tsegest {trtswitch} | R Documentation |
The Two-Stage Estimation (TSE) Method Using g-estimation for Treatment Switching
Description
Obtains the causal parameter estimate using g-estimation based on the logistic regression switching model and the hazard ratio estimate of the Cox model to adjust for treatment switching.
Usage
tsegest(
data,
id = "id",
stratum = "",
tstart = "tstart",
tstop = "tstop",
event = "event",
treat = "treat",
censor_time = "censor_time",
pd = "pd",
pd_time = "pd_time",
swtrt = "swtrt",
swtrt_time = "swtrt_time",
base_cov = "",
conf_cov = "",
low_psi = -2,
hi_psi = 2,
n_eval_z = 101,
strata_main_effect_only = TRUE,
firth = FALSE,
flic = FALSE,
recensor = TRUE,
admin_recensor_only = TRUE,
swtrt_control_only = TRUE,
gridsearch = FALSE,
alpha = 0.05,
ties = "efron",
tol = 1e-06,
offset = 1,
boot = TRUE,
n_boot = 1000,
seed = NA
)
Arguments
data |
The input data frame that contains the following variables:
|
id |
The name of the id variable in the input data. |
stratum |
The name(s) of the stratum variable(s) in the input data. |
tstart |
The name of the tstart variable in the input data. |
tstop |
The name of the tstop variable in the input data. |
event |
The name of the event variable in the input data. |
treat |
The name of the treatment variable in the input data. |
censor_time |
The name of the censor_time variable in the input data. |
pd |
The name of the pd variable in the input data. |
pd_time |
The name of the pd_time variable in the input data. |
swtrt |
The name of the swtrt variable in the input data. |
swtrt_time |
The name of the swtrt_time variable in the input data. |
base_cov |
The names of baseline covariates (excluding treat) in the input data for the Cox model. |
conf_cov |
The names of confounding variables (excluding treat) in the input data for the logistic regression switching model. |
low_psi |
The lower limit of the causal parameter. |
hi_psi |
The upper limit of the causal parameter. |
n_eval_z |
The number of points between |
strata_main_effect_only |
Whether to only include the strata main
effects in the logistic regression switching model. Defaults to
|
firth |
Whether the Firth's bias reducing penalized likelihood should be used. |
flic |
Whether to apply intercept correction to obtain more accurate predicted probabilities. |
recensor |
Whether to apply recensoring to counterfactual
survival times. Defaults to |
admin_recensor_only |
Whether to apply recensoring to administrative
censoring times only. Defaults to |
swtrt_control_only |
Whether treatment switching occurred only in
the control group. The default is |
gridsearch |
Whether to use grid search to estimate the causal
parameter |
alpha |
The significance level to calculate confidence intervals. The default value is 0.05. |
ties |
The method for handling ties in the Cox model, either "breslow" or "efron" (default). |
tol |
The desired accuracy (convergence tolerance) for |
offset |
The offset to calculate the time to event, PD, and
treatment switch. We can set |
boot |
Whether to use bootstrap to obtain the confidence
interval for hazard ratio. Defaults to |
n_boot |
The number of bootstrap samples. |
seed |
The seed to reproduce the bootstrap results. The default is missing, in which case, the seed from the environment will be used. |
Details
We use the following steps to obtain the hazard ratio estimate and confidence interval had there been no treatment switching:
Use a pooled logistic regression switching model to estimate the causal parameter
\psi
based on the patients in the control group who had disease progression:\textrm{logit}(p(E_{ik})) = \alpha U_{i,\psi} + \sum_{j} \beta_j x_{ijk}
where
E_{ik}
is the observed switch indicator for individuali
at observationk
,U_{i,\psi} = T_{C_i} + e^{\psi}T_{E_i}
is the counterfactual survival time for individual
i
given a specific value for\psi
, andx_{ijk}
is the confounderj
for individuali
at observationk
. When applied from a secondary baseline,U_{i,\psi}
refers to post-secondary baseline counterfactual survival, whereT_{C_i}
corresponds to the time spent after the secondary baseline on control treatment, andT_{E_i}
corresponds to the time spent after the secondary baseline on the experimental treatment.Search for
\psi
such that the Z-statistic for\alpha
is close to zero. This will be the estimate of the causal parameter. The confidence interval for\psi
can be obtained as the value of\psi
such that the corresponding two-sided p-value for testingH_0: \alpha = 0
in the switching model is equal to the nominal significance level.Derive the counterfactual survival times for control patients had there been no treatment switching.
Fit the Cox proportional hazards model to the observed survival times for the experimental group and the counterfactual survival times for the control group to obtain the hazard ratio estimate.
If bootstrapping is used, the confidence interval and corresponding p-value for hazard ratio are calculated based on a t-distribution with
n_boot - 1
degrees of freedom.
