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+---
+title: "Multimodal Mediation Analysis"
+format: html
+editor: visual
+author: Yihan Liu, Himel Mallick
+---
+
+# **Multimodal Mediation Analysis** {#sec-MSEA}
+
+```{r}
+#| label: setup
+#| echo: false
+#| results: asis
+remove(list = ls())
+invisible(gc())
+library(rebook)
+chapterPreamble()
+
+```
+
+Building upon the concepts and workflows presented in the previous chapter on 
+mediation analysis, here we demonstrate how to perform **multimodal mediation** 
+**analysis** to identify potential mediators across multiple omics layers. 
+**Multimodal mediation analysis** examines whether and how an exposure (e.g., 
+treatment, diet) affects an outcome (e.g., disease, phenotype) **through** 
+**intermediate variables (mediators) across multiple omics layers** 
+**simultaneously** (e.g., microbiome, metabolomics). It identifies which 
+features across modalities act as mediators, quantifies indirect (mediated) 
+effects while adjusting for covariates, and compares mediation strength across 
+layers, providing mechanistic insights into **how exposures impact outcomes** 
+**via molecular pathways**.
+
+```{r}
+#| label: fig_multimodal_mediation
+#| fig-cap: Directed acyclic graph illustrating multimodal mediation where an exposure affects multiple mediators across modalities (microbial species and metabolites), which in turn affect the outcome. A direct path from exposure to outcome is also included (dashed). While gut microbial species biologically influence metabolite levels, for tractability in high-dimensional mediation analysis we assume species and metabolites act as conditionally independent parallel mediators given exposure, acknowledging this as an approximation
+#| echo: false
+
+library(DiagrammeR)
+
+grViz("
+digraph multimodal_mediation {
+  graph [layout = dot, rankdir = LR]
+  
+  node [fontname = Helvetica, fontsize = 12]
+  
+  Exposure [shape=box, style=filled, fillcolor=lightblue, color=black]
+  Outcome [shape=box, style=filled, fillcolor=palegreen, color=black]
+  
+  M1 [label='Species 1', shape=ellipse, style=filled, fillcolor=lightyellow, color=black]
+  M2 [label='Species 2', shape=ellipse, style=filled, fillcolor=lightyellow, color=black]
+  M3 [label='Metabolite 1', shape=ellipse, style=filled, fillcolor=lightpink, color=black]
+  M4 [label='Metabolite 2', shape=ellipse, style=filled, fillcolor=lightpink, color=black]
+  
+  Exposure -> M1
+  Exposure -> M2
+  Exposure -> M3
+  Exposure -> M4
+  M1 -> Outcome
+  M2 -> Outcome
+  M3 -> Outcome
+  M4 -> Outcome
+  Exposure -> Outcome [style=dashed]
+}
+")
+```
+
+In this chapter, we demonstrate multimodal mediation analysis using microbiome 
+data from the iHMP IBDMDB study from the R/Bioconductor package 
+curatedMetagenomicData. [@Lloyd-Price2019]. Unlike conventional mediation 
+analysis, which typically focuses on a single mediator or a small set of 
+mediators, we performed multimodal mediation analysis with R/Bioconductor 
+package \[multimedia\] [@Jiang2025] here, which can handle many potential 
+mediators across multiple data modalities. For example, species-level taxonomic 
+abundances, pathways abundances, and metabolomic profiles can all serve as 
+potential mediators. This method allows us to estimate and rank each mediator’s 
+contribution while accounting for correlations between mediators in a high- 
+dimensional setting.
+
+In this example, time point (baseline vs. post-treatment) is used as the 
+treatment, and microbiome-based dysbiosis scores are used as the outcome. We 
+will first focus on the relative abundances of gut microbial species as 
+mediators, followed by pathways abundances.
+
+Generally, we will proceed through the following key steps:
+
+1.  Prepare the microbiome taxonomic data from the iHMP IBDMDB project.
+
+2.  Calculate dysbiosis scores as the outcome.
+
+3.  Define the mediation analysis data structure.
+
+4.  Fit the multimodal mediation model using the R package multimedia.
+
+5.  Interpret both the overall indirect effects and the mediator-specific 
+indirect effects.
+
+6.  Visualize the results using forest plots, histograms, and rankings to 
+prioritize findings.
+
+7.  Repeat the process for the iHMP microbial pathways.
