Risk Difference Estimation with Multiple Link Functions and Inverse Probability of Treatment Weigh….

riskdiff

The riskdiff package provides robust methods for calculating risk differences (also known as prevalence differences in cross-sectional studies) using generalized linear models with automatic link function selection and boundary detection.

✨ Now Available on CRAN!

riskdiff v0.2.1 is now published on CRAN with cutting-edge boundary detection capabilities that identify when maximum likelihood estimates lie at the edge of the parameter space - a common issue with identity link models that other packages ignore.

Features

• 🎯 Smart boundary detection: Automatically detects when GLMs hit parameter constraints
• 🔧 Robust model fitting: Tries identity, log, and logit links with graceful fallback\
• 📊 Stratified analysis: Support for multi-level stratification
• 📋 Publication-ready output: Formatted tables and confidence intervals
• 🛡️ Missing data handling: Graceful handling of incomplete cases
• ⚙️ Flexible confidence intervals: Robust methods for boundary cases
• 📈 Multiple link functions: Automatic selection with boundary-aware switching
• 🔍 Transparent diagnostics: Clear reporting of model methods and boundary issues

Author

John D. Murphy, MPH, PhD ORCID: 0000-0002-7714-9976

Installation

CRAN (Stable Release)

Install the latest stable version from CRAN:

install.packages("riskdiff")

Development Version

You can install the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("jackmurphy2351/riskdiff")

Quick Start

library(riskdiff)

# Load example data
data(cachar_sample)

# Simple risk difference with boundary detection
result <- calc_risk_diff(
  data = cachar_sample,
  outcome = "abnormal_screen",
  exposure = "smoking"
)
#> Waiting for profiling to be done...

print(result)
#> Risk Difference Analysis Results (v0.2.1) 
#> ========================================= 
#> 
#> Confidence level: 95% 
#> Number of comparisons: 1 
#> 
#>  Exposure Risk Difference          95% CI P-value    Model    N Boundary
#>   smoking          10.68% (5.95%, 15.75%)  <0.001 identity 2500         
#>  Quality
#>     Good

🎯 Boundary Detection in Action

# Create data that challenges standard GLM methods
set.seed(123)
challenging_data <- data.frame(
  outcome = c(rep(0, 40), rep(1, 60)),  # High baseline risk
  exposure = factor(c(rep("No", 50), rep("Yes", 50))),
  age = rnorm(100, 45, 10)
)

# riskdiff handles this gracefully with boundary detection
result <- calc_risk_diff(
  data = challenging_data,
  outcome = "outcome", 
  exposure = "exposure",
  adjust_vars = "age",
  verbose = TRUE  # Shows diagnostic information
)
#> Warning in doTryCatch(return(expr), name, parentenv, handler): Possible
#> separation detected. Risk difference estimates may be unstable.
#> Formula: outcome ~ exposure + age
#> Sample size: 100
#> Trying identity link...
#> Using starting values: 0.2, 0.8, 0.004
#> Identity link error: cannot find valid starting values: please specify some
#> Trying log link...
#> log link error: no valid set of coefficients has been found: please supply starting values
#> Trying logit link...
#> Boundary detection results:
#>   Boundary detected: TRUE
#>   Boundary type: upper_boundary_near
#>   Probability range: [0.17876, 1]
#> Note: Model converged but MLE is on parameter space boundary.
#> Boundary type: upper_boundary_near
#> ✓logit link converged
#> ⚠ Perfect or quasi-perfect separation detected. Results may be unreliable.
#> ⚠ Boundary case detected: upper_boundary_near
#> Using robust CI method: bootstrap

print(result)
#> Risk Difference Analysis Results (v0.2.1) 
#> ========================================= 
#> 
#> Confidence level: 95% 
#> Number of comparisons: 1 
#> Boundary cases detected: 1 of 1 
#> Boundary CI method: auto 
#> 
#>  Exposure Risk Difference         95% CI P-value Model   N
#>  exposure          80.06% (0.00%, 0.00%)       — logit 100
#>               Boundary  Quality
#>  ⚠ upper_boundary_near Boundary
#> 
#> ⚠  Boundary Case Details:
#> ========================= 
#> Row 1 ( exposure ): Type: upper_boundary_near | CI method: bootstrap 
#> 
#> Boundary Type Guide:
#> • upper_bound: Fitted probabilities near 1 (risk saturation)
#> • lower_bound: Fitted probabilities near 0 (very rare outcomes)
#> • separation: Complete/quasi-separation detected
#> • both_bounds: Mixed boundary issues across observations
#> ⚠  indicates robust confidence intervals were used
#> 
#> Statistical Note:
#> ================
#> Standard asymptotic theory may not apply for boundary cases.
#> Confidence intervals use robust methods when boundary detected.
#> For failed analyses, consider alternative estimation approaches.

