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Simple Two-Stage Estimation (TSEsimp) for Treatment Switching

Source: R/tsesimp.R
tsesimp.Rd

Estimates the causal parameter by fitting an accelerated failure time (AFT) model comparing post-progression survival between switchers and non-switchers, and derives the adjusted hazard ratio from the Cox model using counterfactual unswitched survival times based on the estimated causal parameter.

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 = 0,
  nthreads = 0
)

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 disease progression.

  • 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 treat).

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 baseline and secondary baseline covariates (excluding treat) 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.

ties

The method for handling ties in the Cox model, either "breslow" or "efron" (default).

offset

The offset to calculate the time disease progression to death or censoring. We can set offset equal to 0 (no offset), and 1 (default), 1/30.4375, or 1/365.25 if the time unit is day, month, or year, respectively.

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.

nthreads

The number of threads to use in bootstrapping (0 means the default RcppParallel behavior).

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".

  • pvalue: The two-sided p-value.

  • pvalue_type: The type of two-sided p-value for treatment effect, i.e., "Cox model" or "bootstrap".

  • 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".

  • event_summary: A data frame containing the count and percentage of deaths, disease progressions, and switches by treatment arm.

  • data_aft: A list of input data for the AFT model by treatment group. The variables include id, stratum, "pps", "event", "swtrt", base2_cov, pd_time, swtrt_time, and time.

  • fit_aft: A list of fitted AFT models by treatment group.

  • res_aft: A list of deviance residuals from the AFT models by treatment group.

  • data_outcome: The input data for the outcome Cox model of counterfactual unswitched survival times. The variables include id, stratum, "t_star", "d_star", "treated", base_cov, and treat.

  • km_outcome: The Kaplan-Meier estimates of the survival functions for the treatment and control groups based on the counterfactual unswitched survival times.

  • lr_outcome: The log-rank test results for the treatment effect based on the counterfactual unswitched survival times.

  • fit_outcome: The fitted outcome Cox model.

  • fail: Whether a model fails to converge.

  • psimissing: Whether the psi parameter cannot be estimated.

  • settings: A list containing the input parameter values.

  • 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.

  • fail_boots: The indicators for failed bootstrap samples if boot is TRUE.

  • fail_boots_data: The data for failed bootstrap samples if boot is TRUE.

  • 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.

Details

Assuming one-way switching from control to treatment, the hazard ratio and confidence interval under a no-switching scenario are obtained as follows:

  • Estimate the causal parameter \(\psi\) by fitting an AFT model comparing post-progression survival between switchers and non-switchers in the control group who experienced disease progression.

  • Compute counterfactual survival times for control patients using the estimated \(\psi\).

  • Fit a Cox model to the observed survival times for the treatment group and the counterfactual survival times for the control group to estimate the hazard ratio.

  • When bootstrapping is used, derive the confidence interval and p-value for the hazard ratio from a t-distribution with n_boot - 1 degrees of freedom.

If treatment switching occurs before or in the absence of recorded disease progression, the patient is considered to have progressed at the time of treatment switching.

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.

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples


library(dplyr)

# modify pd and dpd based on co and dco
shilong <- shilong %>%
  mutate(dpd = ifelse(co & !pd, dco, dpd),
         pd = ifelse(co & !pd, 1, pd)) %>%
  mutate(dpd = ifelse(pd & co & dco < dpd, dco, dpd))
  
# 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)

fit1
#>             n event_n event_pct pd_n pd_pct switch_n switch_pct event_out_n
#> Control    93      63      67.7   85   91.4       68       73.1          58
#> Treatment 100      67      67.0   83   83.0       25       25.0          63
#>           event_out_pct bras.f
#> Control            62.4     CT
#> Treatment          63.0    MTA
#> 
#>                                              Estimate Lower 95% Upper 95%
#> Causal parameter psi for control arm         -1.068   -1.534    -0.601   
#> Causal survival time ratio for control arm   2.909    1.824     4.637    
#> Causal parameter psi for treatment arm       -0.984   -1.516    -0.451   
#> Causal survival time ratio for treatment arm 2.674    1.570     4.555    
#> Hazard ratio (HR)                            0.913    0.636     1.310    
#> P-value (Cox model)                          0.6200