+
+### Performing multimodal mediation analysis for iHMP species relative abundance {#sec-relative-abundance}
+
+We begin by loading the relative abundance data and calculating dysbiosis scores 
+for each sample based on Bray–Curtis dissimilarity from a healthy reference set. 
+This represents deviation from a healthy microbiome, where higher dysbiosis 
+scores indicate greater microbial imbalance. We then subset to IBD subjects with 
+samples collected at both baseline (visit 1) and post-treatment (visit 21).
+
+```{r}
+#| label: iHMP_data_preprocessing
+#| message: false
+
+##################
+# Load libraries #
+##################
+
+library(curatedMetagenomicData)
+library(SummarizedExperiment)
+library(dplyr)
+library(vegan)
+library(tidyverse)
+library(multimedia)
+library(stringr)
+library(ggplot2)
+library(mia)
+
+##################
+# Load iHMP data #
+##################
+
+# Load data
+tse <- curatedMetagenomicData(
+  "HMP_2019_ibdmdb.relative_abundance", 
+  rownames = "short",
+  dryrun = FALSE
+  )[[1]]
+
+# Assign SampleID for matching
+tse$SampleID <- colnames(tse)
+
+# Convert relative_abundance assay to relabundance (which is in [0,1] interval)
+tse <- transformAssay(tse, assay.type="relative_abundance", method="relabundance")
+
+########################
+# Reference nonIBD set #
+########################
+
+# Reference set: healthy
+tse$disease_binary <- tse$disease == "healthy"
+
+########################################
+# Calculate Bray-Curtis dissimilarity #
+########################################
+
+# Bray-Curtis dissimilarity
+diss <- as.matrix(getDissimilarity(tse, method = "bray", na.rm=TRUE, assay.type = "relabundance"))
+
+#################################
+# Calculate the dysbiosis score #
+#################################
+
+# Calculate dysbiosis score for each sample
+# For each sample i, we compute the median distance between sample i and all reference samples
+sample_ids <- tse$SampleID
+
+tse$dysbiosis <- sapply(seq_along(tse$disease_binary), function(i) {
+  
+  # Logical vector indicating all other reference samples (excluding i)
+  ref_others <- tse$disease_binary & (sample_ids != sample_ids[i])
+  
+  # Compute median distance between sample i and these reference samples
+  median(diss[i, ref_others], na.rm = TRUE)
+  
+})
+
+#############################################################
+# Subset to IBD only and only one post-baseline time point #
+#############################################################
+
+# Keep IBD only
+tse <- tse[, tse$disease != "healthy"]
+
+# Visit 1 (baseline) or 21 (post)
+tse <- tse[, tse$visit_number %in% c(1, 21)]
+
+# Keep subjects with both visits
+keep_subjects <- names(which(table(tse$subject_id) == 2))
+tse <- tse[, tse$subject_id %in% keep_subjects]
+
+# Define time point label
+tse$Time_point <- ifelse(tse$visit_number == 1, "T0", "T1")
+
+# Define treatment: Pre and Post (Baseline vs. Post-baseline)
+tse$treatment <- factor(tse$Time_point, levels = c("T0", "T1"))
+
+```
+
+Next, we will define the mediation analysis components. By using the processed 
+data, we define:
+
+-   Treatment: time point (baseline vs. post-baseline)
+-   Outcome: dysbiosis score
+-   Mediators: scaled species abundances
+
+These are bundled into a mediation data object (exper), which is passed into the 
+multimedia function to estimate path models for the treatment-to-mediator (α 
+path), mediator-to-outcome (β path), and the combined indirect effect (α×β 
+path).
+
+```{r}
+#| label: define_mediation_data_frame
+#| message: false
+
+#############################
+# Define mediation data set #
+#############################
+
+# Mediators (scaled, directly from SE): Species
+tse <- transformAssay(tse, assay.type="relabundance", method="standardize", name="scaled")
+
+```
+
+We now fit the multimodal mediation model and inspect the overall indirect and 
+direct effects to understand whether microbiome composition mediates the 
+treatment's effect on dysbiosis.
