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 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:
sr): Subjects are randomly
assigned to treatment groups without stratification.pb): Treatment
assignments are balanced within blocks defined by stratification
factors.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.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 ' ' 1The 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.
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 ' ' 1The 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().
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 ' ' 1The 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.
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.
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.
This package is supported by ASA Biopharmaceutical Section Covariate Adjustment Scientific Working Group Software Subteam.
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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.
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