# Check if boundary cases were detected
if (any(result$on_boundary)) {
  cat("\n🚨 Boundary case detected! Using robust inference methods.\n")
  cat("Boundary type:", unique(result$boundary_type[result$on_boundary]), "\n")
  cat("CI method:", unique(result$ci_method[result$on_boundary]), "\n")
}
#> 
#> 🚨 Boundary case detected! Using robust inference methods.
#> Boundary type: upper_boundary_near 
#> CI method: bootstrap

Key Functions

Basic Usage with Enhanced Diagnostics

# Age-adjusted risk difference with boundary detection
rd_adjusted <- calc_risk_diff(
  data = cachar_sample,
  outcome = "abnormal_screen", 
  exposure = "smoking",
  adjust_vars = "age",
  boundary_method = "auto"  # Automatic robust method selection
)

print(rd_adjusted)
#> Risk Difference Analysis Results (v0.2.1) 
#> ========================================= 
#> 
#> Confidence level: 95% 
#> Number of comparisons: 1 
#> 
#>  Exposure Risk Difference         95% CI P-value Model    N Boundary Quality
#>   smoking          10.94% (0.00%, 0.00%)       — logit 2500             Good

Stratified Analysis with Boundary Awareness

# Stratified by residence with boundary detection
rd_stratified <- calc_risk_diff(
  data = cachar_sample,
  outcome = "abnormal_screen",
  exposure = "smoking",
  adjust_vars = "age",
  strata = "residence"
)
#> Waiting for profiling to be done...

print(rd_stratified)
#> Risk Difference Analysis Results (v0.2.1) 
#> ========================================= 
#> 
#> Confidence level: 95% 
#> Number of comparisons: 3 
#> 
#>  Exposure Risk Difference           95% CI P-value    Model    N Boundary
#>   smoking          11.63%   (0.00%, 0.00%)       —    logit 2158         
#>   smoking           9.99% (-5.89%, 25.87%)   0.218 identity  251         
#>   smoking          -3.86%   (0.00%, 0.00%)       —      log   91         
#>  Quality
#>     Good
#>  Wide CI
#>     Good

# Summary of boundary cases across strata
boundary_summary <- rd_stratified[rd_stratified$on_boundary, 
                                  c("residence", "boundary_type", "ci_method")]
if (nrow(boundary_summary) > 0) {
  cat("\nBoundary cases by stratum:\n")
  print(boundary_summary)
}

Table Creation with Boundary Indicators

# Create a simple text table with boundary information
cat(create_simple_table(rd_stratified, "Risk by Smoking Status and Residence"))
#> Risk by Smoking Status and Residence
#> ====================================================================================
#> Exposure             Risk Diff       95% CI                    P-value    Model     
#> ====================================================================================
#> smoking              11.63%          (0.00%, 0.00%)            NA         logit     
#> smoking              9.99%           (-5.89%, 25.87%)          0.218      identity  
#> smoking              -3.86%          (0.00%, 0.00%)            NA         log       
#> ====================================================================================

# Create publication-ready table (requires kableExtra)
library(kableExtra)
create_rd_table(rd_stratified, 
                caption = "Risk of Abnormal Screening Result by Smoking Status",
                include_model_type = TRUE)

🧠 Statistical Methodology

GLM Approach with Boundary Detection

The package uses generalized linear models with different link functions:

1. Identity link (preferred): Directly estimates risk differences
2. Log link: Estimates relative risks, transforms to risk differences\
3. Logit link: Estimates odds ratios, transforms to risk differences

Key Innovation: When models hit parameter space boundaries (common with identity links), the package: - 🔍 Detects boundary cases automatically - ⚠️ Warns users about potential inference issues\

• 🛡️ Uses robust confidence intervals when appropriate - 📊 Reports methodology transparently

Boundary Detection Types

• Upper bound: Fitted probabilities near 1 (risk saturation)
• Lower bound: Fitted probabilities near 0 (risk floor)
• Separation: Complete/quasi-separation in logistic models
• Both bounds: Multiple boundary issues detected

Advanced Features

Boundary Method Control

# Force specific boundary handling
rd_conservative <- calc_risk_diff(
  cachar_sample,
  "abnormal_screen", 
  "smoking",
  boundary_method = "auto"  # Options: "auto", "profile", "wald"
)
#> Waiting for profiling to be done...