+
+```{r}
+#| label: overall_mediation_analysis
+#| message: false
+
+#############################
+# Run mediation (non-delta) #
+#############################
+
+# Convert the TreeSummarizedExperiment to be SummarizedExperiment
+se_relative <- as(tse, "SummarizedExperiment")
+if (is.null(rownames(se_relative))) rownames(se_relative) <- rownames(rowData(se_relative)) <- make.names(rownames(tse), unique = TRUE)
+
+# Use indices for mediators
+medi_idx <- seq_len(nrow(se_relative))
+
+# Create the Mediation Data object
+exper <- mediation_data(
+  se_relative,
+  outcomes   = "dysbiosis",
+  treatments = "treatment",
+  mediators  = medi_idx
+)
+
+# Fit and summarize
+mdl <- multimedia(exper)
+res <- estimate(mdl, exper)
+
+# Summarize overall indirect/direct
+summary(res)
+print(indirect_overall(res, exper))
+print(direct_effect(res, exper))
+
+```
+
+```{r}
+#| label: specific_mediation
+#| message: false
+
+#############################
+# Mediator-specific effects
+#############################
+
+# Extract the treatment-to-mediator path coefficients
+effects_by_mediator <- indirect_pathwise(res, exper)
+
+# Rank
+top_mediators <- effects_by_mediator %>%
+  arrange(desc(abs(indirect_effect))) %>%
+  head(20)
+
+print(top_mediators)
+
+```
+
+To quantify uncertainty around the indirect effects, we use non-parametric 
+bootstrap resampling to compute **95% confidence intervals** for both the 
+overall and mediator-specific indirect effects.
+
+```{r}
+#| label: visualization_for_overall_indirect_effects
+#| message: false
+
+#####################################
+# Bootstrap overall indirect effect # 
+#####################################
+
+set.seed(12345)
+boot_overall <- bootstrap(mdl, exper, c(indirect = indirect_overall), B = 10)
+summary(boot_overall$indirect)
+quantile(boot_overall$indirect$indirect_effect, probs = c(0.025, 0.975))
+
+# Histogram
+ggplot(boot_overall$indirect) +
+  geom_histogram(aes(indirect_effect), bins = 20, fill = "#69b3a2", color = "black") +
+  theme_classic() +
+  labs(
+    x = "Overall Indirect Effect",
+    y = "Frequency",
+    title = "Bootstrap Distribution of Overall Indirect Effect (B = 100)"
+  )
+
+```
+
+Finally, we visualize the **mediator-specific indirect effects** using a forest 
+plot, displaying point estimates and 95% CIs to highlight the most influential 
+mediators.
+
+```{r}
+#| label: visualization_for_mediation_specific_indirect_effects
+#| message: false
+
+###############################################
+# Bootstrap mediator-specific indirect effect # 
+###############################################
+
+# Define an mediation-specific indirect effect function manually
+indirect_each <- function(mdl, exper) {
+  res <- estimate(mdl, exper)
+  alpha <- sapply(res@mediation@estimates, function(m) coef(m)["treatmentT1"])
+  names(alpha) <- sub("\\.treatmentT1$", "", names(alpha))
+  beta <- coef(res@outcome@estimates$dysbiosis)[names(alpha)]
+  indirect <- alpha * beta
+  names(indirect) <- names(alpha)
+  indirect <- indirect[!is.na(indirect)]
+  return(indirect)
+}
+
+set.seed(12345)
+boot_each <- bootstrap(mdl, exper, c(indirect = indirect_each), B = 100)
+summary(boot_each$indirect)
+
+# Summarize the bootstrap results
+lower_upper <- apply(boot_each$indirect, 2, function(x) quantile(x, c(0.025, 0.975), na.rm=TRUE))
+means <- apply(boot_each$indirect, 2, mean, na.rm=TRUE)
+
+# Convert to data frame
+summary_df <- data.frame(
+  mediator = colnames(boot_each$indirect),
+  estimate = means,
+  lower = lower_upper[1,],
+  upper = lower_upper[2,]
+)
+summary_df <- summary_df[-1, ]
+
+# Mark significance if CI does not cross zero
+summary_df$significant <- with(summary_df, lower > 0 | upper < 0)
+
+# Remove the species with 0 confidence interval length
+summary_df <- summary_df %>% 
+  filter((upper - lower) != 0)
+
+# Add rankings
+summary_df$rank <- ifelse(summary_df$significant, 1, 2)  # 1 for significant, 2 for not
+summary_df <- summary_df[order(summary_df$rank, -abs(summary_df$estimate)), ]
+
+# Forest plot
+ggplot(summary_df, aes(x=estimate, y=reorder(mediator, estimate), color=significant)) +
+  geom_point() +
+  geom_errorbarh(aes(xmin=lower, xmax=upper), height=0.2) +
+  geom_vline(xintercept=0, linetype="dashed", color="grey") +
+  theme_classic() +
+  labs(
+    x = "Observed Indirect Effect with Bootstrap CI",
+    y = "Mediator",
+    title = "Forest Plot of Mediation-specific Indirect Effects for Species"
+  ) +
+  scale_color_manual(values=c("black","red")) +
+  theme(legend.position="bottom")
+
+```
+
+Based on the forest plot results, we can see that the Agathobaculum 
+butyriciproducens and Escherichia coli pathways has significant indirect 
+mediation effects.
