The LimROTS approach initially uses the limma package Ritchie et al. (2015) to simulate the intensity data of proteins and metabolites. A linear model is subsequently fitted using the design matrix. Empirical Bayes variance shrinking is then implemented. To obtain the moderated t-statistics (or f-statistics), the adjusted standard error \(SE_{post} = \sqrt{s^2_{\text{post}}} \times \text{unscaled SD}\) for each feature is computed, along with the regression coefficient for each feature (indicating the impact of variations in the experimental settings). Then, by adapting a reproducibility-optimized technique known as ROTS Suomi et al. (2017) to establish an optimality based on the largest overlap of top-ranked features within group-preserving bootstrap datasets (refer to Elo et al. (2008) for further information on the reproducibility-optimization). Finally based on the optimized parameters \({\alpha1}\) and \({\alpha2}\) this equation used to calculates the final statistics: \[t{\alpha(p)} = \frac{\beta_{(p)}}{\alpha1 + \alpha2 \times \text{SEpost}_{(p)}}\]
where \(t_{\alpha(p)}\) is the final statistics for each feature,
\({\beta_{(p)}}\) is the coefficient, and \(SEpost_{(p)}\) is the adjusted
standard error. LimROTS generates p-values from permutation samples
using the implementation available in qvalue package Storey et al. (2024), along
with internal implementation of FDR adapted from ROTS package Suomi et al. (2017).
Additionally, the qvalue package is used to calculate q-values, were
the proportion of true null p-values is set to the bootstrap method. We
recommend using permutation-derived p-values and qvalues.
The number of samples, features, bootstrap iterations, and k, which
denotes the top list size for ranking, are the four primary elements
that determine the amount of computing resources required for the
optimisation process in LimROTS. It is therefore advised to use at least
4 cores to execute LimROTS since it uses a parallel processing
implementation for the bootstrapping step. The optimisation process is
sequential and maybe time-consuming, based on the k value; it is
planned to be modified in order to make the upcoming LimROTS version
faster.
LimROTSLimROTS takes several parameters, and it should be called correctly to
obtain the desired output.
x: The input data, which can be a SummarizedExperiment
object or a matrix where rows represent features (e.g., genes,
proteins) and columns represent samples. The values should be
log-transformed.
B: An integer representing the amount of bootstrap iterations.
Default 1000.
K: An optional integer representing the top list size for
ranking. If not specified, it is set to one-fourth of the number of
features.
a1: Optional numeric value used in the optimization process.
If defined by the user, no optimization occurs.
a2: Optional numeric value used in the optimization process.
If defined by the user, no optimization occurs [0,1].
log: Logical, indicating whether the data is already
log-transformed. Default is TRUE.
progress: Logical, indicating whether to display a progress
bar during bootstrap sampling. Default is FALSE.
verbose: Logical, indicating whether to display messages
during the function’s execution. Default is TRUE.
meta.info: A data frame containing sample-level metadata,
where each row corresponds to a sample. It should include the
grouping variable specified in group.name. If x (data) is a
SummarizedExperiment object, meta.info must be a vector of the
metadata needed for the model to run and can be retrieved using
colData().
group.name: A string specifying the column in meta.info that
represents the groups or conditions for comparison.
seed.cl: An integer specifying the seed for randomization; if
not provided, the default is 1234.
cluster: A parallel cluster object for distributed
computation, e.g., created by makeCluster(). Default is 2.
formula.str: A formula string for modeling. It should include
“~ 0 + …” to exclude the intercept from the model. All the model
parameters must be present in meta.info.
robust: Logical, indicating whether robust fitting should be
used. Default is TRUE.
trend: Logical, indicating whether to include trend fitting in
the differential expression analysis. Default is TRUE.
permutating.group: Logical, If TRUE, the permutation for
calculating the null distribution is performed by permuting the
target group only specified in group.name Preserving all the other
sample information. If FALSE, the entire sample information
retrieved from meta.info will be permuted (recommended to be set
to TRUE).
To demonstrate LimROTS’ ability to detect true negatives complex scenarios, we are using a DIA proteomics data from a UPS1-spiked E. coli protein mixture Gotti et al. (2022) includes 48 samples: 24 samples analyzed with Spectronaut and another 24 analyzed with ScaffoldDIA software, with total of 1656 proteins. Eight different concentrations of UPS1 were used (0.1 to 50 fmol), grouped into two categories: low concentrations (0.1–2.5 fmol, labeled as 2, 12 Samples from each software) and high concentrations (5–50 fmol, labeled as 1, 12 Samples from each software).
