This appendix validates that TSENAT’s transcript diversity measures (Shannon entropy, Simpson index) are mathematically equivalent to SplicingFactory’s implementations. We benchmark both packages on TCGA BRCA RNA-seq data to demonstrate:
Who needs this appendix? Anyone evaluating TSENAT for transcript diversity analysis or validating cross-package comparisons.
Transcript diversity measures how variable isoform expression is within genes. Two standard approaches:
TSENAT’s approach: Generalized Tsallis entropy framework where q=1 gives Shannon and q=2 gives Simpson. This allows sensitivity analysis across the q continuum while maintaining equivalence with established methods.
Key question: Does TSENAT’s mathematical generalization produce identical statistical results?
We use TCGA BRCA RNA-seq data as our validation dataset, which is included in the SplicingFactory package:
Analysis pipeline:
We begin by loading the required libraries and the TCGA BRCA dataset that will serve as our validation benchmark.
suppressPackageStartupMessages({
library("SplicingFactory")
library(TSENAT)
library("SummarizedExperiment")
})
set.seed(12345)
# Load dataset
data(tcga_brca_luma_dataset)
# Extract gene names
genes <- tcga_brca_luma_dataset[, 1]
# Extract read count data without gene names
readcounts <- tcga_brca_luma_dataset[, -1]We filter genes to retain only those with sufficient coverage across samples, ensuring robust diversity estimates.
tokeep <- rowSums(readcounts > 5) > 5
readcounts <- readcounts[tokeep, ]
genes <- genes[tokeep]
# Create SummarizedExperiment object for cleaner data handling
# Important: Set gene names as rownames for compatibility with SplicingFactory
# TSENATAnalysis requires 'gene_id' in rowData
se_data <- SummarizedExperiment(
assays = list(counts = as.matrix(readcounts)),
rowData = DataFrame(gene_id = genes)
)
rownames(se_data) <- genesTo calculate transcript diversity measures (Shannon entropy, Simpson index, and Tsallis entropy at q=1 and q=2), use:
# Create sample group classification based on sample names
# (Normal samples end with _N, Tumor samples don't)
sample_group <- ifelse(grepl("_N$", colnames(se_data)), "Normal", "Tumor")
# Add group metadata to se_data for all downstream analyses
colData(se_data)$group <- sample_group
# SplicingFactory: Calculate diversity for both Shannon (naive) and Simpson methods
sf_methods <- c("naive", "simpson")
splicing_results <- setNames(vector("list", length(sf_methods)), sf_methods)
for (method in sf_methods) {
splicing_results[[method]] <- SplicingFactory::calculate_diversity(
x = se_data,
method = method,
norm = TRUE,
verbose = FALSE
)
# Add sample_type and group metadata to SplicingFactory objects
# (sample_type matches SplicingFactory naming; group matches TSENAT naming for consistency)
colData(splicing_results[[method]])$sample_type <- sample_group
colData(splicing_results[[method]])$group <- sample_group
}
# TSENAT: Single config for q-value sweep
# (Configuration is identical for all q-values)
config <- TSENAT_config(condition_col = "group")
# TSENAT: Create analysis objects and compute diversity for q=1 and q=2
q_values <- c(1, 2)
tsenat_results <- setNames(vector("list", length(q_values)), paste0("q", q_values))
for (q in q_values) {
# Create analysis object (following Bioconductor pattern: config first, then constructor)
tsenat_results[[paste0("q", q)]] <- TSENATAnalysis(se_data, config = config)
# Compute diversity with dynamic output filename using sprintf
# Use explicit namespace to avoid SplicingFactory::calculate_diversity masking
tsenat_results[[paste0("q", q)]] <- TSENAT::calculate_diversity(
analysis = tsenat_results[[paste0("q", q)]],
q = q,
norm = TRUE,
verbose = FALSE
)
}
# Extract for downstream use (aliases maintain backward compatibility with existing code)
shannon_entropy <- splicing_results$naive
simpson_index <- splicing_results$simpson
tsenat_analysis_q1 <- tsenat_results$q1
tsenat_analysis_q2 <- tsenat_results$q2Both packages return a SummarizedExperiment object, that you can investigate further with the assay function.
We apply statistical testing to identify genes with significantly different transcript diversity between Normal and Tumor samples using both SplicingFactory and TSENAT frameworks.
