Network meta analysis

Network Meta-Analysis in R

Overview

Network meta-analysis (NMA) methods for comparing multiple treatments simultaneously using direct and indirect evidence. Covers network structure assessment, frequentist and Bayesian NMA approaches, consistency evaluation, treatment rankings, and visualization techniques.

Network Structure and Data Preparation

Pairwise Data Format

library(netmeta)

# Standard pairwise format for contrast-based NMA
pairwise_data <- data.frame(
  study = c("Study1", "Study1", "Study2", "Study2", "Study3", "Study3",
            "Study4", "Study4", "Study5", "Study5", "Study5"),
  treat1 = c("A", "A", "A", "B", "B", "B", "A", "C", "A", "B", "C"),
  treat2 = c("B", "C", "B", "C", "C", "D", "C", "D", "B", "C", "D"),
  TE = c(0.5, 0.3, 0.4, -0.2, 0.1, 0.3, 0.35, 0.25, 0.45, -0.15, 0.2),
  seTE = c(0.1, 0.12, 0.11, 0.13, 0.15, 0.14, 0.09, 0.11, 0.10, 0.12, 0.13)
)

# Create network meta-analysis object
net <- netmeta(
  TE = TE,
  seTE = seTE,
  treat1 = treat1,
  treat2 = treat2,
  studlab = study,
  data = pairwise_data,
  sm = "MD",                    # Effect measure
  reference.group = "A",        # Reference treatment
  all.treatments = NULL         # Auto-detect
)

summary(net)

Arm-Level Data Format

library(netmeta)

# Convert arm-level to pairwise format
arm_data <- data.frame(
  study = rep(c("S1", "S2", "S3"), c(2, 3, 2)),
  treatment = c("A", "B", "A", "B", "C", "B", "C"),
  n = c(50, 52, 48, 51, 49, 55, 53),
  events = c(15, 22, 12, 25, 18, 28, 20)
)

# Use pairwise() to convert
library(meta)
pw <- pairwise(
  treat = treatment,
  event = events,
  n = n,
  studlab = study,
  data = arm_data,
  sm = "OR"
)

# Create network
net_from_arm <- netmeta(pw)

Network Visualization

library(netmeta)

# Network graph
netgraph(net,
         plastic = FALSE,
         thickness = "number.of.studies",
         multiarm = TRUE,
         points = TRUE,
         cex.points = 3,
         col = "darkblue")

# Improved network graph
netgraph(net,
         seq = "optimal",           # Optimal node arrangement
         plastic = FALSE,
         thickness = "se.fixed",    # Edge thickness by precision
         number.of.studies = TRUE,  # Show number of studies
         col = "#4477AA",
         col.points = "#CC6677",
         cex.points = 4,
         labels = paste0(trts(net), "\n(n=", n.arms(net), ")"))

Frequentist NMA with netmeta

Basic Network Meta-Analysis

library(netmeta)

# Fit NMA (fixed and random effects)
net <- netmeta(
  TE = TE,
  seTE = seTE,
  treat1 = treat1,
  treat2 = treat2,
  studlab = study,
  data = pairwise_data,
  sm = "MD",
  fixed = TRUE,
  random = TRUE,
  reference.group = "A"
)

# Summary
summary(net)

# Results for specific comparison
net$TE.fixed["B", "A"]      # Fixed effect B vs A
net$TE.random["B", "A"]     # Random effects B vs A
net$seTE.random["B", "A"]   # SE for random effects

Forest Plot for NMA

library(netmeta)

# Forest plot: all treatments vs reference
forest(net,
       reference.group = "A",
       sortvar = TE,
       smlab = "Mean Difference vs A",
       drop.reference.group = TRUE,
       label.left = "Favors A",
       label.right = "Favors Treatment")

# Forest plot with subgroup (by comparison type)
forest(net,
       reference.group = "A",
       direct = TRUE)  # Show direct evidence only

League Table

library(netmeta)

# League table (all pairwise comparisons)
league <- netleague(
  net,
  digits = 2,
  bracket = "(",
  separator = " to ",
  fixed = FALSE    # Use random effects
)

# Print league table
print(league, common = FALSE)

# As matrix
league$random

Treatment Rankings

library(netmeta)

# P-scores (frequentist ranking)
netrank(net, small.values = "good")

# Rankogram
set.seed(123)
rank <- rankogram(net, nsim = 1000)
plot(rank)

# SUCRA-like plot
plot(rank, cumulative = TRUE)

Bayesian NMA with gemtc

Basic Bayesian NMA

library(gemtc)

