vignettes/overdispersion.md

In anthony-aylward/chenimbalance: Allelic imbalance mapping procedure from Chen et al. A uniform survey of allele-specific binding and expression over 1000-Genomes-Project individuals (2016)

title: "Weighted expected binomial model" author: "Anthony Aylward" date: "2018-08-02" output: rmarkdown::html_vignette vignette: > %\VignetteIndexEntry{Vignette Title} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8}

Prepare the data.

library(chenimbalance)
total_reads <- rowSums(accb[, c("cA", "cC", "cG", "cT")])
data <- data.frame(
  total = total_reads,
  allelicRatio = sapply(
    1:nrow(accb),
    function(i) {
      accb[[paste("c", accb[["ref"]][[i]], sep = "")]][[i]] / total_reads[[i]]
    }
  )
)
data <- data[1:2000,]
head(data)
#>   total allelicRatio
#> 1    45    1.0000000
#> 2    59    0.5423729
#> 3   114    0.4736842
#> 4    53    0.5094340
#> 5   119    0.5042017
#> 6    21    0.0952381

Empirical distribution

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
)

Expected Binomial and Beta-Binomial distributions

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] 0.00662428

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 0.006624280
#> [2,] 0.1 0.006308586
#> [3,] 0.2 0.013347326
#> [4,] 0.0 0.000000000
#> [5,] 0.0 0.000000000
#> [6,] 0.0 0.000000000

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 = 0.00630858569475557"

Optimize the overdispersion parameter

optimized_overdispersion_details <- optimize_overdispersion_parameter(
  w_grad,
  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] 0.02089844
#> 
#> $sse
#> [1] 0.0003644314

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]))
)

anthony-aylward/chenimbalance documentation built on May 17, 2019, 12:50 p.m.