Merging mixture components for cell population identification in flow cytometry

Abstract

We present a framework for the identification of cell subpopulations in flow cytometry data based on merging mixture components using the flowClust methodology. We show that the cluster merging algorithm under our framework improves model fit and provides a better estimate of the number of distinct cell subpopulations than either Gaussian mixture models or flowClust, especially for complicated flow cytometry data distributions. Our framework allows the automated selection of the number of distinct cell subpopulations and we are able to identify cases where the algorithm fails, thus making it suitable for application in a high throughput FCM analysis pipeline. Furthermore, we demonstrate a method for summarizing complex merged cell subpopulations in a simple manner that integrates with the existing flowClust framework and enables downstream data analysis. We demonstrate the performance of our framework on simulated and real FCM data. The software is available in the flowMerge package through the Bioconductor project.

Figure 1

flowClust_BIC, flowClust_ICL, flowMerge solutions for automated gating of forward versus side scatter across 137 clinical samples of CLL. The flowClust_BIC fit: black solid curve. The flowClust_ICL fit: red dashed curve. The flowMerge fit: green dashed curve.

Figure 2

Examples of the flowClust_BIC, flowClust_ICL, flowMerge cluster solutions for forward versus side scatter in a sample of CLL flow cytometry data. (a) The flowClust_BIC solution with seven clusters. (b) The flowClust_ICL solution with two clusters. (c) The entropy versus number of clusters plot, fit to a two-component piecewise linear regression model. The best fitting model has a changepoint at three clusters. (d) The flowMerge solution corresponding to K = 3 clusters provides a better fit to the lymphocyte population than either the flowClust_BIC or flowClust_ICL solutions and provides a good estimate of the true number of cell populations.

Figure 3

The number of clusters chosen by the flowClust_BIC, flowClust_ICL, flowMerge, and GMM_BIC solutions for automated gating of CD8, CD4, and CD7 across 137 samples of CLL. The flowClust_BIC solution: solid black curve. The flowClust_ICL solution: dashed red curve. The flowMerge solution derived from the flowClust_BIC solution: dashed green curve. The GMM_BIC solution: dashed blue curve.

Figure 4

Example of flowClust_ICL, flowClust_BIC, and flowMerge solutions fitted to a CLL sample in the CD8, CD4, and CD7 dimensions. (a) Three projections of the flowClust_ICL solution. (b) Three projections of the flowClust_BIC solution. (c) Entropy versus number of clusters for a series of flowMerge model fits with a piecewise linear regression fitted to the data. The changepoint located at K = 5 clusters is selected automatically. (d) Three projections of flowMerge solution with K = 5 clusters derived from the flowClust_BIC solution.

Figure 5

Detecting failed cluster merging. (a) Distribution of the entropy (normalized for the number of events and clusters) of the flowMerge solution for forward versus side scatter (left) and fluorescence channels (right) across 137 samples. (b) The relationship between the normalized entropy and the number of clusters in the flowMerge solution for forward scatter versus side scatter (left) and fluorescence channels (right). (c) Example of flowMerge solutions with unusually high normalized entropy from the right tail of the distribution for forward versus side scatter (left) and fluorescence (right). (d) A plot of the normalized entropy versus samples grouped by antibody labels identifies antibody combinations that are problematic for automated gating with the automated merging algorithm.

Figure 5

Detecting failed cluster merging. (a) Distribution of the entropy (normalized for the number of events and clusters) of the flowMerge solution for forward versus side scatter (left) and fluorescence channels (right) across 137 samples. (b) The relationship between the normalized entropy and the number of clusters in the flowMerge solution for forward scatter versus side scatter (left) and fluorescence channels (right). (c) Example of flowMerge solutions with unusually high normalized entropy from the right tail of the distribution for forward versus side scatter (left) and fluorescence (right). (d) A plot of the normalized entropy versus samples grouped by antibody labels identifies antibody combinations that are problematic for automated gating with the automated merging algorithm.

Figure 6

Simulation results for CD4 versus CD8 dimensions of a CLL sample. (a) The 2D kernel density estimate of the real CD4 versus CD8 data. Gates for the CD4+/CD8− , CD8+/CD4− , and CD4−/CD8− subpopulations are represented by light coloured lines. Events outside the gates are considered outliers. (b) An example of the kernel density estimate of simulated data drawn from the distribution defined by the real data. (c) The number of clusters selected by the flowMerge solution, the GMM_BIC solution, the flowClust_BIC, and flowClust_ICL solutions over 100 realizations of simulated data. (d) The median flowClust_BIC flowClust solution with 9 components. (e) The median flowMerge solution with 5 components. (f) The misclassification rate (MCR) for the flowMerge_K solution, the GMM_K solution, and the flowClust_K solution with the number of clusters fixed to the true number of cell subpopulations (K = 3). (g) The misclassification rates for the three components from the optimal GMM_BIC, flowClust_BIC, and flowMerge solutions minimizing the MCR. (h) A GMM, (i) flowClust, (j) and flowMerge_K solution with a fixed number of clusters.

Figure 6

Simulation results for CD4 versus CD8 dimensions of a CLL sample. (a) The 2D kernel density estimate of the real CD4 versus CD8 data. Gates for the CD4+/CD8− , CD8+/CD4− , and CD4−/CD8− subpopulations are represented by light coloured lines. Events outside the gates are considered outliers. (b) An example of the kernel density estimate of simulated data drawn from the distribution defined by the real data. (c) The number of clusters selected by the flowMerge solution, the GMM_BIC solution, the flowClust_BIC, and flowClust_ICL solutions over 100 realizations of simulated data. (d) The median flowClust_BIC flowClust solution with 9 components. (e) The median flowMerge solution with 5 components. (f) The misclassification rate (MCR) for the flowMerge_K solution, the GMM_K solution, and the flowClust_K solution with the number of clusters fixed to the true number of cell subpopulations (K = 3). (g) The misclassification rates for the three components from the optimal GMM_BIC, flowClust_BIC, and flowMerge solutions minimizing the MCR. (h) A GMM, (i) flowClust, (j) and flowMerge_K solution with a fixed number of clusters.