Cytometry inference through adaptive atomic deconvolution

TL;DR

This paper introduces an adaptive statistical method for atomic deconvolution to analyze flow cytometry data, estimating cell surface molecule presence and fluorescence distribution with proven optimal convergence rates.

Contribution

It develops an adaptive estimation procedure using Lepskii's method for automatic bandwidth selection in atomic deconvolution, with theoretical guarantees and real data application.

Findings

Estimates the percentage of cells expressing specific molecules.

Achieves minimax optimal convergence rates in Sobolev classes.

Successfully applied to simulated and real biological data.

Abstract

In this paper we consider a statistical estimation problem known as atomic deconvolution. Introduced in reliability, this model has a direct application when considering biological data produced by flow cytometers. In these experiments, biologists measure the fluorescence emission of treated cells and compare them with their natural emission to study the presence of specific molecules on the cells' surface. They observe a signal which is composed of a noise (the natural fluorescence) plus some additional signal related to the quantity of molecule present on the surface if any. From a statistical point of view, we aim at inferring the percentage of cells expressing the selected molecule and the probability distribution function associated with its fluorescence emission. We propose here an adap-tive estimation procedure based on a previous deconvolution procedure introduced by [vEGS08, GvES11]. For both estimating the mixing parameter and the mixing density automatically, we use the Lepskii method based on the optimal choice of a bandwidth using a bias-variance decomposition. We then derive some concentration inequalities for our estimators and obtain the convergence rates, that are shown to be minimax optimal (up to some log terms) in Sobolev classes. Finally, we apply our algorithm on simulated and real biological data.