Example: Clustering of the Rituximab Dataset
The Core Function
To demonstrate the functionality we use a flow cytometry dataset from a drug-screening project to identify agents that would enhance the anti-lymphoma activity of Rituximab, a therapeutic monoclonal antibody. The dataset is an object of class flowFrame; it consists of eight parameters, among them only the two scattering parameters (FSC.H, SSC.H) and two fluorescence parameters (FL1.H, FL3.H) are of interest in this experiment. Note that, apart from a typical matrix or data.frame object, flowClust may directly take a flowFrame, the standard R implementation of an FCS file, which may be returned from the read.FCS function in the flowCore package, as data input. The following code performs an analysis with one cluster using the two scattering parameters:
## FSC.H SSC.H FL1.H FL2.H FL3.H FL1.A FL1.W
## Min. 59.0000 11.0000 0.0000 0.0000 1.000 0.0000 0.00000
## 1st Qu. 178.0000 130.0000 197.0000 55.0000 150.000 0.0000 0.00000
## Median 249.0000 199.0000 244.0000 116.0000 203.000 0.0000 0.00000
## Mean 287.0822 251.8265 349.1638 126.3994 258.345 73.4589 17.59871
## 3rd Qu. 331.0000 307.0000 445.0000 185.0000 315.000 8.0000 0.00000
## Max. 1023.0000 1023.0000 974.0000 705.0000 1023.000 1023.0000 444.00000
## Time
## Min. 2.0000
## 1st Qu. 140.0000
## Median 285.0000
## Mean 294.0388
## 3rd Qu. 451.0000
## Max. 598.0000## Using the serial version of flowClustB is the maximum number of EM iterations; for demonstration purpose here we set a small value for B. The main purpose of performing an analysis with one cluster here is to identify outliers, which will be removed from subsequent analysis.
Next, we would like to proceed with an analysis using the two fluorescence parameters on cells selected from the first stage. The following code performs the analysis with the number of clusters being fixed from one to six in turn:
rituximab2 <- rituximab[rituximab %in% res1, ]
res2 <-
flowClust(
rituximab2,
varNames = c("FL1.H", "FL3.H"),
K = 1:6,
B = 100
)We select the best model based on the BIC. Values of the BIC can be retrieved through the criterion method. By inspection, the BIC values stay relatively constant beyond three clusters. We therefore choose the model with three clusters and print a summary of the corresponding clustering result:
## [1] -34167.12 -33103.77 -33065.41 -32998.05 -32993.74 -32942.58## ** Experiment Information **
## Experiment name: Flow Experiment
## Variables used: FL1.H FL3.H
## ** Clustering Summary **
## Number of clusters: 3
## Proportions: 0.2240448 0.5975411 0.1784141
## ** Transformation Parameter **
## lambda: 0.472139
## ** Information Criteria **
## Log likelihood: -16467.68
## BIC: -33065.41
## ICL: -33795.22
## ** Data Quality **
## Number of points filtered from above: 0 (0%)
## Number of points filtered from below: 0 (0%)
## Rule of identifying outliers: 90% quantile
## Number of outliers: 102 (7.42%)
## Uncertainty summary:The summary states that the rule used to identify outliers is 90% quantile, which means that a point outside the \(90%\) quantile region of the cluster to which it is assigned will be called an outlier. To specify a different rule, we make use of the ruleOutliers replacement method. The example below applies the more conservative 95% quantile rule to identify outliers:
## Rule of identifying outliers: 95% quantile## ** Experiment Information **
## Experiment name: Flow Experiment
## Variables used: FL1.H FL3.H
## ** Clustering Summary **
## Number of clusters: 3
## Proportions: 0.2240448 0.5975411 0.1784141
## ** Transformation Parameter **
## lambda: 0.472139
## ** Information Criteria **
## Log likelihood: -16467.68
## BIC: -33065.41
## ICL: -33795.22
## ** Data Quality **
## Number of points filtered from above: 0 (0%)
## Number of points filtered from below: 0 (0%)
## Rule of identifying outliers: 95% quantile
## Number of outliers: 38 (2.77%)
## Uncertainty summary:We can also combine the rule set by the z.cutoff argument to identify outliers. Suppose we would like to assign an observation to a cluster only if the associated posterior probability is greater than \(0.6\). We can add this rule with the following command:
## Rule of identifying outliers: 95% quantile,
## probability of assignment < 0.6## ** Experiment Information **
## Experiment name: Flow Experiment
## Variables used: FL1.H FL3.H
## ** Clustering Summary **
## Number of clusters: 3
## Proportions: 0.2240448 0.5975411 0.1784141
## ** Transformation Parameter **
## lambda: 0.472139
## ** Information Criteria **
## Log likelihood: -16467.68
## BIC: -33065.41
## ICL: -33795.22
## ** Data Quality **
## Number of points filtered from above: 0 (0%)
## Number of points filtered from below: 0 (0%)
## Rule of identifying outliers: 95% quantile,
## probability of assignment < 0.6
## Number of outliers: 94 (6.84%)
## Uncertainty summary:This time more points are called outliers. Note that such a change of the rule will not incur a change of the model-fitting process. The information about which points are called outliers is conveyed through the flagOutliers slot, a logical vector in which the positions of TRUE correspond to points being called outliers.
