Rare mutation detection model
Last updated: 2021-09-17
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library(ggplot2)Model
Q: what is the lowest % VAF of mutation we can reliably detect (at >95% confidence) using Nanoseq on bulk WES?
Assumptions
- We consider a human diploid genome (6.4Gb) without SCNAs
- The mutation is heterozygous
- We sequence 15,000 cells
- Our duplex rate is optimal ~81%
- Our ligation efficiency is 20%
- We assume a duplex mutation call equals a real mutation (theoretical error rate of duplex sequencing is <10^-9)
Probability of sequencing a mutant cell
Let \(f\) be the probability of sequencing a mutation from a single fragment, on both strands.
\(f = (v / p) d.l\)
Where:
- \(v\) = target VAF
- \(p\) = ploidy (2)
- \(d\) = duplex efficiency (0.81)
- \(l\) = ligation efficiency
We assume the probability of selecting a mutant cell is binomially distributed. We want to know the probability of selecting at least one mutant cell:
\(P(Bin(f, m)) > 0)\) = 0.95
This is equivalent to:
\(P(Bin(f, m)) = 0)\) = 0.05
Where \(m\) is the number of mutant cells cells (\(15000 (v . 2)\)).
For a range of possible VAFs, \(V = \{0.001, 0.002 .. 0.05\}\), we can plot the probability of missing the mutant cell.
d = 0.81
l = 0.2
v = seq(0.001, 0.05, 0.001)
f = (v / 2) * d * l
n = 15000
m = n * (v * 2)
vafs <- data.frame(vaf=v,
p=dbinom(0, m, v))
ggplot(vafs, aes(vaf, p)) +
geom_point() +
theme_bw() +
geom_hline(yintercept=0.05, alpha=0.4)
| Version | Author | Date |
|---|---|---|
| ebb9d74 | mcmero | 2021-09-17 |
For this range of VAFs, 0.01 (1%) is the smallest VAF for which the probability of missing the mutant is approximately 0.05.
deviation <- abs(0.05 - vafs$p)
print(vafs[which(deviation == min(deviation)),]) vaf p
10 0.01 0.04904089
sessionInfo()R version 4.1.1 (2021-08-10)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Big Sur 10.16
Matrix products: default
LAPACK: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRlapack.dylib
locale:
[1] en_AU.UTF-8/en_AU.UTF-8/en_AU.UTF-8/C/en_AU.UTF-8/en_AU.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] ggplot2_3.3.5 workflowr_1.6.2
loaded via a namespace (and not attached):
[1] Rcpp_1.0.7 highr_0.9 pillar_1.6.2 compiler_4.1.1
[5] later_1.3.0 jquerylib_0.1.4 git2r_0.28.0 tools_4.1.1
[9] digest_0.6.27 evaluate_0.14 lifecycle_1.0.0 tibble_3.1.4
[13] gtable_0.3.0 pkgconfig_2.0.3 rlang_0.4.11 yaml_2.2.1
[17] xfun_0.25 fastmap_1.1.0 withr_2.4.2 dplyr_1.0.7
[21] stringr_1.4.0 knitr_1.33 generics_0.1.0 fs_1.5.0
[25] vctrs_0.3.8 tidyselect_1.1.1 rprojroot_2.0.2 grid_4.1.1
[29] glue_1.4.2 R6_2.5.1 fansi_0.5.0 rmarkdown_2.11
[33] farver_2.1.0 purrr_0.3.4 magrittr_2.0.1 whisker_0.4
[37] scales_1.1.1 promises_1.2.0.1 ellipsis_0.3.2 htmltools_0.5.2
[41] colorspace_2.0-2 httpuv_1.6.3 labeling_0.4.2 utf8_1.2.2
[45] stringi_1.7.4 munsell_0.5.0 crayon_1.4.1