fit_trendfilter: Estimate Cyclic Trend of Gene Expression Using Trendfiltering

In jhsiao999/peco: A Supervised Approach for Predicting Cell Cycle Progression Using Single-Cell RNA-seq Data

Description

Estimate Cyclic Trend of Gene Expression Using Trendfiltering

Usage

fit_trendfilter(yy, polyorder = 2)

Arguments

yy	A vector of gene expression values for a single gene. They must be ordered by cell cycle phase. Also, the expression values should be normalized and transformed to standard normal distribution.
polyorder	Degree of polynomials used in nonparamtric trend filtering.

Details

We applied quadratic (second-order) trend filtering using the trendfilter function in the genlasso package. The trendfilter function implements a nonparametric smoothing method which chooses the smoothing parameter by cross-validation and fits a piecewise polynomial regression.

The trendfilter method determines the folds in cross-validation in a non-random manner: every k-th data point in the ordered sample is placed in the k-th fold, so the folds contain ordered subsamples. We applied five-fold cross-validation and chose the smoothing penalty using the option lambda.1se; among all possible values of the penalty term, the largest value such that the cross-validation standard error is within one standard error of the minimum. Furthermore, we desired that the estimated expression trend be cyclical. To encourage this, we concatenated the ordered gene expression data three times, with one added after another. The quadratic trend filtering was applied to the concatenated data series of each gene.

Value

A list with two elements: trend.yy, the estimated cyclic trend; pve, proportion of variance in gene expression levels explained by the cyclic trend.

Author(s)

Joyce Hsiao

Examples

library(SingleCellExperiment)
data(sce_top101genes)

# select top 10 cyclic genes
sce_top10 <- sce_top101genes[order(rowData(sce_top101genes)$pve_fucci,
                                  decreasing=TRUE)[1:10],]
coldata <- colData(sce_top10)

# cell cycle phase based on FUCCI scores
theta <- coldata$theta
names(theta) <- rownames(coldata)

# normalize expression counts
sce_top10 <- data_transform_quantile(sce_top10, ncores=2)
exprs_quant <- assay(sce_top10, "cpm_quantNormed")

# order FUCCI phase and expression
theta_ordered <- theta[order(theta)]
yy_ordered <- exprs_quant[1, names(theta_ordered)]

fit <- fit_trendfilter(yy_ordered)

plot(x=theta_ordered, y=yy_ordered, pch=16, cex=.7, axes=FALSE,
  ylab="quantile-normalized expression values", xlab="FUCCI phase",
  main = "trendfilter fit")
points(x=theta_ordered, y=fit$trend.yy, col="blue", pch=16, cex=.7)
axis(2)
axis(1,at=c(0,pi/2, pi, 3*pi/2, 2*pi),
  labels=c(0,expression(pi/2), expression(pi), expression(3*pi/2),
  expression(2*pi)))
abline(h=0, lty=1, col="black", lwd=.7)

jhsiao999/peco documentation built on Nov. 21, 2020, 5:34 p.m.