KNN for differential abundance
There are many ways to assess differential abundance in CyTOF data (and high dimensional data in general). Here, we use our KNN as a proxy for variance across each cell in the manifold. In our case, we test two tubes that should in theory be the same (eg. PBMCs from the same donor, with the same markers). SCONE automatically outputs the per-knn percentage of cells in the non-baseline condition, shown below. The dataset we use is the Wanderlust dataset (paper: https://www.ncbi.nlm.nih.gov/pubmed/24766814, dataset: https://www.c2b2.columbia.edu/danapeerlab/html/wanderlust-data.html), between a single normal and IL-7 treated patient.
## [1] 0.6000000 0.4000000 0.7000000 0.5000000 0.7666667 0.2666667 0.3333333
## [8] 0.4666667 0.4666667 0.5000000We can plot this as a distrubtion between 0 and 100%. We hypothesize that this distribution of n cells and k nearest neighbors per cell will have the median and standard deviation of a coin tossed k times, with this action repeated n times. This is known formally as the binomial distribution with a probability set at 0.5. The analysis is below.
## Warning: Use of `dat[[grep(column.label, colnames(dat))]]` is discouraged. Use
## `.data[[grep(column.label, colnames(dat))]]` instead.## Warning: Removed 2 rows containing missing values (geom_bar).
## [1] 0.5## [1] 0.1083417We now compare to our coin flipping.
# Compare to a coin toss distribution
# Flips a coin k number of times, n repetitions, and returns the vector
# containing the per-k percent heads
KFlip <- function(k, n) {
# The result
result <- sapply(1:n, function(i) {
# Get the fraction heads for n flips
flips <- sample(c(0, 1), k, replace = TRUE)
percent.heads <- sum(flips)/length(flips)
return(percent.heads)
})
}
coin.toss <- data.frame("binomial" = KFlip(30, 1000))
MakeHist(coin.toss, 30, "binomial", "fraction heads")## Warning: Use of `dat[[grep(column.label, colnames(dat))]]` is discouraged. Use
## `.data[[grep(column.label, colnames(dat))]]` instead.## Warning: Removed 2 rows containing missing values (geom_bar).
## [1] 0.5## [1] 0.09543641We can see that the Wanderlust dataset example has a standard deviation that is higher (0.08) than that of the aforementioned binomial distribution (0.05). We can also see that the Wanderlust dataset distribution has a slight tail to the right. If we consider the Wanderlust dataset as a “benchmark” in terms of data quality, we can see that new CyTOF datasets should be within a few hundreths of the standard deviation of the binomial distribution with the same number of trials as the number of nearest neighbors used.
Of note, we can approximate the standard deviation of the binomical distribution with a probability of 0.5 for any value k by using the formula sd = 0.5/sqrt(k). This is derived from the DeMoivre-Laplace theorem https://en.wikipedia.org/wiki/De_Moivre%E2%80%93Laplace_theorem. This means one does not need to simulate a distibution of coin tosses every time the k in the KNN is changed. I do it here just to show what it looks like.
Given that the observed variation (sd = 0.108) is higher than that of our aforementioned binomial distribution (sd = 0.093), and we observed the slight tail to the right, we hypothesize that this slight tail to the right could be a specific cell subset that is overrepresented in the IL-7 tube. To this end, we visualize our results colored on a t-SNE map below. If our hypothesis is true, a specific region of the map will be enriched by higher “fraction IL-7” values.
One can see with the t-SNE map that the IL-7 condition appears to be slightly overrepresented in the more mature B cell compartment, as represented above by high IgM expression, which is consistent with our hypothesis. Given that the IL-7 stimulatory condition was only for 15 minutes (and therefore likely did not kill the stem cells), the result here leads to the hypothesis that the IL-7 tube had slightly more mature B cells in it than stem cells to begin with. While this particular case is not substantial and did not affect the identification of the IL-7 responsive population, results like this could help a user fine-tune a data analysis pipeline using this hypothesis-driven search for technical artifact.
