trtswitch (version 0.1.4)

tsegest: The Two-Stage Estimation (TSE) Method Using g-estimation for Treatment Switching

Description

Obtains the causal parameter estimate of 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",
  swtrt_time_upper = "",
  base_cov = "",
  conf_cov = "",
  low_psi = -3,
  hi_psi = 3,
  n_eval_z = 100,
  strata_main_effect_only = TRUE,
  firth = FALSE,
  flic = FALSE,
  recensor = TRUE,
  admin_recensor_only = TRUE,
  swtrt_control_only = TRUE,
  alpha = 0.05,
  ties = "efron",
  tol = 1e-06,
  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., "logistic 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".

• 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 include id, stratum (if applicable), swtrt, and swtrt_time. If swtrt == 0, then swtrt_time is censored at the time from secondary baseline to either death or censoring.

  • km_switch: The list of Kaplan-Meier plots 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 of psi values. Used to plot and check if the range of psi values to search for the solution and limits of confidence interval of psi need be modified.

  • data_nullcox: The list of input data for counterfactual survival times for the null Cox model by treatment group.

  • 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.

  • 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.

• fit_outcome: The fitted outcome Cox model.

• 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 between low_psi and hi_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.

  • alpha: The significance level to calculate confidence intervals.

  • ties: The method for handling ties in the Cox model.

  • tol: The desired accuracy (convergence tolerance) for psi.

  • 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 id to identify observations belonging to the same subject for counting process data with time-dependent covariates.

• stratum: The stratum.

• tstart: The starting time of the time interval for counting-process data with time-dependent covariates.

• tstop: The stopping time of the time interval for counting-process data with time-dependent covariates.

• 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.

• swtrt_time_upper: The upper bound of treatment switching time.

• base_cov: The baseline covariates (excluding treat).

• conf_cov: The confounding variables for predicting treatment switching (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.

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.

swtrt_time_upper

The name of the swtrt_time_upper 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 low_psi and hi_psi (inclusive) at which to evaluate the Wald statistics for the coefficient of 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. Defaults to TRUE, otherwise all possible strata combinations will be considered in the switching model.

firth

Whether the Firth's bias reducing penalized likelihood should be used. The default is FALSE.

flic

Whether to apply intercept correction to obtain more accurate predicted probabilities. The default is FALSE.

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).

tol

The desired accuracy (convergence tolerance) for psi.

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:

• 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 individual \(i\) at observation \(k\), $$U_{i,\psi} = T_{C_i} + e^{\psi}T_{E_i}$$ is the counterfactual survival time for individual \(i\) given a specific value for \(\psi\), and \(x_{ijk}\) are the confounders for individual \(i\) at observation \(k\). When applied from a secondary baseline, \(U_{i,\psi}\) refers to post-secondary baseline counterfactual survival, where \(T_{C_i}\) corresponds to the time spent after the secondary baseline on control treatment, and \(T_{E_i}\) corresponds to the time spent after the secondary baseline on the experimental treatment.

• Search for \(\psi\) such that the estimate of \(\alpha\) is close to zero. This will be the estimate of the caual parameter. The confidence interval for \(\psi\) can be obtained as the value of \(\psi\) such that the corresponding two-sided p-value for testing \(H_0:\alpha = 0\) 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.

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

# Example 1: one-way treatment switching (control to active)

sim1 <- tsegestsim(
  n = 500, allocation1 = 2, allocation2 = 1, pbprog = 0.5, 
  trtlghr = -0.5, bprogsl = 0.3, shape1 = 1.8, 
  scale1 = 0.000025, shape2 = 1.7, scale2 = 0.000015, 
  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, swtrt_control_only = TRUE,
  outputRawDataset = 1, seed = 2000)
  
fit1 <- tsegest(
  data = sim1$paneldata, id = "id", 
  tstart = "tstart", tstop = "tstop", event = "died", 
  treat = "trtrand", censor_time = "censor_time", 
  pd = "progressed", pd_time = "timePFSobs", swtrt = "xo", 
  swtrt_time = "xotime", swtrt_time_upper = "xotime_upper",
  base_cov = "bprog", conf_cov = "bprog*catlag", 
  low_psi = -3, hi_psi = 3, 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)

# Example 2: two-way treatment switching

sim2 <- tsegestsim(
  n = 500, allocation1 = 2, allocation2 = 1, pbprog = 0.5, 
  trtlghr = -0.5, bprogsl = 0.3, shape1 = 1.8, 
  scale1 = 0.000025, shape2 = 1.7, scale2 = 0.000015, 
  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, swtrt_control_only = FALSE,
  outputRawDataset = 1, seed = 2000)
  
fit2 <- tsegest(
  data = sim2$paneldata, id = "id", 
  tstart = "tstart", tstop = "tstop", event = "died", 
  treat = "trtrand", censor_time = "censor_time", 
  pd = "progressed", pd_time = "timePFSobs", swtrt = "xo", 
  swtrt_time = "xotime", swtrt_time_upper = "xotime_upper",
  base_cov = "bprog", conf_cov = "bprog*catlag", 
  low_psi = -3, hi_psi = 3, strata_main_effect_only = TRUE,
  recensor = TRUE, admin_recensor_only = TRUE, 
  swtrt_control_only = FALSE, alpha = 0.05, ties = "efron", 
  tol = 1.0e-6, boot = FALSE)
  
c(fit2$hr, fit2$hr_CI)