Ipd Meta Analysis

Individual Participant Data Meta-Analysis in R

Overview

Individual participant data (IPD) meta-analysis methods for synthesizing patient-level data across studies. Covers one-stage and two-stage approaches, mixed-effects models, combining IPD with aggregate data, treatment-covariate interactions, and handling missing data in multi-study settings.

Two-Stage IPD Meta-Analysis

Stage 1: Study-Level Analysis

library(dplyr)
library(purrr)
library(broom)

# IPD from multiple studies
ipd_data 
  group_by(study) |>
  nest() |>
  mutate(
    model = map(data, ~lm(outcome ~ treatment + age, data = .x)),
    tidy_model = map(model, tidy, conf.int = TRUE)
  ) |>
  unnest(tidy_model) |>
  filter(term == "treatment") |>
  select(study, estimate, std.error, conf.low, conf.high)

print(study_results)

Stage 2: Meta-Analysis of Study Effects

library(metafor)

# Stage 2: Meta-analyze study-level estimates
ma_result 
  filter(term == "treatment")

Binary Outcomes

library(lme4)

# Logistic mixed-effects model
fit_logistic 
  group_by(study) |>
  nest() |>
  mutate(
    model = map(data, ~lm(outcome ~ treatment, data = .x)),
    results = map(model, ~tibble(
      yi = coef(.x)["treatment"],
      vi = vcov(.x)["treatment", "treatment"],
      source = "IPD"
    ))
  ) |>
  unnest(results) |>
  select(study, yi, vi, source)

# Studies with only aggregate data
agd_studies 
  group_by(study) |>
  mutate(
    age_mean = mean(age),              # Study-level mean
    age_centered = age - age_mean       # Individual deviation
  ) |>
  ungroup()

# Model with separated effects
fit_interaction 
  group_by(age_group) |>
  nest() |>
  mutate(
    model = map(data, ~lmer(outcome ~ treatment + (1 | study), data = .x)),
    effect = map(model, ~fixef(.x)["treatment"])
  ) |>
  unnest(effect)

Handling Missing Data

Multiple Imputation for IPD-MA

library(mice)
library(mitml)

# Multiple imputation accounting for clustering
# Use multilevel imputation methods

# Set up imputation
imp 
    mutate(outcome = if_else(.imp > 0 & is_missing, outcome + d, outcome))

  # Analyze
  fit <- lmer(outcome ~ treatment + age + (1 | study),
              data = imp_adjusted)

  tibble(
    delta = d,
    estimate = fixef(fit)["treatment"],
    se = sqrt(vcov(fit)["treatment", "treatment"])
  )
})

IPD Network Meta-Analysis

library(multinma)

# IPD-NMA with individual patient data
ipd_network <- set_ipd(
  data = ipd_nma_data,
  study = study,
  trt = treatment,
  y = outcome  # Continuous outcome
)

# For binary outcome
ipd_network_bin <- set_ipd(
  data = ipd_nma_data,
  study = study,
  trt = treatment,
  r = events  # Binary outcome
)

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

summary(nma_ipd)
relative_effects(nma_ipd)

IPD-NMA with Covariate Adjustment

library(multinma)

# Population-adjusted NMA
nma_adj <- nma(
  ipd_network,
  trt_effects = "random",
  regression = ~age + sex,  # Covariate adjustment
  class_interactions = "common"
)

# Predict effects for specific population
predict(nma_adj, newdata = data.frame(age = 65, sex = 1))

Diagnostics and Model Checking

Residual Analysis

library(lme4)
library(DHARMa)

# Fit model
fit <- lmer(outcome ~ treatment + age + (1 + treatment | study), data = ipd_data)

# Residual diagnostics
# Level 1 residuals (within-study)
resid_l1 <- residuals(fit, type = "pearson")

# Random effects
ranef_fit <- ranef(fit)$study

# DHARMa residual diagnostics
sim_res <- simulateResiduals(fit)
plot(sim_res)

# Check for heteroscedasticity
plot(fitted(fit), resid_l1)
abline(h = 0, col = "red")

Influence Diagnostics

library(influence.ME)

# Study-level influence
infl <- influence(fit, group = "study")

# Cook's distance by study
cooks.distance(infl)

# DFBETAs
dfbetas(infl)

# Plot influence
plot(infl, which = "cook")

Reporting IPD-MA Results

# Create comprehensive summary table
create_ipd_ma_summary <- function(fit_one_stage, fit_two_stage) {

  summary_table <- tibble(
    Method = c("One-stage (mixed effects)", "Two-stage (meta-analysis)"),
    Estimate = c(
      fixef(fit_one_stage)["treatment"],
      fit_two_stage$beta
    ),
    SE = c(
      sqrt(vcov(fit_one_stage)["treatment", "treatment"]),
      fit_two_stage$se
    ),
    CI_Lower = Estimate - 1.96 * SE,
    CI_Upper = Estimate + 1.96 * SE,
    Heterogeneity = c(
      VarCorr(fit_one_stage)$study["treatment", "treatment"],
      fit_two_stage$tau2
    )
  )

  return(summary_table)
}

Key Packages Summary

| Package | Purpose | |---------|---------| | lme4 | Linear/generalized mixed-effects models | | metafor | Two-stage meta-analysis | | coxme | Mixed-effects Cox models | | survival | Stratified/frailty survival models | | mice | Multiple imputation | | mitml | MI pooling for multilevel | | multinma | IPD network meta-analysis | | ipdmeta | IPD-MA utilities | | joineR | Joint models for IPD | | DHARMa | Residual diagnostics |

Best Practices

1. Data sharing: Establish data governance before IPD collection
2. Harmonization: Standardize variable definitions across studies
3. One vs two-stage: One-stage preferred for treatment-covariate interactions
4. Random effects: Include random treatment effects to allow for heterogeneity
5. Missing data: Use multilevel MI methods; conduct sensitivity analyses
6. Confounding: Separate within vs between-study covariate effects
7. Reporting: Follow PRISMA-IPD guidelines
8. Sensitivity: Compare one-stage and two-stage results

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.