title: "Estimate overdispersion on the ATAC-seq dataset from the NPBin paper" author: "Anthony Aylward" date: "2018-09-13" output: rmarkdown::html_vignette vignette: > %\VignetteIndexEntry{Vignette Title} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8}
This vignette requires the npbin package.
library(chenimbalance)
library(npbin)
#>
#> Attaching package: 'npbin'
#> The following object is masked from 'package:chenimbalance':
#>
#> color_palette
total_reads <- atac[["m"]]
data <- data.frame(
total = total_reads,
allelicRatio = atac[["xm"]] / atac[["m"]]
)
data <- data[total_reads >= 5,]
data <- data[1:2000,]
head(data)
#> total allelicRatio
#> 1 9 0.6666667
#> 2 71 0.6197183
#> 3 65 0.4307692
#> 4 7 0.4285714
#> 5 7 0.8571429
#> 6 14 0.7857143
Compute the empirical allelic ratio distribution
binSize <- 40
bins <- pretty(0:1, binSize)
minN <- 6
maxN <- min(2500, max(data[["total"]]))
empirical <- empirical_allelic_ratio(
data,
bins,
maxN = maxN,
minN = minN,
plot = TRUE
)
Compute the weighted expected binomial distribution
w <- weight_by_empirical_counts(data[["total"]])
d_combined_sorted_binned <- nulldistrib(
w,
minN = minN,
binSize = binSize
)
Compute the sum of squared errors for the empirical distribution vs the weighted expected binomial distribution.
sse <- sum((empirical - d_combined_sorted_binned[,2])^2)
sse
#> [1] 0.007110035
Choose the overdispersion parameter for the beta-binomial distribution
w_grad <- graded_weights_for_sse_calculation(r_min = 0, r_max = 1, bins = bins)
overdispersion_details <- choose_overdispersion_parameter(
w_grad,
w,
empirical,
sse
)
head(overdispersion_details[["b_and_sse"]])
#> b sse
#> [1,] 0.0 0.0071100351
#> [2,] 0.1 0.0007273913
#> [3,] 0.2 0.0031788478
#> [4,] 0.0 0.0000000000
#> [5,] 0.0 0.0000000000
#> [6,] 0.0 0.0000000000
Generate a plot of the weighted expected binomial and weighted expected beta-binomial distributions overlaid on the empirical distribution
plot_distributions(
minN,
maxN,
bins,
empirical,
d_combined_sorted_binned,
overdispersion_details[["e_combined_sorted_binned"]],
yuplimit = 0.15
)
overdispersion_details
is a list whose elements include the chosen value of
b
and the sum of squared errors.
paste(
"b_chosen =",
overdispersion_details[["b_choice"]],
", SSE_chosen =",
overdispersion_details[["sse"]]
)
#> [1] "b_chosen = 0.1 , SSE_chosen = 0.000727391258190998"
Optimize the overdispersion parameter
optimized_overdispersion_details <- optimize_overdispersion_parameter(
w_grad,
w,
overdispersion_details[["b_and_sse"]],
overdispersion_details[["b_choice"]],
overdispersion_details[["sse"]],
empirical,
overdispersion_details[["counter"]],
minN = minN,
binSize = binSize
)
plot_distributions(
minN,
maxN,
bins,
empirical,
d_combined_sorted_binned,
optimized_overdispersion_details[["e_combined_sorted_binned"]],
yuplimit = 0.15
)
Check the optimized value
list(
b = optimized_overdispersion_details[["b_choice"]],
sse = optimized_overdispersion_details[["sse"]]
)
#> $b
#> [1] 0.06796875
#>
#> $sse
#> [1] 0.0004410953
Plot the parameter search space
b_and_sse <- (
optimized_overdispersion_details[["b_and_sse"]]
[1:(optimized_overdispersion_details[["counter"]] + 2),]
)
plot(
b_and_sse[order(b_and_sse[,1]),],
type = "b",
pch = 16,
xlim = c(min(b_and_sse[,1]), max(b_and_sse[,1])),
ylim = c(min(b_and_sse[,2]), max(b_and_sse[,2]))
)
par(new = TRUE)
plot(
optimized_overdispersion_details[["b_choice"]],
optimized_overdispersion_details[["sse"]],
bty = "n",
ylab = "",
xlab = "",
yaxt = "n",
xaxt = "n",
col = "red",
pch = 8,
xlim = c(min(b_and_sse[,1]), max(b_and_sse[,1])),
ylim = c(min(b_and_sse[,2]), max(b_and_sse[,2]))
)
Compute the symmetric shape parameter and plot the estimated null beta (gold) superimposed with the null beta estimated from NPBin (blue).
shape = 1 / (2 * optimized_overdispersion_details[["b_choice"]]) - 1 / 2
plot_estimated_null(
data[["allelicRatio"]],
shape1_shape2 = c(13.41442, 12.97),
shape3_shape4 = c(shape, shape)
)
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