+
+Next we repeat the mediation analysis with the iHMP pathway abundances using the 
+same setup as before, using the time point as the treatment, dysbiosis score as 
+the outcome, but pathways abundances as the mediation variables instead of the 
+relative species abundance.
+
+```{r}
+#| label: default_visualization_plot_mediators_pathway
+#| message: false
+
+# pick top mediators from the already-computed bootstrap summary (fast)
+top_meds <- summary_df %>%
+  dplyr::arrange(dplyr::desc(abs(estimate))) %>%
+  dplyr::slice_head(n = 12) %>%
+  dplyr::pull(mediator)
+
+# construct a minimal effect table that plot_mediators() can use
+ie_pw_fast <- tibble::tibble(
+  outcome = "dysbiosis",
+  mediator = top_meds,
+  direct_setting = levels(tse$treatment)[1],
+  contrast = paste(levels(tse$treatment)[1], "-", levels(tse$treatment)[2]),
+  indirect_effect = summary_df$estimate[match(top_meds, summary_df$mediator)]
+)
+
+plot_mediators(ie_pw_fast, exper, n_panels = 12)
+
+
+```
+Mediators are standardized (z-scored) for comparability across features; hence values may be negative. Besides, many microbial features are sparse; several mediators exhibit near-zero values for most samples, producing vertical bands.
+
+
+
+### Performing multimodal mediation analysis for pathways abundances {#sec-pathways-abundances}
+
+Let's extract the pathway abundance data from the iHMP data first, as well as 
+other data pre-processing.
+
+```{r}
+#| label: load_pkg_data
+#| message: false
+
+tse <- curatedMetagenomicData(
+  "HMP_2019_ibdmdb.pathway_abundance", 
+  rownames = "short",
+  dryrun = FALSE
+  )[[1]]
+
+tse$SampleID <- colnames(tse)
+tse <- tse[, colSums(is.na(assay(tse))) == 0]
+
+rows_to_keep <- !grepl("\\|", rownames(tse))
+rows_to_keep[which(rows_to_keep)[1:2]] <- FALSE
+tse <- tse[rows_to_keep, ]
+assay(tse) <- assay(tse) / 100
+tse$disease_binary <- tse$disease == "healthy"
+
+diss <- as.matrix(vegdist(t(assay(tse)), method = "bray", na.rm = TRUE))
+tse$dysbiosis <- sapply(seq_along(tse$disease_binary), function(i) {
+  median(diss[i, tse$disease_binary & 
+              (tse$SampleID != tse$SampleID[i])], 
+         na.rm = TRUE)
+})
+
+tse <- tse[, tse$disease != "healthy"]
+tse <- tse[, tse$visit_number %in% c(1, 27)]
+keep_subjects <- names(which(table(tse$subject_id) == 2))
+tse <- tse[, tse$subject_id %in% keep_subjects]
+
+tse$Time_point <- ifelse(tse$visit_number == 1, "T0", "T1")
+
+tse$treatment <- factor(tse$Time_point, levels = c("T0", "T1"))
+
+```
+
+We will define the mediation analysis data set then.
+
+```{r}
+#| label: define_mediation_data_frame
+#| message: false
+
+tse <- transformAssay(tse, assay.type="pathway_abundance", method="standardize", name="scaled")
+
+```
+
+Next, we continue to fit the multimodal mediation model, and extract the overall 
+and mediation-specific indirect effects.
+
+```{r}
+#| label: mediation_analysis
+#| message: false
+
+raw <- rownames(tse)
+clean1 <- str_remove_all(raw, "\\[|\\]")
+clean2 <- str_replace_all(clean1, "[: \\.,]", "_")
+safe_names <- make.names(clean2, unique = TRUE)
+rownames(tse) <- safe_names
+
+medi_idx <- seq_len(nrow(tse))
+
+exper <- mediation_data(
+  tse,
+  outcomes   = "dysbiosis",
+  treatments = "treatment",
+  mediators  = medi_idx
+)
+
+mdl <- multimedia(exper)
+res <- estimate(mdl, exper)
+summary(res)
+print(indirect_overall(res, exper))
+print(direct_effect(res, exper))
+
+effects_by_mediator <- indirect_pathwise(res, exper)
+
+top_mediators <- effects_by_mediator %>%
+  arrange(desc(abs(indirect_effect))) %>%
+  head(20)
+
+print(top_mediators)
+
+```
+
+The non-parametric bootstrap resampling is also used to compute **95% CIs** for 
+both the overall and mediator-specific pathway indirect effects.
