OLE Analysis Workflow
Lei Shi
2026-05-06
Source:vignettes/OLE_analysis_workflow.Rmd
OLE_analysis_workflow.RmdOLE 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 IPW
bootstrap_obj <- setup_bootstrap(
replicates = 50,
bootstrap_CI_type = "perc"
)
method_DID_obj <- setup_method_DID(
method_name = "IPW",
bootstrap_flag = TRUE,
bootstrap_obj = bootstrap_obj,
model_form_piS = "S ~ x1 + x2 + x3 + x4 + x5",
model_form_piA = "A ~ x1 + x2 + x3 + x4 + x5"
)
analysis_OLE_obj <- 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_DID_obj
)
res <- run_analysis(analysis_OLE_obj)1.2 AIPW
bootstrap_obj <- setup_bootstrap(
replicates = 50,
bootstrap_CI_type = "perc"
)
model_form_mu <- 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_obj <- setup_method_DID(
method_name = "AIPW",
bootstrap_flag = TRUE,
bootstrap_obj = bootstrap_obj,
model_form_piS = "S ~ x1 + x2 + x3 + x4 + x5",
model_form_piA = "A ~ x1 + x2 + x3 + x4 + x5",
model_form_mu0_ext = model_form_mu
)
analysis_OLE_obj <- 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_DID_obj
)
res <- run_analysis(analysis_OLE_obj)1.3 OR
bootstrap_obj <- setup_bootstrap(
replicates = 50,
bootstrap_CI_type = "perc"
)
model_form_mu <- 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_obj <- setup_method_DID(
method_name = "OR",
bootstrap_flag = TRUE,
bootstrap_obj = bootstrap_obj,
model_form_mu0_ext = model_form_mu,
model_form_mu0_rct = model_form_mu,
model_form_mu1_rct = model_form_mu
)
analysis_OLE_obj <- 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_DID_obj
)
res <- run_analysis(analysis_OLE_obj)
res## point_estimates lower_CI_boot upper_CI_boot
## tau3 1.568947 -1.06647 4.138741
## tau4 4.407834 1.91722 7.1076742 SCM method: with parallel computing
bootstrap_obj <- setup_bootstrap(
replicates = 50,
bootstrap_CI_type = "perc"
)
method_SCM_obj <- setup_method_SCM(
method_name = "SCM",
bootstrap_flag = TRUE,
bootstrap_obj = bootstrap_obj,
lambda.min = 0,
lambda.max = 1e-3,
nlambda = 10,
parallel = "no",
ncpus = 1
)
analysis_OLE_obj <- 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_SCM_obj
)
run_analysis(analysis_OLE_obj)## Running the synthetic control method...
## Performing cross validation for tuning parameter selection...## ℹ In a future CVXR release, `solve()` will return the optimal value directly
## (like `psolve()`).
## ℹ The `$getValue()`/`$getDualValue()` interface will be removed.
## ℹ New API: `psolve(prob)`, then `value(x)`, `dual_value(constr)`,
## `status(prob)`.
## This message is displayed once per session.## Warning: `getValue()` is deprecated.
## ℹ Use `value(x)` after solving instead.
## This warning is displayed once per session.## Constructing pseudo controls for internal data...
## Performing bootstrap inference with SCM estimates...## Warning: Solution may be inaccurate. Try another solver, adjusting the solver settings,
## or solve with `verbose = TRUE` for more information.## Warning: Solution may be inaccurate. Try another solver, adjusting the solver settings,
## or solve with `verbose = TRUE` for more information.
## Solution may be inaccurate. Try another solver, adjusting the solver settings,
## or solve with `verbose = TRUE` for more information.
## Solution may be inaccurate. Try another solver, adjusting the solver settings,
## or solve with `verbose = TRUE` for more information.
## Solution may be inaccurate. Try another solver, adjusting the solver settings,
## or solve with `verbose = TRUE` for more information.
## Solution may be inaccurate. Try another solver, adjusting the solver settings,
## or solve with `verbose = TRUE` for more information.
## Solution may be inaccurate. Try another solver, adjusting the solver settings,
## or solve with `verbose = TRUE` for more information.## time elapsed for bootstrap: 8.76## point_estimates lower_CI_boot upper_CI_boot
## tau3 2.134082 0.6776431 4.008635
## tau4 3.950783 1.3126432 6.8957323 SCM method: without parallel computing
bootstrap_obj <- setup_bootstrap(
replicates = 50,
bootstrap_CI_type = "perc"
)
method_SCM_obj <- setup_method_SCM(
method_name = "SCM",
bootstrap_flag = TRUE,
bootstrap_obj = bootstrap_obj,
lambda.min = 0,
lambda.max = 1e-3,
nlambda = 10,
parallel = "no"
)
analysis_OLE_obj <- 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_SCM_obj
)
run_analysis(analysis_OLE_obj)## Running the synthetic control method...
## Performing cross validation for tuning parameter selection...
## Constructing pseudo controls for internal data...
## Performing bootstrap inference with SCM estimates...## Warning: Solution may be inaccurate. Try another solver, adjusting the solver settings,
## or solve with `verbose = TRUE` for more information.
## Solution may be inaccurate. Try another solver, adjusting the solver settings,
## or solve with `verbose = TRUE` for more information.
## Solution may be inaccurate. Try another solver, adjusting the solver settings,
## or solve with `verbose = TRUE` for more information.
## Solution may be inaccurate. Try another solver, adjusting the solver settings,
## or solve with `verbose = TRUE` for more information.## time elapsed for bootstrap: 9.18## point_estimates lower_CI_boot upper_CI_boot
## tau3 2.134082 0.5584951 3.910489
## tau4 3.950783 1.1203356 7.356058References
- 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.