# Check which methods were used
table(rd_conservative$ci_method)
#> 
#> profile 
#>       1

Link Function Selection with Boundary Awareness

# Force a specific link function
rd_logit <- calc_risk_diff(
  cachar_sample, 
  "abnormal_screen", 
  "smoking",
  link = "logit"
)

# Check which model was used and if boundaries detected
cat("Model used:", rd_logit$model_type, "\n")
#> Model used: logit
cat("Boundary detected:", rd_logit$on_boundary, "\n")
#> Boundary detected: FALSE

Confidence Intervals with Robust Methods

# 90% confidence intervals with boundary detection
rd_90 <- calc_risk_diff(
  cachar_sample,
  "abnormal_screen", 
  "smoking",
  alpha = 0.10  # 1 - 0.10 = 90% CI
)
#> Waiting for profiling to be done...

print(rd_90)
#> Risk Difference Analysis Results (v0.2.1) 
#> ========================================= 
#> 
#> Confidence level: 90% 
#> Number of comparisons: 1 
#> 
#>  Exposure Risk Difference          95% CI P-value    Model    N Boundary
#>   smoking          10.68% (6.68%, 14.91%)  <0.001 identity 2500         
#>  Quality
#>     Good

# The package automatically uses appropriate CI methods for boundary cases

📊 Understanding Results

Enhanced Result Structure

# Examine the enhanced result structure
data(cachar_sample)
result <- calc_risk_diff(cachar_sample, "abnormal_screen", "smoking")
#> Waiting for profiling to be done...
names(result)
#>  [1] "exposure_var"     "rd"               "ci_lower"         "ci_upper"        
#>  [5] "p_value"          "model_type"       "on_boundary"      "boundary_type"   
#>  [9] "boundary_warning" "ci_method"        "n_obs"

# Key columns:
# - on_boundary: Was a boundary case detected?
# - boundary_type: What type of boundary?
# - boundary_warning: Detailed diagnostic message
# - ci_method: Which CI method was used?

Example Dataset

The package includes a realistic simulated cancer screening dataset:

data(cachar_sample)
str(cachar_sample)
#> 'data.frame':    2500 obs. of  12 variables:
#>  $ id                : int  1 2 3 4 5 6 7 8 9 10 ...
#>  $ age               : int  53 25 18 28 51 25 56 20 58 18 ...
#>  $ sex               : Factor w/ 2 levels "male","female": 2 1 2 2 1 2 1 1 1 1 ...
#>  $ residence         : Factor w/ 3 levels "rural","urban",..: 3 1 1 1 1 1 1 1 1 1 ...
#>  $ smoking           : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 2 1 1 1 ...
#>  $ tobacco_chewing   : Factor w/ 2 levels "No","Yes": 2 1 1 2 2 1 2 1 2 2 ...
#>  $ areca_nut         : Factor w/ 2 levels "No","Yes": 2 2 2 2 1 1 2 1 2 2 ...
#>  $ alcohol           : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 2 1 2 ...
#>  $ abnormal_screen   : int  0 0 0 0 0 0 1 0 1 0 ...
#>  $ head_neck_abnormal: int  0 0 0 0 0 0 0 0 0 0 ...
#>  $ age_group         : Factor w/ 3 levels "Under 40","40-60",..: 2 1 1 1 2 1 2 1 2 1 ...
#>  $ tobacco_areca_both: Factor w/ 2 levels "No","Yes": 2 1 1 2 1 1 2 1 2 2 ...

# Summary statistics showing realistic associations
table(cachar_sample$smoking, cachar_sample$abnormal_screen)
#>      
#>          0    1
#>   No  1851  317
#>   Yes  248   84

# Risk difference analysis
rd_analysis <- calc_risk_diff(cachar_sample, "abnormal_screen", "smoking")
#> Waiting for profiling to be done...
cat("Smoking increases risk of abnormal screening result by", 
    sprintf("%.1f", rd_analysis$rd * 100), "percentage points\n")
#> Smoking increases risk of abnormal screening result by 10.7 percentage points

When to Use Risk Differences

Risk differences are particularly valuable when:

• Policy decisions: You need the absolute impact size
• Clinical practice: Communicating real-world effect sizes
• Common outcomes: When outcome prevalence > 10%
• Causal inference: For intervention planning
• Public health: When relative measures can mislead

Comparison with Other Measures

🔬 Statistical Foundation

This package implements methods based on:

• Donoghoe & Marschner (2018) - Robust GLM fitting methods for log-binomial models
• Marschner & Gillett (2012) - Boundary detection for log-binomial models
• Rothman, Greenland & Lash (2008) - Modern epidemiological methods
• Austin (2011) - Propensity score methods for causal inference
• Hernán & Robins (2020) - Causal inference methodology

Getting Help

• 📖 Vignettes: browseVignettes("riskdiff")
• 🐛 Bug reports: GitHub Issues
• 💡 Feature requests: GitHub Issues
• 📧 Questions: Use GitHub Discussions
• 📋 CRAN page: https://CRAN.R-project.org/package=riskdiff

Citation

If you use this package in your research, please cite:

citation("riskdiff")

Related Packages

• epitools: Basic epidemiological calculations (no boundary detection)
• epi: Extended epidemiological functions (no boundary detection)
• fmsb: Medical statistics and epidemiology (no boundary detection)
• Epi: Statistical analysis in epidemiology (no boundary detection)

riskdiff uniquely provides boundary detection for robust inference!

Code of Conduct

Please note that the riskdiff project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.