trtswitch (version 0.1.4)

tsesimp: The Simple Two-Stage Estimation (TSE) Method for Treatment Switching

Description

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.

Usage

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
)

Value

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.

Arguments

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.

Author

Kaifeng Lu,

Details

We use the following steps to obtain the hazard ratio estimate and confidence interval had there been no treatment switching:

• Fit an AFT model to post-progression survival data to estimate the causal parameter \(\psi\) based on the patients in the control group who had disease progression.

• 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.

References

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.

Examples

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)