The Simple Two-Stage Estimation (TSE) Method for Treatment Switching
Obtains the causal parameter estimate of the AFT model for switching after disease progression and the hazard ratio estimate of the outcome Cox model to adjust for treatment switching.
tsesimp( data, id = "id", stratum = "", time = "time", event = "event", treat = "treat", censor_time = "censor_time", pd = "pd", pd_time = "pd_time", swtrt = "swtrt", swtrt_time = "swtrt_time", base_cov = "", base2_cov = "", aft_dist = "weibull", strata_main_effect_only = TRUE, recensor = TRUE, admin_recensor_only = TRUE, swtrt_control_only = TRUE, alpha = 0.05, ties = "efron", offset = 1, boot = TRUE, n_boot = 1000, seed = NA )
data: The input data frame that contains the following variables:
id: The subject id.stratum: The stratum.time: The survival time for right censored data.event: The event indicator, 1=event, 0=no event.treat: The randomized treatment indicator, 1=treatment, 0=control.censor_time: The administrative censoring time. It should be provided for all subjects including those who had events.pd: The disease progression indicator, 1=PD, 0=no PD.pd_time: The time from randomization to PD.swtrt: The treatment switch indicator, 1=switch, 0=no switch.swtrt_time: The time from randomization to treatment switch.base_cov: The baseline covariates (excluding treat).base2_cov: The baseline and secondary baseline covariates (excluding swtrt).id: The name of the id variable in the input data.
stratum: The name(s) of the stratum variable(s) in the input data.
time: The name of the time 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 outcome Cox model.
base2_cov: The names of secondary baseline covariates (excluding swtrt) in the input data for the AFT model for post-progression survival.
aft_dist: The assumed distribution for time to event for the AFT model. Options include "exponential", "weibull" (default), "loglogistic", and "lognormal".
strata_main_effect_only: Whether to only include the strata main effects in the AFT model. Defaults to TRUE, otherwise all possible strata combinations will be considered in the AFT model.
recensor: Whether to apply recensoring to counterfactual survival times. Defaults to TRUE.
admin_recensor_only: Whether to apply recensoring to administrative censoring times only. Defaults to TRUE. If FALSE, recensoring will be applied to the actual censoring times for dropouts.
swtrt_control_only: Whether treatment switching occurred only in the control group. The default is TRUE.
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).
offset: The offset to calculate the time to event, PD, and treatment switch. We can set offset equal to 1 (default), 1/30.4375, or 1/365.25 if the time unit is day, month, or year.
boot: Whether to use bootstrap to obtain the confidence interval for hazard ratio. Defaults to TRUE.
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.
A list with the following components:
psi: The estimated causal parameter for the control group.
psi_CI: The confidence interval for psi.
psi_CI_type: The type of confidence interval for psi, i.e., "AFT model" or "bootstrap".
logrank_pvalue: The two-sided p-value of the log-rank test for an intention-to-treat (ITT) analysis.
cox_pvalue: The two-sided p-value for treatment effect based on the Cox model.
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".
data_aft: A list of input data for the AFT model by treatment group.
fit_aft: A list of fitted AFT models by treatment group.
data_outcome: The input data for the outcome Cox model.
fit_outcome: The fitted outcome Cox model.
settings: A list with the following components:
aft_dist: The distribution for time to event for the AFT model.strata_main_effect_only: Whether to only include the strata main effects in the AFT model.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.alpha: The significance level to calculate confidence intervals.ties: The method for handling ties in the Cox model.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 if swtrt_control_only is FALSE.
psi_trt_CI: The confidence interval for psi_trt if swtrt_control_only is FALSE.
hr_boots: The bootstrap hazard ratio estimates if boot is TRUE.
psi_boots: The bootstrap psi estimates if boot is TRUE.
psi_trt_boots: The bootstrap psi_trt estimates if boot is TRUE and swtrt_control_only is FALSE.
We use the following steps to obtain the hazard ratio estimate and confidence interval had there been no treatment switching:
n_boot - 1 degrees of freedom.library(dplyr) # the eventual survival time shilong1 <- shilong %>% arrange(bras.f, id, tstop) %>% group_by(bras.f, id) %>% slice(n()) %>% select(-c("ps", "ttc", "tran")) # the last value of time-dependent covariates before pd shilong2 <- shilong %>% filter(pd == 0 | tstart <= dpd) %>% arrange(bras.f, id, tstop) %>% group_by(bras.f, id) %>% slice(n()) %>% select(bras.f, id, ps, ttc, tran) # combine baseline and time-dependent covariates shilong3 <- shilong1 %>% left_join(shilong2, by = c("bras.f", "id")) # apply the two-stage method fit1 <- tsesimp( data = shilong3, id = "id", time = "tstop", event = "event", treat = "bras.f", censor_time = "dcut", pd = "pd", pd_time = "dpd", swtrt = "co", swtrt_time = "dco", base_cov = c("agerand", "sex.f", "tt_Lnum", "rmh_alea.c", "pathway.f"), base2_cov = c("agerand", "sex.f", "tt_Lnum", "rmh_alea.c", "pathway.f", "ps", "ttc", "tran"), aft_dist = "weibull", alpha = 0.05, recensor = TRUE, swtrt_control_only = FALSE, offset = 1, boot = FALSE) c(fit1$hr, fit1$hr_CI)
Nicholas R Latimer, KR Abrams, PC Lambert, MK Crowther, AJ Wailoo, JP Morden, RL Akehurst, and MJ Campbell. Adjusting for treatment switching in randomised controlled trials - A simulation study and a simplified two-stage method. Statistical Methods in Medical Research. 2017;26(2):724-751.
Kaifeng Lu, kaifenglu@gmail.com
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