# Prepare data for gemtc (arm-level)
network_data <- list(
  data.ab = data.frame(
    study = c("S1", "S1", "S2", "S2", "S3", "S3", "S3"),
    treatment = c("A", "B", "A", "C", "A", "B", "C"),
    responders = c(15, 22, 12, 18, 20, 28, 24),
    sampleSize = c(50, 52, 48, 49, 55, 58, 54)
  )
)

# Create network object
network <- mtc.network(data.ab = network_data$data.ab)

# Plot network
plot(network)

# Consistency model
model <- mtc.model(
  network,
  type = "consistency",
  likelihood = "binom",
  link = "logit",
  linearModel = "random"
)

# Run MCMC
set.seed(123)
result <- mtc.run(
  model,
  n.adapt = 5000,
  n.iter = 20000,
  thin = 1
)

summary(result)

Model Diagnostics

library(gemtc)
library(coda)

# Trace plots
plot(result)

# Gelman-Rubin diagnostic
gelman.diag(result$samples)
gelman.plot(result$samples)

# Effective sample size
effectiveSize(result$samples)

# Autocorrelation
autocorr.plot(result$samples)

# Density plots
densplot(result$samples)

Treatment Rankings (Bayesian)

library(gemtc)

# Rank probabilities
ranks <- rank.probability(result)
print(ranks)

# Plot rank probabilities
plot(ranks)

# SUCRA
sucra <- sucra(ranks)
print(sucra)

# Cumulative ranking plot
plot(ranks, beside = TRUE)

Bayesian NMA with multinma

Using multinma Package

library(multinma)

# Prepare data
nma_data <- set_agd_arm(
  data = arm_data,
  study = study,
  trt = treatment,
  r = events,
  n = n
)

# Network plot
plot(nma_data)

# Fit Bayesian NMA
nma_fit <- nma(
  nma_data,
  trt_effects = "random",
  prior_intercept = normal(scale = 10),
  prior_trt = normal(scale = 10),
  prior_het = half_normal(scale = 1)
)

# Summary
summary(nma_fit)
print(nma_fit, pars = "d")

# Treatment effects
relative_effects(nma_fit, all_contrasts = TRUE)

Population-Adjusted NMA

library(multinma)

# With individual patient data (IPD) and aggregate data (AgD)
# IPD data
ipd_data <- set_ipd(
  data = ipd_df,
  study = study,
  trt = treatment,
  y = outcome
)

# AgD data
agd_data <- set_agd_arm(
  data = agd_df,
  study = study,
  trt = treatment,
  r = events,
  n = n
)

# Combine networks
combined_network <- combine_network(ipd_data, agd_data)

# Fit with covariate adjustment
nma_cov <- nma(
  combined_network,
  trt_effects = "random",
  regression = ~age + sex
)

Consistency Assessment

Global Inconsistency Tests

library(netmeta)

# Design-by-treatment interaction model
decomp <- decomp.design(net)
print(decomp)

# Q statistics
decomp$Q.decomp           # Overall Q decomposition
decomp$Q.het.design       # Within-design heterogeneity
decomp$Q.inc.detach       # Between-design inconsistency

# Net heat plot (visual inconsistency)
netheat(net)

Local Inconsistency (Node-Splitting)

library(netmeta)

# Node-splitting for all comparisons with direct evidence
netsplit_result <- netsplit(net)
print(netsplit_result)

# Forest plot of node-splitting
forest(netsplit_result)

# Using gemtc for Bayesian node-splitting
library(gemtc)

# Node-split model
nodesplit <- mtc.nodesplit(network, comparisons = NULL)  # All comparisons

# Run each comparison
ns_results <- lapply(nodesplit, function(model) {
  mtc.run(model, n.adapt = 5000, n.iter = 20000)
})

# Summary
mtc.nodesplit.comparisons(nodesplit)

Inconsistency Model

library(gemtc)

# Unrelated mean effects (inconsistency) model
model_ume <- mtc.model(
  network,
  type = "ume",
  likelihood = "binom",
  link = "logit"
)

result_ume <- mtc.run(model_ume, n.adapt = 5000, n.iter = 20000)

# Compare DIC
summary(result)$DIC      # Consistency model
summary(result_ume)$DIC  # Inconsistency model

# Model comparison
mtc.deviance(result)

Heterogeneity Assessment

library(netmeta)

# Heterogeneity statistics
net$tau           # Tau (between-study SD)
net$tau2          # Tau-squared
net$I2            # I-squared
net$Q             # Q statistic
net$df.Q          # Degrees of freedom
net$pval.Q        # P-value for Q