By default, when \(10\) or more points accumulate on the upper or lower boundary of any parameter, the flowClust function will filter those points. To change the threshold count from the default, users may specify max.count and min.count when running flowClust. To suppress filtering at the upper and/or the lower boundaries, set max.count and/or min.count as \(-1\). We can also use the max and min arguments to control filtering of points, but from a different perspective. For instance, if we are only interested in cells which have a FL1.H measurement within \((0, 400)\) and FL3.H within \((0, 800)\), we may use the following code to perform the cluster analysis:
flowClust(
rituximab2,
varNames = c("FL1.H", "FL3.H"),
K = 2,
B = 100,
min = c(0, 0),
max = c(400, 800)
)## Using the serial version of flowClust## Object of class 'flowClust'
## This object has the following slots:
## expName, varNames, K, w, mu, sigma, lambda, nu, z, u, label, uncertainty, ruleOutliers, flagOutliers, rm.min, rm.max, logLike, BIC, ICL,priorVisualization of Clustering Results
Information such as the cluster assignment, cluster shape and outliers may be visualized by calling the plot method to make a scatterplot:
## Rule of identifying outliers: 80% quantileThe level and/or z.cutoff arguments are needed when we want to apply a rule different from that stored in the ruleOutliers slot of the flowClust object to identify outliers.
To look for densely populated regions, a contour/image plot can be made:
When we want to examine how the fitted model and/or the data are distributed along one chosen dimension, we can use the hist method:
The subset argument may also take a numeric value:
Since FL1.H is the first element of res2[[3]]@varNames, this line produces exactly the same histogram as the one generated by the line taking subset="FL1.H". Likewise, the subset argument of both plot methods accepts either a numeric or a character vector to specify which two variables are to be shown on the plot.
Integration with flowCore
As mentioned in Overview, effort has been made to integrate flowClust with the flowCore package. Users will find that most methods defined in flowCore also work in the context of flowClust.
The very first step of integration is to replace the core function flowClust with a call to the constructor tmixFilter followed by the filter method. The aim is to wrap clustering in a filtering operation like those found in flowCore. The tmixFilter function creates a filter object to store all settings required for the filtering operation. The object created is then passed to the actual filtering operation implemented by the filter method. The use of a dedicated tmixFilter-class object separates the task of specifying the settings (tmixFilter) from the actual filtering operation (filter), facilitating the common scenario in FCM gating analysis that filtering with the same settings is performed upon a set of data files.
