Automated High-Dimensional Flow Cytometric Data Analysis

Abstract

Flow cytometric analysis allows rapid single cell interrogation of surface and intracellular determinants by measuring fluorescence intensity of fluorophore-conjugated reagents. The availability of new platforms, allowing detection of increasing numbers of cell surface markers, has challenged the traditional technique of identifying cell populations by manual gating and resulted in a growing need for the development of automated, high-dimensional analytical methods. We present a direct multivariate finite mixture modeling approach, using skew and heavy-tailed distributions, to address the complexities of flow cytometric analysis and to deal with high-dimensional cytometric data without the need for projection or transformation. We demonstrate its ability to detect rare populations, to model robustly in the presence of outliers and skew, and to perform the critical task of matching cell populations across samples that enables downstream analysis. This advance will facilitate the application of flow cytometry to new, complex biological and clinical problems.finite mixture model ͉ flow cytometry ͉ multivariate skew distribution F low cytometry transformed clinical immunology and hematology over 2 decades ago by allowing the rapid interrogation of cell surface determinants and, more recently, by enabling the analysis of intracellular events using fluorophore-conjugated antibodies or markers. Although flow cytometry initially allowed the investigation of only a single fluorophore, recent advances allow close to 20 parallel channels for monitoring different determinants (1-4). These advances have now surpassed our ability to interpret manually the resulting high-dimensional data and have led to growing interest and recent activity in the development of new computational tools and approaches (5-8).The difficulty in data analysis arises from the traditional technique of identifying discrete cell populations by manual gating, which is a labor-intensive process and varies by user experience. The initial computational packages for flow cytometric analyses focused largely on different preprocessing tasks such as data acquisition, normalization, and live cell gating. Besides visualization and transformation of flow cytometric data, useful tools such as Flowjo (www.flowjo.com) and the packages in BioConductor (www.bioconductor.org) (such as prada, flowCore, flowViz, flowUtils, and rflowcyt) allow some form of software-assisted gating and extraction of populations of interest. The operator subjectively demarcates a cell population while moving through successive 2-or 3-dimensional projections of the data. This process limits the reproducibility of data processing. A more fundamental problem is that this lower dimensional visualization hinders the identification of higher-dimensional features. Furthermore, current methods extract only a limited number of sample parameters, such as the mean fluorescence intensity of a cell population, which can lead to loss of critical information in defining the properties of a cell population....

Maximum likelihood inference for mixtures of skew Student-t-normal distributions through practical EM-type algorithms

“…Flow cytometry is extensively used in a large number of biomedical applications such as molecular and cellular biology (e.g., to measure DNA content), hematology (e.g., to test leukemia samples) and immunology (e.g., to conduct CD4 tests for HIV AIDS). Very recently, it was shown by Pyne et al (2009) andFrühwirth-Schnatter andPyne (2010) that flow cytometric data are ideally suited for multimodal asymmetric finite mixture modelling.…”

“…Lin et al (2007a) proposed a novel mixture model using the skew t (ST) distribution of Azzalini and Capitaino (2003), called the STMIX model, allowing for accommodation of both skewness and thick tails for making more robust inferences. More recently, Pyne et al (2009) and Lin (2010) extended the STMIX model to multivariate cases using two variants of multivariate skew t distribution proposed by Azzalini and Capitaino (2003) and Sahu et al (2003), respectively. Karlis and Santourian (2009) considered the use of finite mixtures of the normal inverse Gaussian distribution and its multivariate extensions.…”

A robust factor analysis model using the restricted skew- $$t$$ t distribution

“…Based on Pyne et al (2009), a p-dimensional random vector Y is said to follow a rMST distribution with location vector μ ∈ R p , scale covariance matrix , skewness vector λ ∈ R p and df ν ∈ (0, ∞), denoted as r St p (μ, , λ, ν), if it can be represented by…”

“…In many biological applications (cf. Pyne et al 2009;Rossin et al 2011;Ho et al 2012) and other applied problems, however, the data often involve observations whose distributions are highly asymmetric as well as having fat tails.…”

Location and scale mixtures of Gaussians with flexible tail behaviour: Properties, inference and application to multivariate clustering

“…Another popular distributional form allowing for skewness and heavy or light tails includes different forms of the multivariate skew-t. As presented by Lee and McLachlan (2013c), most formulations adopt either a restricted or unrestricted characterization. Unrestricted forms include the proposals and implementations of Sahu et al (2003), Lee and McLachlan (2014b) and Lin (2010) while restricted forms include that of Azzalini and Capitanio (2003), Basso et al (2010), Branco and Dey (2001), Cabral et al (2012) and Pyne et al (2009). In more recent work, Lee and McLachlan (2014a) pointed out that both restricted an unrestricted characterizations could be unified under a more general formulation referred to as Canonical fundamental skew-t distribution.…”