FedGEE

FedGEE (Federated Generalized Estimating Equations) provides a robust framework for fitting generalized estimating equations across distributed datasets (e.g., multi-center health networks) without pooling patient-level data. It includes small-sample variance corrections (Kauermann-Carroll and Mancl-DeRouen) which are applied directly in the score space to preserve privacy and statistical validity when the number of contributing sites is small.

Installation

You can install the development version of FedGEE from source using the devtools package:

# install from source available on GitHub:
# devtools::install_github("soumikp/2026_fedGee")

Features

• Privacy-Preserving: Only summary-level matrices (e.g., Bread and Score matrices) are aggregated at the server.
• Small-Sample Corrections: Includes KC (Kauermann-Carroll) and MD (Mancl-DeRouen) corrections.
• Cluster/Patient-Level Adjustments: Allows sandwich variance estimation at the site-level or patient-level.

Toy Example

Here is a small example using a known built-in R dataset (ChickWeight), simulating a scenario where longitudinal patient records are distributed across multiple "sites".

library(FedGEE)

# 1. Prepare data using the built-in 'ChickWeight' dataset
# We'll split the data into 3 arbitrary "sites" based on the Chick ID modulo 3
data(ChickWeight)
df <- ChickWeight

# Create a mock 'site' variable
df$site <- paste0("Site_", as.numeric(df$Chick) %% 3 + 1)

# Split the dataframe into a list of dataframes by site
data_list <- split(df, df$site)

# 2. Fit the Federated GEE Model
# We model weight ~ Time + Diet across our dummy sites
fed_model <- fedgee(
  data_list      = data_list,
  main_formula   = weight ~ Time + Diet,
  family_obj     = gaussian(link = "identity"),
  corstr         = "exchangeable",     # Working correlation structure
  id_col         = "Chick",            # Column indicating clusters
  sandwich_level = "site",             # Level for sandwich variance
  correction     = "KC",               # Kauermann-Carroll small-sample correction
  verbose        = FALSE
)

# 3. Fit the Pooled GEE Model for Comparison
# This requires the geepack package and the pooled dataset
library(geepack)
pooled_model <- geeglm(
  weight ~ Time + Diet, 
  data = df[order(df$Chick), ], 
  id = Chick, 
  family = gaussian(link = "identity"), 
  corstr = "exchangeable"
)

# 4. Compare via Forest Plot
library(dplyr)
library(ggplot2)

fed_df <- data.frame(
  term = names(fed_model$coefficients),
  estimate = fed_model$coefficients,
  std.error = fed_model$se,
  model = "FedGEE"
)

pooled_sum <- summary(pooled_model)$coefficients
pooled_df <- data.frame(
  term = rownames(pooled_sum),
  estimate = pooled_sum$Estimate,
  std.error = pooled_sum$Std.err,
  model = "Pooled GEE"
)

plot_data <- bind_rows(fed_df, pooled_df) |>
  mutate(
    conf.low = estimate - 1.96 * std.error,
    conf.high = estimate + 1.96 * std.error
  )

ggplot(plot_data, aes(x = estimate, y = term, color = model)) +
  geom_point(position = position_dodge(width = 0.5), size = 2) +
  geom_errorbar(aes(xmin = conf.low, xmax = conf.high), 
                position = position_dodge(width = 0.5), width = 0.2) +
  geom_vline(xintercept = 0, linetype = "dashed", color = "gray50") +
  theme_minimal() +
  labs(
    title = "Comparison of FedGEE vs Pooled GEE",
    x = "Estimate (95% CI)",
    y = "Coefficient",
    color = "Model"
  )