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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
)
set.seed(1)
run_analysis(analysis)## point_estimates standard_deviation lower_CI_boot upper_CI_boot
## tau3 2.075926 1.075571 -0.5383522 4.529989
## tau4 4.389438 1.508449 0.7651932 8.041151model_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
)
set.seed(1)
run_analysis(analysis)## point_estimates standard_deviation lower_CI_boot upper_CI_boot
## tau3 2.041727 1.253924 -0.9601101 4.902500
## tau4 4.036118 1.532951 0.9831966 7.465598model_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
)
set.seed(1)
run_analysis(analysis)## point_estimates standard_deviation lower_CI_boot upper_CI_boot
## tau3 1.568947 1.0759314 -1.463867 3.569813
## tau4 4.407834 0.9722213 1.918617 6.407367scm() solves one optimization for each trial control
patient in each bootstrap replicate, so it is slow. This example uses
only 3 replicates so that the vignette builds quickly. Its interval is
for demonstration only: boot warns that it uses the extreme
replicates, and it can even exclude the point estimate. A real analysis
needs many more replicates, for example
bootstrap = 1000.
method <- 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
)
set.seed(1)
run_analysis(analysis)## Warning in norm.inter(t, alpha): extreme order statistics used as endpoints
## Warning in norm.inter(t, alpha): extreme order statistics used as endpoints## point_estimates standard_deviation lower_CI_boot upper_CI_boot
## tau3 2.064756 0.5305223 1.831022 2.854466
## tau4 3.943234 2.1379553 1.909084 6.089916These 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.