# SplicingFactory: Differential analysis for Shannon entropy
entropy_significance <- SplicingFactory::calculate_difference(
x = shannon_entropy,
samples = "sample_type",
control = "Normal",
method = "mean",
test = "wilcoxon",
verbose = FALSE
)
# SplicingFactory: Differential analysis for Simpson index
simpson_significance <- SplicingFactory::calculate_difference(
x = simpson_index,
samples = "sample_type",
control = "Normal",
method = "mean",
test = "wilcoxon",
verbose = FALSE
)
# TSENAT: Differential analysis for Tsallis q=1 (Shannon equivalent)
# Extract the diversity results for q=1 using the results() accessor
# Returns SummarizedExperiment with diversity values (genes x samples)
div_result_q1 <- results(tsenat_analysis_q1, type = "diversity", q = 1.0, format = "se")
# Apply SplicingFactory's calculate_difference to TSENAT q=1 diversity
# Use "group" column already in colData (from se_data)
tsenat_shannon_diff <- SplicingFactory::calculate_difference(
x = div_result_q1,
samples = "group",
control = "Normal",
method = "mean",
test = "wilcoxon",
verbose = FALSE
)
# TSENAT: Differential analysis for Tsallis q=2 (Simpson equivalent)
# Extract the diversity results for q=2 using the results() accessor
# Returns SummarizedExperiment with diversity values (genes x samples)
div_result_q2 <- results(tsenat_analysis_q2, type = "diversity", q = 2.0, format = "se")
# Apply SplicingFactory's calculate_difference to TSENAT q=2 diversity
# Use "group" column already in colData (from se_data)
tsenat_simpson_diff <- SplicingFactory::calculate_difference(
x = div_result_q2,
samples = "group",
control = "Normal",
method = "mean",
test = "wilcoxon",
verbose = FALSE
)For the benchmark comparison with TSENAT, we will compute Tsallis entropy at q=1 (equivalent to Shannon) and q=2 (equivalent to Simpson). This allows direct comparison with the SplicingFactory results shown above.
| Method | Genes Tested | Significant (padj<0.05) | Mean log2FC | SD log2FC |
|---|---|---|---|---|
| SplicingFactory (Shannon/naive) | 214 | 26 | -0.0009354 | 1.582967 |
| TSENAT (Tsallis q=1) | 213 | 26 | 0.0003618 | 1.586675 |
Interpretation: Both methods similarly identify significantly different transcript diversity between Normal and Tumor samples. The comparable number of significant genes (padj<0.05) and mean log2FC values demonstrate equivalent statistical power and effect size detection.
| Gene | Normal Mean | Tumor Mean | Mean Diff | log2FC | p-value | adj p-value |
|---|---|---|---|---|---|---|
| C1orf213 | 0.8122 | 0.1400 | -0.6722 | -2.5365 | 3.97e-07 | 8.50e-05 |
| HAPLN3 | 0.7030 | 0.4299 | -0.2731 | -0.7096 | 4.17e-05 | 4.46e-03 |
| COL1A2 | 0.0000 | 0.1643 | 0.1643 | Inf | 6.68e-05 | 4.77e-03 |
| F10 | 0.1311 | 0.3720 | 0.2409 | 1.5050 | 1.37e-04 | 7.31e-03 |
| DUSP14 | 0.2989 | 0.1302 | -0.1688 | -1.1995 | 1.89e-04 | 8.10e-03 |
| MBD2 | 0.0027 | 0.0371 | 0.0344 | 3.7876 | 2.39e-04 | 8.54e-03 |
| C1orf86 | 0.1479 | 0.0029 | -0.1450 | -5.6777 | 4.59e-04 | 9.85e-03 |
| GFPT1 | 0.0231 | 0.0025 | -0.0207 | -3.2253 | 3.80e-04 | 9.85e-03 |
| HNRNPR | 0.5162 | 0.5907 | 0.0746 | 0.1947 | 4.60e-04 | 9.85e-03 |
| OSR1 | 0.0497 | 0.2891 | 0.2394 | 2.5411 | 4.10e-04 | 9.85e-03 |
| Gene | Normal Mean | Tumor Mean | Mean Diff | log2FC | p-value | adj p-value |
|---|---|---|---|---|---|---|
| C1orf213 | 0.8122 | 0.1400 | -0.6722 | -2.5365 | 3.97e-07 | 8.46e-05 |
| HAPLN3 | 0.7030 | 0.4299 | -0.2731 | -0.7096 | 4.17e-05 | 4.44e-03 |
| COL1A2 | 0.0000 | 0.1643 | 0.1643 | Inf | 6.68e-05 | 4.74e-03 |
| F10 | 0.1311 | 0.3720 | 0.2409 | 1.5050 | 1.37e-04 | 7.27e-03 |
| DUSP14 | 0.2989 | 0.1302 | -0.1688 | -1.1995 | 1.89e-04 | 8.06e-03 |
| MBD2 | 0.0027 | 0.0371 | 0.0344 | 3.7876 | 2.39e-04 | 8.50e-03 |
| C1orf86 | 0.1479 | 0.0029 | -0.1450 | -5.6777 | 4.59e-04 | 9.80e-03 |
| HNRNPR | 0.5162 | 0.5907 | 0.0746 | 0.1947 | 4.60e-04 | 9.80e-03 |
| OSR1 | 0.0497 | 0.2891 | 0.2394 | 2.5411 | 4.10e-04 | 9.80e-03 |
| GFPT1 | 0.0231 | 0.0025 | -0.0207 | -3.2253 | 3.80e-04 | 9.80e-03 |
| Method | Genes Tested | Significant (padj<0.05) | Mean log2FC | SD log2FC |
|---|---|---|---|---|
| SplicingFactory (Simpson) | 214 | 26 | -0.0012687 | 1.812772 |
| TSENAT (Tsallis q=2) | 213 | 26 | -0.0000521 | 1.817060 |
Interpretation: Simpson index results parallel Shannon entropy findings, with both methods identifying similar numbers of significantly different isoform dominance patterns. The agreement across both diversity measures provides strong evidence for TSENAT’s mathematical and statistical equivalence to SplicingFactory.
