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RobinCar2: ROBust INference for Covariate Adjustment in Randomized Clinical Trials

Dong Xi1, Marlena Bannick2, Gregory Chen3, Liming Li4,
Daniel Sabanés Bové5, Ting Ye2, Yanyao Yi6

1Gilead Sciences, 2University of Washington, 3MSD, 4AstraZeneca,
5RCONIS, 6Eli Lilly and Company

April 30, 2026

Source: vignettes/articles/biometric_bulletin.Rmd
biometric_bulletin.Rmd

Introduction

Covariate adjustment is a powerful statistical technique that can increase efficiency in randomized clinical trials (RCTs) by reducing variability in treatment effect estimates. The U.S. Food and Drug Administration (FDA) finalized the guideline on covariate adjustment, providing recommendations and best practices for using these methods in drug development (FDA, 2023). However, a gap has existed between the extensive statistical literature on covariate adjustment and software that is easy to use and follows these best practices.

The RobinCar2 R package, which stands for ROBust INference for Covariate Adjustment in Randomized clinical trials, addresses this gap. It is a streamlined version of the original RobinCar package (Bannick et al., 2026a), designed with minimal dependencies and extensive validation for use in drug development, particularly for Good Practice (GxP) purposes. The package is supported by the ASA Biopharmaceutical Section Covariate Adjustment Scientific Working Group Software Subteam.

This paper provides an introduction to RobinCar2, covering its core functionality for three common outcome types in clinical trials: continuous, binary, and time-to-event outcomes. It also provides best practices of using RobinCar and RobinCar2 packages for covariate adjustment.

Covariate Adjustment in RCTs

Covariate adjustment leverages baseline variables to improve the precision of treatment effect estimates. Unlike traditional regression interpretations, covariate-adjusted estimators in RCTs target the same unconditional (marginal) treatment effect as unadjusted analyses, but with potentially smaller variance. This is because randomization ensures treatment assignment is independent of baseline covariates, allowing model-assisted approaches that are robust to model misspecification.

RobinCar2 supports three covariate-adaptive randomization schemes:

  • Simple randomization (sr): Subjects are randomly assigned to treatment groups without stratification.
  • Permuted-block randomization (pb): Treatment assignments are balanced within blocks defined by stratification factors.
  • Pocock-Simon minimization (ps): An adaptive method that minimizes imbalance across multiple stratification factors.

The package provides two variance estimation approaches:

  • vcovG: The default heteroskedasticity-consistent variance estimator that accounts for covariate-adaptive randomization.
  • vcovHC: The Huber-White sandwich estimator, which is appropriate for linear covariate adjustment and only when treatment-by-covariate interactions are not included in the model.

Analysis of Continuous Outcomes

For continuous outcomes, RobinCar2 provides the robin_lm() function, which fits a linear model and returns covariate-adjusted treatment effect estimates with robust inference. The following code fits an ANHECOVA (Analysis of Heterogeneous Covariance) model (Ye et al., 2023a), which includes the treatment assignment (treatment), the stratification factor (s1), the treatment-by-stratification interaction (treatment * s1), and a continuous covariate (covar). The randomization scheme is permuted-block randomization stratified by s1, specified as treatment ~ pb(s1). The variance estimation method is vcovG.

library(RobinCar2)

result_lm <- robin_lm(
  y ~ treatment * s1 + covar,
  data = glm_data,
  treatment = treatment ~ pb(s1),
  vcov = "vcovG"
)

print(result_lm)
## Model        :  y ~ treatment * s1 + covar 
## Randomization:  treatment ~ pb(s1)  ( Permuted-Block )
## Variance Type:  vcovG 
## Marginal Mean: 
##      Estimate  Std.Err    2.5 % 97.5 %
## pbo  0.200321 0.067690 0.067651 0.3330
## trt1 0.763971 0.075929 0.615152 0.9128
## trt2 0.971250 0.076543 0.821228 1.1213
## 
## Contrast     :  h_diff
##                Estimate Std.Err Z Value  Pr(>|z|)    
## trt1 v.s. pbo   0.56365 0.10074  5.5952 2.203e-08 ***
## trt2 v.s. pbo   0.77093 0.10133  7.6082 2.779e-14 ***
## trt2 v.s. trt1  0.20728 0.10683  1.9402   0.05235 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The output has three main parts. The first part reiterates the input parameters and the model specification. The second part provides results on Marginal Mean, which includes estimated response means for each treatment group with standard errors and confidence intervals. The last part provides the Contrast results, including pairwise treatment comparisons (the difference in means) with test statistics and p-values. The Huber-White variance estimator can be applied when the linear model does not include treatment-by-stratification/covariate interactions, by specifying vcov = "vcovHC" (Rosenblum and van der Laan, 2009; Lin, 2013). The confidence interval of treatment effect contrasts can be obtained via the confint() function.

