Sequential Dirichlet process mixtures of multivariate skew $t$-distributions for model-based clustering of flow cytometry data

Flow cytometry is a high-throughput technology used to quantify multiple surface and intracellular markers at the level of a single cell. This enables us to identify cell subtypes and to determine their relative proportions. Improvements of this technology allow us to describe millions of individual cells from a blood sample using multiple markers. This results in high-dimensional datasets, whose manual analysis is highly time-consuming and poorly reproducible. While several methods have been developed to perform automatic recognition of cell populations most of them treat and analyze each sample independently. However, in practice individual samples are rarely independent, especially in longitudinal studies. Here we analyze new longitudinal flow-cytometry data from the DALIA-1 trial, which evaluates a therapeutic vaccine against HIV, by proposing a new Bayesian nonparametric approach with Dirichlet process mixture (DPM) of multivariate skew t-distributions to perform model based clustering of flow-cytometry data. DPM models directly estimate the number of cell populations from the data, avoiding model selection issues, and skew t-distributions provides robustness to outliers and nonelliptical shape of cell populations. To accommodate repeated measurements, we propose a sequential strategy relying on a parametric approximation of the posterior. We illustrate the good performance of our method on simulated data and on an experimental benchmark dataset. This sequential strategy outperforms all other methods evaluated on the benchmark dataset and leads to improved performance on the DALIA-1 data.