| Gene | Normal Mean | Tumor Mean | Mean Diff | log2FC | p-value | adj p-value |
|---|---|---|---|---|---|---|
| C1orf213 | 0.3852 | 0.0515 | -0.3337 | -2.9037 | 3.97e-07 | 8.50e-05 |
| HAPLN3 | 0.4823 | 0.2558 | -0.2266 | -0.9152 | 5.17e-06 | 5.53e-04 |
| COL1A2 | 0.0000 | 0.0626 | 0.0626 | Inf | 6.68e-05 | 4.77e-03 |
| F10 | 0.0697 | 0.2494 | 0.1797 | 1.8400 | 1.10e-04 | 5.86e-03 |
| DUSP14 | 0.1686 | 0.0617 | -0.1069 | -1.4499 | 2.11e-04 | 7.32e-03 |
| HNRNPR | 0.5376 | 0.6134 | 0.0758 | 0.1903 | 1.79e-04 | 7.32e-03 |
| MBD2 | 0.0005 | 0.0107 | 0.0102 | 4.5028 | 2.39e-04 | 7.32e-03 |
| CXorf40A | 0.7455 | 0.7939 | 0.0484 | 0.0907 | 2.75e-04 | 7.34e-03 |
| GFPT1 | 0.0051 | 0.0004 | -0.0047 | -3.5271 | 3.80e-04 | 8.78e-03 |
| OSR1 | 0.0124 | 0.1156 | 0.1032 | 3.2168 | 4.10e-04 | 8.78e-03 |
| Gene | Normal Mean | Tumor Mean | Mean Diff | log2FC | p-value | adj p-value |
|---|---|---|---|---|---|---|
| C1orf213 | 0.7703 | 0.1029 | -0.6674 | -2.9037 | 3.97e-07 | 8.46e-05 |
| HAPLN3 | 0.7235 | 0.3836 | -0.3398 | -0.9152 | 5.17e-06 | 5.50e-04 |
| COL1A2 | 0.0000 | 0.1251 | 0.1251 | Inf | 6.68e-05 | 4.74e-03 |
| F10 | 0.1045 | 0.3741 | 0.2696 | 1.8400 | 1.10e-04 | 5.83e-03 |
| HNRNPR | 0.6144 | 0.7010 | 0.0866 | 0.1903 | 1.79e-04 | 7.28e-03 |
| DUSP14 | 0.2529 | 0.0926 | -0.1603 | -1.4499 | 2.11e-04 | 7.28e-03 |
| MBD2 | 0.0009 | 0.0213 | 0.0204 | 4.5028 | 2.39e-04 | 7.28e-03 |
| CXorf40A | 0.8387 | 0.8931 | 0.0544 | 0.0907 | 2.75e-04 | 7.31e-03 |
| OSR1 | 0.0249 | 0.2312 | 0.2063 | 3.2168 | 4.10e-04 | 8.74e-03 |
| GFPT1 | 0.0103 | 0.0009 | -0.0094 | -3.5271 | 3.80e-04 | 8.74e-03 |
Both methods share the same mathematical formula:
\[Simpson = Tsallis_{q=2} = 1 - \sum_{i=1}^n p_i^2\]
where \(p_i = \frac{x_i}{\sum_i x_i}\) (transcript proportions).
Howerver, SplicingFactory returns raw values, while TSENAT normalizes by the theoretical maximum \((1-1/n)\):
| SplicingFactory | TSENAT | |
|---|---|---|
| Formula | \(1 - \sum p_i^2\) | \(\frac{1 - \sum p_i^2}{1 - 1/n}\) |
| Range | 0 to ~1 | 0 to 1 |
| Scale difference | Raw | ~2x for 2-isoform genes |
This explains observed differences like C1orf213 Normal: 0.3852 (SplicingFactory) vs 0.7703 (TSENAT). Since C1orf213 has 2 expressed isoforms, the normalization factor is \(1 - 1/2 = 0.5\). The calculation: \(0.3852 / 0.5 = 0.7704\) confirms this scaling factor. Despite raw value differences, statistical analysis yields identical results:
log2 fold changes: Normalization factor cancels in ratios: \(\log_2\left(\frac{S_{norm,t}}{S_{norm,n}}\right) = \log_2\left(\frac{S_{raw,t}/K}{S_{raw,n}/K}\right) = \log_2\left(\frac{S_{raw,t}}{S_{raw,n}}\right)\)
P-values and rankings: Wilcoxon rank-sum tests depend only on gene ranks, not absolute values, so both methods identify the same significant genes
Statistical validity: Both approaches are correct-SplicingFactory favors unbounded diversity, TSENAT favors interpretable [0,1] scaling
This appendix has demonstrated that TSENAT’s implementation of transcript diversity measures is mathematically and statistically equivalent to SplicingFactory’s established methods for both Shannon entropy and Simpson index calculations.
sessionInfo()
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