Analysis of Binary and Count Outcomes

For binary and count outcomes, RobinCar2 provides robin_glm(), which extends the framework to generalized linear models (Ye et al., 2023b, Bannick et al. 2025). The following code fits a logistic model (family = binomial(link = "logit")), which includes the treatment assignment (treatment), the stratification factor (s1), the treatment-by-stratification interaction (treatment * s1), and a continuous covariate (covar). The randomization scheme is permuted-block randomization stratified by s1, specified as treatment ~ pb(s1). Currently, vcovG is the only supported method for variance estimation in generalized linear models.

result_binary <- robin_glm(
  y_b ~ treatment * s1 + covar,
  data = glm_data,
  treatment = treatment ~ pb(s1),
  family = binomial(link = "logit"),
  contrast = "difference"
)

print(result_binary)
## Model        :  y_b ~ treatment * s1 + covar 
## Randomization:  treatment ~ pb(s1)  ( Permuted-Block )
## Variance Type:  vcovG 
## Marginal Mean: 
##      Estimate  Std.Err    2.5 % 97.5 %
## pbo  0.356097 0.033599 0.290243 0.4219
## trt1 0.580696 0.034418 0.513238 0.6482
## trt2 0.621386 0.034019 0.554711 0.6881
## 
## Contrast     :  difference
##                Estimate  Std.Err Z Value  Pr(>|z|)    
## trt1 v.s. pbo  0.224599 0.047711  4.7075 2.508e-06 ***
## trt2 v.s. pbo  0.265290 0.047534  5.5810 2.391e-08 ***
## trt2 v.s. trt1 0.040691 0.047941  0.8488     0.396    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The output of robin_glm() has a similar structure to robin_lm(). The default contrast for binary outcomes is the difference in probabilities (contrast = "difference"). RobinCar2 supports other contrast functions, including risk ratio, odds ratio, and their log transformations ("log_risk_ratio", "log_odds_ratio"). The confidence interval of treatment effect contrasts can be obtained via the confint() function. Any family argument handled by glm() can be used with robin_glm().

Analysis of Time-to-Event Outcomes

For survival outcomes, RobinCar2 provides robin_surv(), which implements stratified and covariate-adjusted log-rank tests and hazard ratio estimation (Ye et al., 2024). The following code fits a stratified log-rank test and estimates hazard ratios, stratified by the factor strata. The treatment variable (sex) is specified via the treatment formula. The randomization scheme is permuted-block randomization stratified by strata, specified as sex ~ pb(strata).

result_tte <- robin_surv(
  Surv(time, status) ~ 1 + strata(strata),
  data = surv_data,
  treatment = sex ~ pb(strata)
)

print(result_tte)
## Model        : Surv(time, status) ~ 1 + strata(strata)
## Randomization: sex ~ pb(strata) (Permuted-Block)
## Stratification variables:  strata 
## 
## Contrast     : Stratified Log Hazard Ratio
## 
##                  Estimate Std.Err Z Value Pr(>|z|)   
## Male v.s. Female  0.55482 0.17063  3.2516 0.001147 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Test         : Stratified Log-Rank
## 
##                  Test Stat. Pr(>|z|)   
## Male v.s. Female     3.2856 0.001018 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The output of robin_surv() has a similar structure to robin_lm() and robin_glm(). The Contrast section provides unconditional (marginal) hazard ratios for all pairwise treatment comparisons. The Test section provides the log-rank test results. The confidence interval of hazard ratios can be obtained via the confint() function.

Best Practices of using RobinCar and RobinCar2

RobinCar2 is a streamlined version of the original RobinCar package with the following characteristics (Bannick et al., 2026b):

Feature RobinCar RobinCar2
Dependencies More extensive Minimal
Validation Standard GxP-ready
Methods Comprehensive Curated subset
Support Research community ASA BIOP Covariate Adjustment Working Group

Methods included in RobinCar2 have undergone additional validation and are recommended for interactions with regulatory agencies. Previous users of RobinCar should therefore consider transitioning to RobinCar2 when possible.

Conclusions

RobinCar2 provides a validated, user-friendly implementation of covariate adjustment methods for randomized clinical trials. Its simple interface, based on familiar R formula syntax, makes it accessible to clinical trial statisticians while ensuring robust inference aligned with the FDA guideline. The package covers the most common outcome types encountered in clinical trials: continuous, binary, and time-to-event outcomes. Future development of RobinCar2 may include additional variance estimation methods, the Mantel-Haenszel risk difference estimator (currently available in RobinCar), and bootstrap methods.

For more information, including additional vignettes and documentation, visit the package GitHub repository at github.com/openpharma/RobinCar2.

Acknowledgements

This package is supported by ASA Biopharmaceutical Section Covariate Adjustment Scientific Working Group Software Subteam.

References

Bannick M, Shao J, Liu J, Du Y, Yi Y, Ye T (2025). A General Form of Covariate Adjustment in Randomized Clinical Trials. Biometrika, 112(3) asaf029.

Bannick M, Qian Y, Ye T, Yi Y, Bian F (2026a). RobinCar: Robust Inference for Covariate Adjustment in Randomized Clinical Trials. R package version 1.1.0, https://CRAN.R-project.org/package=RobinCar.

Bannick M, Bian Y, Chen G, Li L, Qian Y, Sabanés Bové D, Xi D, Ye T, Yi Y (2026b). The RobinCar Family: R Tools for Robust Covariate Adjustment in Randomized Clinical Trials. arXiv preprint, arXiv:2601.14498.

Food and Drug Administration (2023). Adjusting for Covariates in Randomized Clinical Trials for Drugs and Biological Products: Final Guidance for Industry, https://www.fda.gov/media/148910/download.

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Ye T, Shao J, Yi Y (2024). Covariate-Adjusted Log-Rank Test: Guaranteed Efficiency Gain and Universal Applicability. Biometrika, 111(2):691-705.