+
+```{r}
+#| label: visualization_for_overall_indirect_effects
+#| message: false
+
+set.seed(1234)
+boot_overall <- bootstrap(mdl, exper, c(indirect = indirect_overall), B = 100)
+summary(boot_overall$indirect)
+quantile(boot_overall$indirect$indirect_effect, probs = c(0.025, 0.975))
+
+ggplot(boot_overall$indirect) +
+  geom_histogram(aes(indirect_effect), bins = 20, fill = "#69b3a2", color = "black") +
+  theme_classic() +
+  labs(
+    x = "Overall Indirect Effect",
+    y = "Frequency",
+    title = "Bootstrap Distribution of Overall Indirect Effect (B = 100)"
+  )
+
+```
+
+We visualize the **mediator-specific indirect effects** using a forest plot for 
+pathway aubundance as well. with the point estimates and 95% CIs.
+
+```{r}
+#| label: visualization_for_mediation_specific_indirect_effects
+#| message: false
+
+indirect_each <- function(mdl, exper) {
+  res <- estimate(mdl, exper)
+  alpha <- sapply(res@mediation@estimates, function(m) coef(m)["treatmentT1"])
+  names(alpha) <- sub("\\.treatmentT1$", "", names(alpha))
+  beta <- coef(res@outcome@estimates$dysbiosis)[names(alpha)]
+  indirect <- alpha * beta
+  names(indirect) <- names(alpha)
+  indirect <- indirect[!is.na(indirect)]
+  return(indirect)
+}
+
+set.seed(1234)
+boot_each <- bootstrap(mdl, exper, c(indirect = indirect_each), B = 100)
+
+lower_upper <- apply(boot_each$indirect, 2, function(x) quantile(x, c(0.025, 0.975), na.rm=TRUE))
+means <- apply(boot_each$indirect, 2, mean, na.rm=TRUE)
+summary_df <- data.frame(
+  mediator = colnames(boot_each$indirect),
+  estimate = means,
+  lower = lower_upper[1,],
+  upper = lower_upper[2,]
+)
+
+summary_df <- summary_df[-1, ]
+summary_df$significant <- with(summary_df, lower > 0 | upper < 0)
+summary_df <- summary_df[summary_df$upper != summary_df$lower, ]
+
+# Clean the pathway names
+pwy <- rownames(summary_df)
+pwy <- gsub("PWY0\\.", "PWY0-", pwy) # PWY0.xxx → PWY0-xxx
+pwy <- gsub("PWY\\.", "PWY-", pwy) # PWY.xxx → PWY-xxx
+pwy <- gsub("\\.", " ", pwy) # leftover dots → spaces
+pwy <- gsub("__", ": ", pwy) # double underscores → colon
+pwy <- gsub("_\\.", " ", pwy) # underscore then dot → space
+pwy <- gsub("_", " ", pwy) # remaining underscores → space
+pwy <- gsub("\\.\\.", " ", pwy) # double dots → space
+pwy <- gsub("\\.$", "", pwy) # remove ending period
+# pwy <- trimws(pwy) # final cleanup
+rownames(summary_df) <- pwy
+
+ggplot(summary_df, aes(x=estimate, y=reorder(mediator, estimate), color=significant)) +
+  geom_point() +
+  geom_errorbarh(aes(xmin=lower, xmax=upper), height=0.2) +
+  geom_vline(xintercept=0, linetype="dashed", color="grey") +
+  theme_classic() +
+  labs(
+    x = "Observed Indirect Effect with Bootstrap CI",
+    y = "Mediator",
+    title = "Forest Plot of Mediation-specific Indirect Effects for Pathway"
+  ) +
+  scale_color_manual(values=c("black","red")) +
+  theme(legend.position="bottom")
+
+```
+
+Based on the forest plot results, we can see that the tRNA charging pathway has 
+significant indirect mediation effects on the dysbiosis scores.