RobinCar2 provides robust covariate adjustment methods for estimating and inferring treatment effects through generalized linear models (glm) under different randomization schema.

Common Usage

A minimal call of robin_lm() and robin_glm(), consisting of only formula, data arguments and the randomization scheme, will produce an object of class treatment_effect.

library(RobinCar2)
head(dummy_data)
#>   id treatment s1 s2      covar           y y_b
#> 1  1       pbo  b  c  0.5119022 -0.02761963   0
#> 2  2       pbo  a  c -0.7941720  0.49919508   0
#> 3  3      trt1  b  d  0.8988804  0.48037375   0
#> 4  4      trt2  b  c -0.4821317  0.67490126   1
#> 5  5      trt1  a  d -0.2285514  0.55499267   0
#> 6  6      trt2  a  c  0.2742069  2.39830584   1

Data Introduction

In the dummy_data, we have the following columns:

id is the patient identifier.
treatment is the treatment assignment.
s1 is the first stratification factor.
s2 is the second stratification factor.
covar is the continuous covariate.
y is the continuous outcome.
y_b is the binary outcome.

Obtain Treatment Effect for Continuous Outcomes Using the General Variance

For the continuous outcome y, the linear model includes covar as a covariate, s1 as a stratification factor. The randomization scheme is a permuted-block randomization stratified by s1. The model formula also includes the treatment by stratification interaction as y ~ treatment * s1 + covar.

robin_lm(y ~ treatment * s1 + covar,
  data = dummy_data,
  treatment = treatment ~ pb(s1)
)
#> 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

We can also use the Huber-White variance estimator by setting vcov = "vcovHC". Please note that in this case, the model formula should not contain the treatment by stratification (covariate) interaction.

robin_lm(y ~ treatment + s1 + covar,
  data = dummy_data,
  treatment = treatment ~ pb(s1),
  vcov = "vcovHC"
)
#> Model        :  y ~ treatment + s1 + covar 
#> Randomization:  treatment ~ pb(s1)  ( Permuted-Block )
#> Variance Type:  vcovG 
#> Marginal Mean: 
#>      Estimate  Std.Err    2.5 % 97.5 %
#> pbo  0.200449 0.067690 0.067779 0.3331
#> trt1 0.763978 0.075930 0.615158 0.9128
#> trt2 0.971285 0.076539 0.821271 1.1213
#> 
#> Contrast     :  h_diff
#>                Estimate Std.Err Z Value  Pr(>|z|)    
#> trt1 v.s. pbo   0.56353 0.10074  5.5941 2.218e-08 ***
#> trt2 v.s. pbo   0.77084 0.10133  7.6074 2.796e-14 ***
#> trt2 v.s. trt1  0.20731 0.10683  1.9405   0.05232 .  
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Note that robin_glm can also handle continuous outcomes using the default family and the default link function family = gaussian().

Obtain Treatment Effect for Binary Outcomes

For binary outcomes, the logistic model includes covar as a covariate, s1 as a stratification factor. The randomization scheme is a permuted-block randomization stratified by s1. The model formula also includes the treatment by stratification interaction as y_b ~ treatment * s1 + covar. Note here we need to specify family to be binomial(link = "logit").

robin_glm(y_b ~ treatment * s1 + covar,
  data = dummy_data,
  treatment = treatment ~ pb(s1),
  family = binomial(link = "logit")
)
#> 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     :  h_diff
#>                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

Obtain Treatment Effect for Counts

For counts, the log link model includes covar as a covariate, s1 as a stratification factor. The randomization scheme is a permuted-block randomization stratified by s1. The model formula also includes the treatment by stratification interaction as y_count ~ treatment * s1 + covar. Note here we need to specify family to be poisson(link = "log") to use the Poisson model or to be MASS::negative.binomial(theta = NA) to use the negative binomial model. A fixed theta could be provided if it is known.

dummy_data$y_count <- rpois(nrow(dummy_data), lambda = 20)
robin_glm(
  y_count ~ treatment * s1 + covar,
  data = dummy_data,
  treatment = treatment ~ pb(s1),
  family = MASS::negative.binomial(theta = 1)
)
#> Model        :  y_count ~ treatment * s1 + covar 
#> Randomization:  treatment ~ pb(s1)  ( Permuted-Block )
#> Variance Type:  vcovG 
#> Marginal Mean: 
#>      Estimate  Std.Err    2.5 % 97.5 %
#> pbo  20.05954  0.30825 19.45538 20.664
#> trt1 19.60018  0.32111 18.97081 20.230
#> trt2 20.02415  0.29517 19.44564 20.603
#> 
#> Contrast     :  h_diff
#>                 Estimate   Std.Err Z Value Pr(>|z|)
#> trt1 v.s. pbo  -0.459361  0.445037 -1.0322   0.3020
#> trt2 v.s. pbo  -0.035388  0.426614 -0.0829   0.9339
#> trt2 v.s. trt1  0.423974  0.435775  0.9729   0.3306

Using Different Covariate-Adaptive Randomization Schema

If the randomization schema is not permuted-block randomization, we can use other randomization schema. Currently RobinCar2 supports sp for the simple randomization, pb for the permuted-block randomization, and ps for the Pocock-Simon randomization.

robin_glm(y_b ~ treatment * s1 + covar,
  data = dummy_data,
  treatment = treatment ~ ps(s1),
  family = binomial(link = "logit")
)
#> Model        :  y_b ~ treatment * s1 + covar 
#> Randomization:  treatment ~ ps(s1)  ( Pocock-Simon )
#> 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     :  h_diff
#>                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