OLE Analysis Workflow

OLE phase

This vignette demonstrates the open-label extension (OLE) phase analysis workflow using the difference-in-differences (DID) and synthetic control method (SCM) estimators proposed in Zhou et al. (2024) for estimating long-term treatment effects when the control group switches to treatment.

1 DID methods

1.1 DID-EC-IPW

method <- did_ec_ipw(
  ps_formula = "S ~ x1 + x2 + x3 + x4 + x5",
  trt_formula = "A ~ x1 + x2 + x3 + x4 + x5",
  bootstrap = 50
)

analysis <- setup_analysis_OLE(
  data = SyntheticData,
  trial_status_col_name = "S",
  treatment_col_name = "A",
  outcome_col_name = c("y1", "y2", "y3", "y4"),
  covariates_col_name = c("x1", "x2", "x3", "x4", "x5"),
  T_cross = 2,
  method_OLE_obj = method
)

run_analysis(analysis)

##      point_estimates lower_CI_boot upper_CI_boot
## tau3        2.075926     0.1198765      4.230701
## tau4        4.389438     0.8192601      7.040613

1.2 DID-EC-AIPW

model_forms <- c(
  "y1 ~ x1 + x2 + x3 + x4 + x5",
  "y2 ~ x1 + x2 + x3 + x4 + x5",
  "y3 ~ x1 + x2 + x3 + x4 + x5",
  "y4 ~ x1 + x2 + x3 + x4 + x5"
)

method <- did_ec_aipw(
  ps_formula = "S ~ x1 + x2 + x3 + x4 + x5",
  trt_formula = "A ~ x1 + x2 + x3 + x4 + x5",
  outcome_formula = model_forms,
  bootstrap = 50
)

analysis <- setup_analysis_OLE(
  data = SyntheticData,
  trial_status_col_name = "S",
  treatment_col_name = "A",
  outcome_col_name = c("y1", "y2", "y3", "y4"),
  covariates_col_name = c("x1", "x2", "x3", "x4", "x5"),
  T_cross = 2,
  method_OLE_obj = method
)

run_analysis(analysis)

##      point_estimates lower_CI_boot upper_CI_boot
## tau3        2.041727    -1.3020727      4.372254
## tau4        4.036118     0.6559398      7.388494

1.3 DID-EC-OR

model_forms <- c(
  "y1 ~ x1 + x2 + x3 + x4 + x5",
  "y2 ~ x1 + x2 + x3 + x4 + x5",
  "y3 ~ x1 + x2 + x3 + x4 + x5",
  "y4 ~ x1 + x2 + x3 + x4 + x5"
)

method <- did_ec_or(
  outcome_formula_ext = model_forms,
  outcome_formula_rct_ctrl = model_forms,
  outcome_formula_rct_trt = model_forms,
  bootstrap = 50
)

analysis <- setup_analysis_OLE(
  data = SyntheticData,
  trial_status_col_name = "S",
  treatment_col_name = "A",
  outcome_col_name = c("y1", "y2", "y3", "y4"),
  covariates_col_name = c("x1", "x2", "x3", "x4", "x5"),
  T_cross = 2,
  method_OLE_obj = method
)

run_analysis(analysis)

##      point_estimates lower_CI_boot upper_CI_boot
## tau3        1.568947      -1.06647      4.138741
## tau4        4.407834       1.91722      7.107674

2 Synthetic control method

method <- scm(
  lambda_min = 0,
  lambda_max = 1e-3,
  nlambda = 2,
  bootstrap = 10,
  bootstrap_ci_type = "perc"
)

analysis <- setup_analysis_OLE(
  data = SyntheticData,
  trial_status_col_name = "S",
  treatment_col_name = "A",
  outcome_col_name = c("y1", "y2", "y3", "y4"),
  covariates_col_name = c("x1", "x2", "x3", "x4", "x5"),
  T_cross = 2,
  method_OLE_obj = method
)

run_analysis(analysis)

##      point_estimates lower_CI_boot upper_CI_boot
## tau3        2.064756      1.518103      2.677024
## tau4        3.943234      1.931972      7.565861

References

Zhou X, Pang H, Drake C, Burger HU, Zhu J (2024). “Estimating treatment effect in randomized trial after control to treatment crossover using external controls.” Journal of Biopharmaceutical Statistics. doi: 10.1080/10543406.2024.2444222.
Shi L, Pang H, Chen C, Zhu J (2025). “rdborrow: an R package for causal inference incorporating external controls in randomized controlled trials with longitudinal outcomes.” Journal of Biopharmaceutical Statistics, 35(6), 1043-1066. doi: 10.1080/10543406.2025.2489283.

Lei Shi, Matthew Secrest