Meta Analysis

Meta-Analysis Methods in R

Overview

Comprehensive pairwise meta-analysis methods covering effect size calculation, fixed and random effects models, heterogeneity assessment, publication bias detection, subgroup analysis, meta-regression, and sensitivity analyses for synthesizing evidence across studies.

Effect Size Calculation

Continuous Outcomes

library(metafor)

# Standardized mean difference (SMD/Cohen's d/Hedges' g)
dat 
  mutate(
    log_hr = log(hr),
    se_log_hr = (log(hr_upper) - log(hr_lower)) / (2 * 1.96)
  )

Fixed and Random Effects Models

Using meta Package

library(meta)

# Continuous outcomes
m_cont 75%: Considerable heterogeneity

# Create heterogeneity summary
het_summary 
  spread_draws(b_Intercept, r_study[study,]) |>
  mutate(study_effect = b_Intercept + r_study) |>
  ggplot(aes(y = study, x = study_effect)) +
  stat_halfeye()

Diagnostic Meta-Analysis

library(mada)

# Bivariate random-effects model for diagnostic accuracy
fit_diag <- reitsma(
  data = diag_data,
  formula = cbind(TP, FN, FP, TN) ~ 1
)

summary(fit_diag)

# SROC curve
plot(fit_diag, sroclwd = 2)

# Summary sensitivity and specificity
summary_sens <- fit_diag$coefficients["tsens..Intercept."]
summary_spec <- fit_diag$coefficients["tfpr..Intercept."]

Reporting Meta-Analysis Results

Summary Table

library(meta)

# Create summary table
summary_table <- data.frame(
  Model = c("Fixed Effect", "Random Effects"),
  Estimate = c(m_cont$TE.fixed, m_cont$TE.random),
  CI_Lower = c(m_cont$lower.fixed, m_cont$lower.random),
  CI_Upper = c(m_cont$upper.fixed, m_cont$upper.random),
  p_value = c(m_cont$pval.fixed, m_cont$pval.random)
)

# Heterogeneity
het_table <- data.frame(
  Q = m_cont$Q,
  df = m_cont$df.Q,
  p_value = m_cont$pval.Q,
  I2 = m_cont$I2,
  tau2 = m_cont$tau2
)

PRISMA Flow Diagram

library(PRISMAstatement)

prisma_flow <- prisma(
  found = 1000,
  found_other = 50,
  no_dupes = 800,
  screened = 800,
  screen_exclusions = 600,
  full_text = 200,
  full_text_exclusions = 150,
  qualitative = 50,
  quantitative = 45
)

prisma_flow

Key Packages Summary

| Package | Purpose | |---------|---------| | meta | User-friendly meta-analysis with forest plots | | metafor | Comprehensive meta-analysis and meta-regression | | dmetar | Meta-analysis helpers and additional functions | | metasens | Sensitivity analysis and bias assessment | | robumeta | Robust variance estimation for dependent effects | | clubSandwich | Cluster-robust standard errors | | mada | Diagnostic test accuracy meta-analysis | | brms | Bayesian meta-analysis | | PRISMAstatement | PRISMA flow diagrams |

Best Practices

1. Pre-register protocol: Define inclusion criteria and analysis plan a priori
2. Use appropriate effect measure: Match to outcome type and clinical meaning
3. Assess heterogeneity: Report Q, I², tau² and interpret in context
4. Investigate sources: Use subgroup analysis and meta-regression
5. Evaluate bias: Use multiple methods (funnel, Egger, trim-fill)
6. Sensitivity analysis: Leave-one-out, influence diagnostics, different estimators
7. Report transparently: Follow PRISMA guidelines
8. Consider prediction intervals: More relevant for clinical application than CI

Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

• Author: choxos
• Source: choxos/BiostatAgent
• License: MIT

Install and usage instructions live in the source repository linked above.