As an example, the filtering operation that resembles the second-stage clustering using FL1.H and FL3.H with three clusters (see Section~) is implemented by the following code:
s2filter <- tmixFilter("s2filter", c("FL1.H", "FL3.H"), K = 3, B = 100)
res2f <- filter(rituximab2, s2filter)## The prior specification has no effect when usePrior=no## Using the serial version of flowClustThe object res2f is of class tmixFilterResult, which extends the multipleFilterResult class defined in flowCore. Users may apply various subsetting operations defined for the multipleFilterResult class in a similar fashion on a tmixFilterResult object:
## flowFrame object 'A02'
## with 1272 cells and 8 observables:
## name desc range maxRange minRange
## $P1 FSC.H FSC-Height 1024 1023 0
## $P2 SSC.H Side Scatter 1024 1023 0
## $P3 FL1.H Anti-BrdU FITC 1024 1023 0
## $P4 FL2.H <NA> 1024 1023 0
## $P5 FL3.H 7 AAD 1024 1023 0
## $P6 FL1.A <NA> 1024 1023 0
## $P7 FL1.W <NA> 1024 1023 0
## $P8 Time Time (204.80 sec.) 1024 1023 0
## 135 keywords are stored in the 'description' slot## $sc1
## flowFrame object 'A02 (1,2)'
## with 1064 cells and 8 observables:
## name desc range maxRange minRange
## $P1 FSC.H FSC-Height 1024 1023 0
## $P2 SSC.H Side Scatter 1024 1023 0
## $P3 FL1.H Anti-BrdU FITC 1024 1023 0
## $P4 FL2.H <NA> 1024 1023 0
## $P5 FL3.H 7 AAD 1024 1023 0
## $P6 FL1.A <NA> 1024 1023 0
## $P7 FL1.W <NA> 1024 1023 0
## $P8 Time Time (204.80 sec.) 1024 1023 0
## 3 keywords are stored in the 'description' slot
##
## $sc2
## flowFrame object 'A02 (3)'
## with 208 cells and 8 observables:
## name desc range maxRange minRange
## $P1 FSC.H FSC-Height 1024 1023 0
## $P2 SSC.H Side Scatter 1024 1023 0
## $P3 FL1.H Anti-BrdU FITC 1024 1023 0
## $P4 FL2.H <NA> 1024 1023 0
## $P5 FL3.H 7 AAD 1024 1023 0
## $P6 FL1.A <NA> 1024 1023 0
## $P7 FL1.W <NA> 1024 1023 0
## $P8 Time Time (204.80 sec.) 1024 1023 0
## 136 keywords are stored in the 'description' slotThe Subset method above outputs a flowFrame consisting of observations within the data-driven filter constructed. The split method separates the data into two populations upon the removal of outliers: the first population is formed by observations assigned to clusters~1 and 2 constructed by the filter, and the other population consists of observations assigned to cluster~3. The two populations are returned as two separate flowFrame’s, which are stored inside a list and labelled with sc1 and sc2 respectively.
The %in% operator from flowCore is also defined for a tmixFilterResult object. A logical vector will be returned in which a TRUE value means that the corresponding observation is accepted by the filter. In fact, the implementation of the Subset method needs to call \%in\%.
The object returned by tmixFilter is of class tmixFilter, which extends the filter class in flowCore. Various operators, namely, &, |, ! and %subset%, which have been constructed for filter objects in flowCore, also produce similar outcomes when applied to a tmixFilter object. For example, to perform clustering on a subset of data enclosed by a rectangle gate, we may apply the following code:
rectGate <-
rectangleGate(
filterId = "rectRegion",
"FL1.H" = c(0, 400),
"FL3.H" = c(0, 800)
)
MBCfilter <- tmixFilter("MBCfilter", c("FL1.H", "FL3.H"), K = 2, B = 100)
filter(rituximab2, MBCfilter %subset% rectGate)## The prior specification has no effect when usePrior=no## Using the serial version of flowClust## A filterResult produced by the filter named 'MBCfilter in rectRegion'
## resulting in multiple populations:
## 2
## 1Using Priors
flowClust also supports priors through a Multivariate Normal-Inverse Wishart model.
One way to construct a prior is to use an existing flowClust model fit. For example, we can construct a prior from the rituximab fit. Then we can adjust the prior so that the FL1-/FL3- population is centered at \(200,200\) a priori, and both populations have an a priori smaller variance.
The parameter kappa acts as a weighting factor for the prior, while Nt controls the number of equivalent observations for the prior.
set.seed(100)
prior <- flowClust2Prior(res2[[2]], kappa = 1, Nt = 5000)
prior2 <- prior
prior2$Mu0[1, ] <- rep(box(200, prior2$lambda), 2)
prior2$Lambda0 <- prior2$Lambda0 / 2
pfit2 <-
flowClust(
rituximab2,
varNames = c("FL1.H", "FL3.H"),
K = 2,
prior = prior2,
usePrior = "yes"
)## Using the serial version of flowClust## Rule of identifying outliers: 90% quantile
## Rule of identifying outliers: 90% quantile