A synthetic, unbalanced fake batches assigned to the samples. The assignment follows the ratio of:
Additionally, 100 E. coli proteins were randomly selected, and an effect size of 10 was added to each. The expected outcome is that only the UPS1 human proteins will be identified as truly significant, while none of the remaining proteins should show significant differences between the concentration groups.
This scenario resembles a real-world case where the experiment involves unbalanced batch assignments or, for instance, an uneven gender ratio among the samples.
LimROTS can take a SummarizedExperiment object with all the metadata needed to run the model. In this example we importing UPS1.Case4 data available in LimROTS.
The original source of the dataset can be found here Gotti et al. (2022)
# Load necessary packages
library(LimROTS)
library(parallel)
library(ggplot2)# Load the dataset
data("UPS1.Case4")
print(UPS1.Case4)Although seed.cl internally control the seed randomization during the
parallel bootstrapping process. It is advisable to establish a
consistent seed prior to executing LimROTS
set.seed(1234, kind = "default")# Set metadata and formula for LimROTS analysis
meta.info <- c("Conc.", "tool", "fake.batch")
B <- 100 # Number of bootstrap samples
K <- 100 # Set the value for K based on the data size
K <- floor(K)
num_cores <- 2 # Number of cores for parallel processing
cluster <- makeCluster(num_cores) # Create a parallel cluster
group.name <- "Conc."
formula.str <- "~ 0 + Conc. + tool + fake.batch" # Formula for group comparison
# Run LimROTS analysis with trend and robust settings enabled
limrots.result <- LimROTS(
x = UPS1.Case4,
B = B, K = K, meta.info = meta.info,
cluster = cluster, group.name = group.name,
formula.str = formula.str, trend = TRUE,
robust = TRUE, permutating.group = FALSE,
seed.cl = 1234
)NOTE: “In this instance, we configure the number of bootstrap iterations (B) and the count of top-ranked features for reproducibility optimization (K) to 100 both, in order to minimize the example’s run-time. For actual analyses, it is advisable to utilize a greater number of bootstraps (e.g., 1000). Also, for the number of cores to use we recommend to use at least 4 cores.
Utilising a Volcano plot and mapping the human UPS1 proteins at q-values of 1% and 5%, it is evident that LimROTS accurately identified the majority of actual positive proteins while detecting a limited number of simulated E.coli proteins.
# Create a data frame from the LimROTS results
limrots.result.df <- data.frame(
proteins = row.names(limrots.result$data),
LimROTS.FC = limrots.result$corrected.logf,
q.value = limrots.result$q_values$qvalues
)
# Mark proteins as true positives (HUMAN UPS1 proteins)
limrots.result.df$TP <- ifelse(grepl("HUMAN", limrots.result.df$proteins),
"HUMAN_TP", "ECOLI_FP"
)
# Create a volcano plot
ggplot(limrots.result.df, aes(
x = LimROTS.FC, y = -log10(q.value),
color = factor(TP)
)) +
geom_point(alpha = 0.8) +
theme_bw() +
labs(
title = "Volcano Plot", x = "Log Fold Change", y = "-Log10 q.value",
color = "True Positive"
) +
scale_color_manual(values = c("grey", "red")) +
geom_hline(yintercept = -log10(0.05), linetype = "dashed", color = "blue")+
geom_hline(yintercept = -log10(0.01), linetype = "dashed", color = "black")LimROTS generates p-values from permutation samples, along with FDR.
Additionally, the qvalue package is used to calculate q-values and
Benjamini-Hochberg adjusted p-values based on the permutation-derived
p-values. These can be used as Quality Control for the LimROTS results.
We recommend using permutation-derived p-values and qvalues, though they
should generally be very similar to the FDR and Benjamini-Hochberg
adjusted p-values.
## Quality Control Plots
# Plot of q-values
plot(limrots.result$q_values,
main = "Q-values", xlab = "Index",
ylab = "Q-value"
)
# Histogram of q-values
hist(limrots.result$q_values,
main = "Q-value Distribution",
xlab = "Q-value", col = "lightgreen", border = "white"
)
# Summary of q-values
summary(limrots.result$q_values)sessionInfo()