netprioR requires the following data as input
In the following steps we simulate data for a set of N = 1000 genes and a two class prioritisation task (positive vs. negative) and benchmark the performance of our model against the case where we prioritise soleley based on phenotypes.
We simulate the case where we know 100 labels a priori, which corresponds to 10% labelled data. We simulate equal numberos of 50 positives and 50 negatives, setting
members_per_class <- c(N/2, N/2) %>% floor
Then we simulate the labels, randomly choosing equal numbers of a priori known labels for each class.
class.labels <- simulate_labels(values = c("Positive", "Negative"), sizes = members_per_class, nobs = c(nlabel/2, nlabel/2))
The list of simulated labels contains the complete vector of 1000 labels
and the vector of observed labels
labels.obs. Unknown labels are set to
 "labels.true" "labels.obs" "labelled" "unlabelled"
Next, we simulate high noise and low noise network data in the form of 1000 x 1000 adjacency matrices. The low noise networks obey the class structure defined above, whereas the high noise networks do not.
networks <- list(LOW_NOISE1 = simulate_network_scalefree(nmemb = members_per_class, pclus = 0.8), LOW_NOISE2 = simulate_network_scalefree(nmemb = members_per_class, pclus = 0.8), HIGH_NOISE = simulate_network_random(nmemb = members_per_class, nnei = 1))
The networks are sparse binary adjacency matrices, which we can visualise as images. This allows to see the structure within the low noise networks, where we observe 80% of all edges in the 2nd and 4th quadrant, i.e. within each class, as defined above.
We simulate phenotype matching our simulated labels from two normal distributions with a difference in means that reflects our phenotype effect size. We set the effect size to
effect_size <- 0.25
and simulate the phenotypes
phenotypes <- simulate_phenotype(labels.true = class.labels$labels.true, meandiff = effect_size, sd = 1)
The higher the phenotype effect size is, the easier it is to separate the two classes soleley based on the phenotype. We visualise the phenotypes for the two classes as follows
data.frame(Phenotype = phenotypes[, 1], Class = rep(c("Positive", "Negative"), each = N/2)) %>% ggplot() + geom_density(aes(Phenotype, fill = Class), alpha = 0.25, adjust = 2) + theme_bw()
Based on the simulated data above, we now fit the netprioR model for gene prioritisation.
In this example, we will use hyperparameters
a = b = 0.01 for the Gamma prior of the network
weights in order to yield a sparsifying prior We will fit only one model, setting
nrestarts to 1,
whereas in practise multiple restarts are used in order to avoid cases where the EM gets stuck
in local minima. The convergence threshold for the relative change in the log likelihood is set to
np <- netprioR(networks = networks, phenotypes = phenotypes, labels = class.labels$labels.obs, nrestarts = 1, thresh = 1e-06, a = 0.1, b = 0.1, fit.model = TRUE, use.cg = FALSE, verbose = FALSE)
We can investigate the
netprioR object using the
#Genes: 1000 #Networks: 3 #Phenotypes: 1 #Labels: 100 Classes: Negative Positive Model: Likelihood[log]: -2935.808 Fixed effects: 0.3153685 Network weights: Network Weight LOW_NOISE1 593.53021 LOW_NOISE2 362.49191 HIGH_NOISE 54.27568
It is also possible to plot the
netprioR object to get an overview of the model
plot(np, which = "all")
We can also plot individual plots by setting
which = "weights|ranks|lik".
We can see that the relative weight of the low noise networks is much higher than for the high noise networks indicating that, as expected, the low noise networks are more informative for the learning task.
Second, we evaluate the performance of the prioritised list of genes by comparing
the imputed, missing labels
Yimp[u] against the true underlying labels
computing receiver operator characteristic (ROC)
roc.np <- ROC(np, true.labels = class.labels$labels.true, plot = TRUE, main = "Prioritisation: netprioR")
In addition, we compute the ROC curve for the case where we prioritise soleley based on the phenotype
unlabelled <- which(is.na(class.labels$labels.obs)) roc.x <- roc(cases = phenotypes[intersect(unlabelled, which(class.labels$labels.true == levels(class.labels$labels.true))), 1], controls = phenotypes[intersect(unlabelled, which(class.labels$labels.true == levels(class.labels$labels.true))), 1], direction = ">") plot.roc(roc.x, main = "Prioritisation: Phenotype-only", print.auc = TRUE, print.auc.x = 0.2, print.auc.y = 0.1)
Comparing the area under the receiver operator characteristic curve (AUC) values for both cases, we can see that by integrating network data and a priori known labels for TPs and TNs, we gain about 0.09 in AUC.
Here is the output of
sessionInfo() on the system on which this document was compiled:
R version 4.0.0 (2020-04-24) Platform: x86_64-pc-linux-gnu (64-bit) Running under: Ubuntu 18.04.4 LTS Matrix products: default BLAS: /home/biocbuild/bbs-3.11-bioc/R/lib/libRblas.so LAPACK: /home/biocbuild/bbs-3.11-bioc/R/lib/libRlapack.so locale:  LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C  LC_TIME=en_US.UTF-8 LC_COLLATE=C  LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8  LC_PAPER=en_US.UTF-8 LC_NAME=C  LC_ADDRESS=C LC_TELEPHONE=C  LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C attached base packages:  stats graphics grDevices utils datasets methods base other attached packages:  Matrix_1.2-18 pROC_1.16.2 netprioR_1.14.0 ggplot2_3.3.0  pander_0.6.3 dplyr_0.8.5 knitr_1.28 BiocStyle_2.16.0 loaded via a namespace (and not attached):  Rcpp_184.108.40.206 formatR_1.7 plyr_1.8.6  pillar_1.4.3 compiler_4.0.0 BiocManager_1.30.10  iterators_1.0.12 tools_4.0.0 digest_0.6.25  evaluate_0.14 lifecycle_0.2.0 tibble_3.0.1  gtable_0.3.0 lattice_0.20-41 pkgconfig_2.0.3  rlang_0.4.5 foreach_1.5.0 magick_2.3  parallel_4.0.0 yaml_2.2.1 xfun_0.13  gridExtra_2.3 withr_2.2.0 stringr_1.4.0  vctrs_0.2.4 grid_4.0.0 tidyselect_1.0.0  glue_1.4.0 R6_2.4.1 sparseMVN_0.2.1.1  rmarkdown_2.1 bookdown_0.18 farver_2.0.3  purrr_0.3.4 magrittr_1.5 codetools_0.2-16  scales_1.1.0 ellipsis_0.3.0 htmltools_0.4.0  assertthat_0.2.1 colorspace_1.4-1 labeling_0.3  stringi_1.4.6 munsell_0.5.0 doParallel_1.0.15  crayon_1.3.4