Selective and robust external-control (srEC) integrative estimation

The srEC package is to develop a data-adaptive borrowing framework to incorporate external-controls (EC) with the trial data, which could potentially facilitate the drug development. By adopting the subject-level bias framework, the comparability of each EC subject is assessed via a penalized estimation. The final integrative estimator will only incorporate the ECs with the estimated bias being zero (i.e., a comparable subset).

Installation with devtools:

devtools::install_github("Gaochenyin/SelectiveIntegrative")

Example 1: data-adaptive borrowing for continuous outcomes

# omega: guage the unmeasured confounding for EC
omega <- 3
# RT data and EC data
data_rt <- list(X = X.rt, A = A.rt, Y = Y.rt)
data_ec <- list(X = X.ec, A = A.ec, Y = Y.ec)
str(data_rt)
#> List of 3
#>  $ X: num [1:2986, 1:3] 1 1 1 1 1 1 1 1 1 1 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : NULL
#>   .. ..$ : chr [1:3] "" "X1" "X2"
#>  $ A: int [1:2986] 1 1 1 1 1 0 1 0 1 1 ...
#>  $ Y: num [1:2986] 0.621 -3.899 0.904 -0.107 -4.758 ...
str(data_ec)
#> List of 3
#>  $ X: num [1:1014, 1:3] 1 1 1 1 1 1 1 1 1 1 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : NULL
#>   .. ..$ : chr [1:3] "" "X1" "X2"
#>  $ A: num 0
#>  $ Y: num [1:1014] 5.18 4.48 8.06 8.34 8.64 ...

Now, we have generated the RT dataset data_rt and the EC dataset data_ec. We are ready to implement our selective integrative estimation by calling srEC().

out <- srEC(data_rt = data_rt,
     data_ec = list(data_ec),
     method = 'glm')
#> Loading required package: ggplot2
#> Loading required package: lattice

# AIPW
print(paste('AIPW: ', round(out$est$AIPW, 3), 
      ', S.E.: ', round(out$sd$AIPW, 3)))
#> [1] "AIPW:  -0.229 , S.E.:  0.161"
# ACW
print(paste('ACW: ', round(out$est$ACW, 3), 
      ', S.E.: ', round(out$sd$ACW, 3)))
#> [1] "ACW:  -0.52 , S.E.:  0.157"
# selective integrative estimation
print(paste('Our: ', round(out$est$ACW.final, 3), 
      ', S.E.: ', round(out$sd$ACW.final, 3)))
#> [1] "Our:  -0.235 , S.E.:  0.158"

Example 2: data-adaptive borrowing for survival outcomes

# omega: guage the unmeasured confounding for EC
omega <- 0.5
# RT data and EC data
data_rt <- data.frame(Y = pmin(event.timeR, cens.timeR),
                      D = as.numeric(event.timeR <= cens.timeR), 
                      X.R, A = A)
data_ec <- data.frame(Y = pmin(event.timeE, cens.timeE), 
                    D = as.numeric(event.timeE <= cens.timeE),
                    X.E)
head(data_rt)
#>            Y D          X1          X2        X3 A
#> 1 0.21071985 0  0.04001744  0.31599294 0.3233869 1
#> 2 0.04700862 1 -1.12705449  0.23351994 0.3128803 0
#> 3 0.40752655 0  1.62962950 -1.16486405 0.8914390 1
#> 4 2.80010600 1 -2.06646239  0.28221082 2.3744909 1
#> 5 0.22524576 1 -1.28563288  0.83940768 0.8075524 1
#> 6 0.66835014 0  2.35225073  0.05560586 1.5876957 1
head(data_ec)
#>            Y D         X1          X2          X3
#> 1 0.34947475 1  1.6358954 -1.67439772 -1.04312329
#> 2 0.03582542 0 -1.9807189 -1.28329416  0.76766774
#> 3 0.24573391 1 -0.5391487 -0.61115066 -0.89693185
#> 4 0.07190597 1  1.1221320  0.06017221 -0.02517464
#> 5 1.01936194 0 -1.0958985  0.36200646 -0.40039740
#> 6 1.09258864 0  0.5181361  0.01479075 -1.27158364

Now, we have generated the RT dataset data_rt and the EC dataset data_ec for the survival outcomes. We are ready to implement our selective integrative estimation by calling srEC_Surv().

out_Surv <- srEC_Surv(data_rt = data_rt,
                 data_ec = data_ec, 
                 k_grid = 1:4, 
                 X.pred.R = c('X1', 'X2', 'X3'),
                 X.pred.A = c('X1', 'X2', 'X3'),
                 X.pred.c = c('X1', 'X2', 'X3'),
                 X.pred.f = c('A', 'X1', 'X2', 'X3'))

# AIPW
out_Surv$aipcw.RCT
#> $est
#>      tau        S1           S0      RMST
#> [1,]   1 0.5426229  0.339123465 0.1017497
#> [2,]   2 0.3906198  0.022647286 0.3874857
#> [3,]   3 0.1626788  0.073588191 0.6160173
#> [4,]   4 0.1615468 -0.003297191 0.7429846
# ACW
out_Surv$aipcw
#> $est
#>      tau        S1         S0       RMST
#> [1,]   1 0.5426229 0.35309687 0.09476302
#> [2,]   2 0.3906198 0.10889752 0.33038719
#> [3,]   3 0.1626788 0.05829815 0.52343867
#> [4,]   4 0.1615468 0.04490456 0.63395013
# selective integrative estimation
out_Surv$aipcw_lasso
#> $est
#>      tau        S1         S0      RMST
#> [1,]   1 0.5426229 0.30719354 0.1177147
#> [2,]   2 0.3906198 0.07999399 0.3907423
#> [3,]   3 0.1626788 0.04636410 0.6042126
#> [4,]   4 0.1615468 0.03292925 0.7266787

Referenced Papers:

1. C. Gao, S. Yang*, M. Shan, W. Ye, I. Lipkovich, D. Faries. Improving randomized controlled trial analysis with data-adaptive borrowing. Biometrika (2025).

2. C. Gao, S. Yang*, M. Shan, W. Ye, I. Lipkovich, D. Faries. Doubly protected estimation for survival outcomes utilizing external controls for randomized clinical trials. International Conference on Machine Learning (ICML) (2025).