Value
A list with the following components:
-
psi
: The estimated causal parameter for the control group. -
psi_CI
: The confidence interval forpsi
. -
psi_CI_type
: The type of confidence interval forpsi
, i.e., "grid search", "root finding", or "bootstrap". -
logrank_pvalue
: The two-sided p-value of the log-rank test for the ITT analysis. -
cox_pvalue
: The two-sided p-value for treatment effect based on the Cox model applied to counterfactual unswitched survival times. Ifboot
isTRUE
, this value represents the bootstrap p-value. -
hr
: The estimated hazard ratio from the Cox model. -
hr_CI
: The confidence interval for hazard ratio. -
hr_CI_type
: The type of confidence interval for hazard ratio, either "Cox model" or "bootstrap". -
analysis_switch
: A list of data and analysis results related to treatment switching.-
data_switch
: The list of input data for the time from secondary baseline to switch by treatment group. The variables includeid
,stratum
,"swtrt"
, and"swtrt_time"
. Ifswtrt == 0
, thenswtrt_time
is censored at the time from secondary baseline to either death or censoring. -
km_switch
: The list of Kaplan-Meier plot data for the time from secondary baseline to switch by treatment group. -
eval_z
: The list of data by treatment group containing the Wald statistics for the coefficient of the counterfactual in the logistic regression switching model, evaluated at a sequence ofpsi
values. Used to plot and check if the range ofpsi
values to search for the solution and limits of confidence interval ofpsi
need be modified. -
data_nullcox
: The list of input data for counterfactual survival times for the null Cox model by treatment group. The variables includeid
,stratum
,"t_star"
and"d_star"
. -
fit_nullcox
: The list of fitted null Cox models for counterfactual survival times by treatment group, which contains the martingale residuals. -
data_logis
: The list of input data for pooled logistic regression models for treatment switching using g-estimation. The variables includeid
,stratum
,"tstart"
,"tstop"
,"cross"
,"counterfactual"
,conf_cov
,pd_time
,swtrt
, andswtrt_time
. -
fit_logis
: The list of fitted pooled logistic regression models for treatment switching using g-estimation.
-
-
data_outcome
: The input data for the outcome Cox model of counterfactual unswitched survival times. The variables includeid
,stratum
,"t_star"
,"d_star"
,"treated"
,base_cov
andtreat
. -
fit_outcome
: The fitted outcome Cox model. -
fail
: Whether a model fails to converge. -
settings
: A list with the following components:-
low_psi
: The lower limit of the causal parameter. -
hi_psi
: The upper limit of the causal parameter. -
n_eval_z
: The number of points betweenlow_psi
andhi_psi
(inclusive) at which to evaluate the Wald statistics for the coefficient for the counterfactual in the logistic regression switching model. -
strata_main_effect_only
: Whether to only include the strata main effects in the logistic regression switching model. -
firth
: Whether the Firth's penalized likelihood is used. -
flic
: Whether to apply intercept correction. -
recensor
: Whether to apply recensoring to counterfactual survival times. -
admin_recensor_only
: Whether to apply recensoring to administrative censoring times only. -
swtrt_control_only
: Whether treatment switching occurred only in the control group. -
gridsearch
: Whether to use grid search to estimate the causal parameterpsi
. -
alpha
: The significance level to calculate confidence intervals. -
ties
: The method for handling ties in the Cox model. -
tol
: The desired accuracy (convergence tolerance) forpsi
. -
offset
: The offset to calculate the time to event, PD, and treatment switch. -
boot
: Whether to use bootstrap to obtain the confidence interval for hazard ratio. -
n_boot
: The number of bootstrap samples. -
seed
: The seed to reproduce the bootstrap results.
-
-
psi_trt
: The estimated causal parameter for the experimental group ifswtrt_control_only
isFALSE
. -
psi_trt_CI
: The confidence interval forpsi_trt
ifswtrt_control_only
isFALSE
. -
fail_boots
: The indicators for failed bootstrap samples ifboot
isTRUE
. -
hr_boots
: The bootstrap hazard ratio estimates ifboot
isTRUE
. -
psi_boots
: The bootstrappsi
estimates ifboot
isTRUE
. -
psi_trt_boots
: The bootstrappsi_trt
estimates ifboot
isTRUE
andswtrt_control_only
isFALSE
.
Author(s)
Kaifeng Lu, kaifenglu@gmail.com
References
NR Latimer, IR White, K Tilling, and U Siebert. Improved two-stage estimation to adjust for treatment switching in randomised trials: g-estimation to address time-dependent confounding. Statistical Methods in Medical Research. 2020;29(10):2900-2918.
Examples
sim1 <- tsegestsim(
n = 500, allocation1 = 2, allocation2 = 1, pbprog = 0.5,
trtlghr = -0.5, bprogsl = 0.3, shape1 = 1.8,
scale1 = 360, shape2 = 1.7, scale2 = 688,
pmix = 0.5, admin = 5000, pcatnotrtbprog = 0.5,
pcattrtbprog = 0.25, pcatnotrt = 0.2, pcattrt = 0.1,
catmult = 0.5, tdxo = 1, ppoor = 0.1, pgood = 0.04,
ppoormet = 0.4, pgoodmet = 0.2, xomult = 1.4188308,
milestone = 546, outputRawDataset = 1, seed = 2000)
fit1 <- tsegest(
data = sim1$paneldata, id = "id",
tstart = "tstart", tstop = "tstop", event = "event",
treat = "trtrand", censor_time = "censor_time",
pd = "progressed", pd_time = "timePFSobs",
swtrt = "xo", swtrt_time = "xotime",
base_cov = "bprog", conf_cov = "bprog*catlag",
strata_main_effect_only = TRUE,
recensor = TRUE, admin_recensor_only = TRUE,
swtrt_control_only = TRUE, alpha = 0.05, ties = "efron",
tol = 1.0e-6, boot = FALSE)
c(fit1$hr, fit1$hr_CI)