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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.
The SyntheticData dataset has outcomes y1,
y2, y3, y4 measured at four time
points, and T_cross = 2. This means y1 and
y2 are from the placebo-controlled phase (Period I) and
y3 and y4 are from the open-label extension
(Period II). T_cross is the last column index of Period I
in outcome_col_name.
## A S y1 y2 y3 y4
## 1 1 1 3.4512377 -0.7642287 -2.4713591 3.935466
## 2 1 1 0.4518106 6.3516296 4.5231869 -0.198674
## 3 0 1 3.0532714 -2.0453190 5.9064870 -1.374919
## 4 1 1 -9.1183948 0.2304339 4.7858172 8.490757
## 5 0 1 -1.4270057 1.5878794 3.7006101 9.449632
## 6 0 1 -2.6967072 -0.6130288 0.7482786 -2.413717method <- 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 -0.2531514 3.994431
## tau4 4.389438 0.5095401 7.982780model_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 -1.232759 4.558105
## tau4 4.036118 1.492481 7.712051model_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 -0.7157897 3.610432
## tau4 4.407834 1.4696074 6.400508method <- scm(
lambda_min = 0,
lambda_max = 1e-3,
nlambda = 2,
bootstrap = 3,
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 0.8669477 4.262813
## tau4 3.943234 3.0478559 7.319810These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.