Oracle Calculations"

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Abstract

We provide some example usage of the oracle calculations available in updog. These are particularly useful for read-depth determination. These calculations are described in detail in Gerard et al. (2018).

Controlling Misclassification Error

Suppose we have a sample of tetraploid individuals derived from an S1 cross (a single generation of selfing). Using domain expertise (either from previous studies or a pilot analysis), we've determined that our sequencing technology will produce relatively clean data. That is, the sequencing error rate will not be too large (say, ~0.001), the bias will be moderate (say, ~0.7 at the most extreme), and the majority of SNPs will have reasonable levels of overdispersion (say, less than 0.01). We want to know how deep we need to sequence.

Using oracle_mis, we can see how deep we need to sequence under the worst-case scenario we want to control (sequencing error rate = 0.001, bias = 0.7, overdispersion = 0.01) in order to obtain a misclassification error rate of at most, say, 0.05.

bias   <- 0.7
od     <- 0.01
seq    <- 0.001
maxerr <- 0.05

Before we do this, we also need the distribution of the offspring genotypes. We can get this distribution assuming various parental genotypes using the get_q_array function. Typically, error rates will be larger when the allele-frequency is closer to 0.5. So we'll start in the worst-case scenario of assuming that the parent has 2 copies of the reference allele.

library(updog)
ploidy <- 4
pgeno <- 2
gene_dist <- get_q_array(ploidy = ploidy)[pgeno + 1, pgeno + 1, ]

This is what the genotype distribution for the offspring looks like:

library(ggplot2)
distdf <- data.frame(x = 0:ploidy, y = 0, yend = gene_dist)
ggplot(distdf, mapping = aes(x = x, y = y, xend = x, yend = yend)) +
  geom_segment(lineend = "round", lwd = 2) +
  theme_bw() +
  xlab("Allele Dosage") +
  ylab("Probability")

Now, we are ready to iterate through read-depth's until we reach one with an error rate less than 0.05.

err    <- Inf
depth  <- 0
while(err > maxerr) {
  depth <- depth + 1
  err <- oracle_mis(n = depth,
                    ploidy = ploidy,
                    seq = seq,
                    bias = bias,
                    od = od,
                    dist = gene_dist)
}
depth

Looks like we need a depth of r depth in order to get a misclassification error rate under r maxerr.

Note that oracle_mis returns the best misclassification error rate possible under these conditions (ploidy = r ploidy, bias = r bias, seq = r seq, od = r od, and pgeno = r pgeno). In your actual analysis, you will have a worse misclassification error rate than that returned by oracle_mis. However, if you have a lot of individuals in your sample, then this will act as a reasonable approximation to the error rate. In general though, you should sequence a little deeper than suggested by oracle_mis.

Visualizing the Joint Distribution

Suppose we only have a budget to sequence to a depth of 30. Then what errors can we expect? We can use oracle_joint and oracle_plot to visualize the errors we can expect.

depth <- 30
jd <- oracle_joint(n = depth,
                   ploidy = ploidy,
                   seq = seq,
                   bias = bias,
                   od = od,
                   dist = gene_dist)
oracle_plot(jd)

Most of the errors will be mistakes between genotypes 2/3 and mistakes between genotypes 1/2.

omiss <- oracle_mis(n = depth,
                    ploidy = ploidy,
                    seq = seq,
                    bias = bias,
                    od = od,
                    dist = gene_dist)

ocorr <- oracle_cor(n = depth,
                    ploidy = ploidy,
                    seq = seq,
                    bias = bias,
                    od = od,
                    dist = gene_dist)

Even though the misclassification error rate is pretty high (r round(omiss, digits = 2)), the correlation of the oracle estimator with the true genotype is pretty reasonable (r round(ocorr, digits = 2)). You can obtain this using the oracle_cor function.

ocorr <- oracle_cor(n = depth,
                    ploidy = ploidy,
                    seq = seq,
                    bias = bias,
                    od = od,
                    dist = gene_dist)
ocorr

References

Gerard, David, Luís Felipe Ventorim Ferrão, Antonio Augusto Franco Garcia, and Matthew Stephens. 2018. "Genotyping Polyploids from Messy Sequencing Data." Genetics 210 (3). Genetics: 789–807. https://doi.org/10.1534/genetics.118.301468.



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updog documentation built on Oct. 18, 2022, 9:07 a.m.