show that our framework is also robust to modelmisspecification. Finally, we also demonstrate how our approach can be extendedto testing multivariate differential expression across multiple biomarkercombinations using a Dirichlet-multinomial model and illustrate thismultivariate approach using single-cell gene expression data and simulations.

Mixture Models for Single Cell Assays with Applications to Vaccine Studies