# Prediction intervals
net$lower.predict  # Lower prediction interval
net$upper.predict  # Upper prediction interval

Network Meta-Regression

library(netmeta)

# With study-level covariate
net_reg <- netmeta(
  TE = TE,
  seTE = seTE,
  treat1 = treat1,
  treat2 = treat2,
  studlab = study,
  data = pairwise_data,
  sm = "MD"
)

# Meta-regression using netmetareg (requires netmeta >= 2.0)
# net_reg <- netmetareg(net, ~year)

# Alternative: Use gemtc with covariates
library(gemtc)

# Add study-level covariate
network_cov <- mtc.network(
  data.ab = network_data$data.ab,
  studies = data.frame(
    study = c("S1", "S2", "S3"),
    year = c(2010, 2015, 2020)
  )
)

model_reg <- mtc.model(
  network_cov,
  type = "regression",
  regressor = list(coefficient = "shared", variable = "year")
)

result_reg <- mtc.run(model_reg, n.adapt = 5000, n.iter = 20000)
summary(result_reg)

Subgroup and Sensitivity Analysis

library(netmeta)

# Subgroup NMA by risk of bias
net_low_rob <- netmeta(
  TE = TE[rob == "low"],
  seTE = seTE[rob == "low"],
  treat1 = treat1[rob == "low"],
  treat2 = treat2[rob == "low"],
  studlab = study[rob == "low"],
  sm = "MD"
)

# Compare results
comparison_table <- data.frame(
  Model = c("All studies", "Low RoB only"),
  Tau = c(net$tau, net_low_rob$tau),
  Effect_B_vs_A = c(net$TE.random["B", "A"], net_low_rob$TE.random["B", "A"])
)

Reporting and Visualization

PRISMA-NMA Flow Diagram

# Recommended reporting items for NMA
# 1. Network geometry
# 2. Assessment of transitivity
# 3. Presentation of results (forest, league table)
# 4. Ranking with uncertainty
# 5. Assessment of inconsistency
# 6. Assessment of heterogeneity

Comparison-Adjusted Funnel Plot

library(netmeta)

# Funnel plot for NMA
funnel(net,
       order = c("A", "B", "C", "D"),
       pooled = "random",
       pch = 1:4,
       legend = TRUE)

Summary of Evidence Table

# Create summary table for publication
create_nma_summary <- function(net, ref = "A") {
  treatments <- net$trts[net$trts != ref]

  summary_df <- data.frame(
    Comparison = paste(treatments, "vs", ref),
    Effect_Fixed = sapply(treatments, function(t) net$TE.fixed[t, ref]),
    CI_Lower_Fixed = sapply(treatments, function(t) net$lower.fixed[t, ref]),
    CI_Upper_Fixed = sapply(treatments, function(t) net$upper.fixed[t, ref]),
    Effect_Random = sapply(treatments, function(t) net$TE.random[t, ref]),
    CI_Lower_Random = sapply(treatments, function(t) net$lower.random[t, ref]),
    CI_Upper_Random = sapply(treatments, function(t) net$upper.random[t, ref])
  )

  # Format
  summary_df <- summary_df |>
    mutate(
      Fixed = paste0(round(Effect_Fixed, 2), " (",
                    round(CI_Lower_Fixed, 2), ", ",
                    round(CI_Upper_Fixed, 2), ")"),
      Random = paste0(round(Effect_Random, 2), " (",
                     round(CI_Lower_Random, 2), ", ",
                     round(CI_Upper_Random, 2), ")")
    ) |>
    select(Comparison, Fixed, Random)

  return(summary_df)
}

Key Packages Summary

Package	Purpose
netmeta	Frequentist NMA (contrast-based)
gemtc	Bayesian NMA with JAGS
multinma	Bayesian NMA with Stan
bnma	Bayesian NMA
pcnetmeta	Patient-centered NMA
NMAoutlier	Outlier detection in NMA
nmathresh	Decision thresholds for NMA

Best Practices

1. Network geometry: Check connectivity before analysis
2. Transitivity: Assess similarity of study populations across comparisons
3. Consistency: Always assess local and global inconsistency
4. Heterogeneity: Report tau, I², and consider prediction intervals
5. Ranking: Present uncertainty (CrI for ranks, rankograms)
6. Sensitivity: Conduct analyses excluding high RoB studies
7. Reporting: Follow PRISMA-NMA extension guidelines
8. Model selection: Compare fixed vs random effects, check model fit