trtswitch (version 0.1.4)

ipcw: Inverse Probability of Censoring Weights (IPCW) Method for Treatment Switching

Description

Uses the inverse probability of censoring weights (IPCW) method to obtain the hazard ratio estimate of the Cox model to adjust for treatment switching.

Usage

ipcw(
  data,
  id = "id",
  stratum = "",
  tstart = "tstart",
  tstop = "tstop",
  event = "event",
  treat = "treat",
  swtrt = "swtrt",
  swtrt_time = "swtrt_time",
  swtrt_time_lower = "",
  swtrt_time_upper = "",
  base_cov = "",
  numerator = "",
  denominator = "",
  logistic_switching_model = FALSE,
  strata_main_effect_only = TRUE,
  firth = FALSE,
  flic = FALSE,
  ns_df = 3,
  relative_time = TRUE,
  stabilized_weights = TRUE,
  trunc = 0,
  trunc_upper_only = TRUE,
  swtrt_control_only = TRUE,
  alpha = 0.05,
  ties = "efron",
  boot = TRUE,
  n_boot = 1000,
  seed = NA
)

Value

A list with the following components:

• 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_switch: A list of input data for the switching models by treatment group.

• fit_switch: A list of fitted switching models for the denominator and numerator by treatment group.

• data_outcome: The input data for the outcome Cox model including the inverse probability of censoring weights.

• fit_outcome: The fitted outcome Cox model.

• settings: A list with the following components:

  • logistic_switching_model: Whether a pooled logistic regression switching model is used.

  • strata_main_effect_only: Whether to only include the strata main effects in the logistic regression switching model.

  • firth: Whether the Firth's bias reducing penalized likelihood should be used.

  • flic: Whether to apply intercept correction to obtain more accurate predicted probabilities.

  • ns_df: Degrees of freedom for the natural cubic spline.

  • relative_time: Whether to use the relative time as the intercepts.

  • stabilized_weights: Whether to use the stabilized weights.

  • trunc: The truncation fraction of the weight distribution.

  • trunc_upper_only: Whether to truncate the weights from the upper end of the distribution only.

  • swtrt_control_only Whether treatment switching occurred only in the control group.

  • alpa: The significance level to calculate confidence intervals.

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

  • 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.

• hr_boots: The bootstrap hazard ratio estimates if boot is TRUE.

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.

• swtrt: The treatment switch indicator, 1=switch, 0=no switch.

• swtrt_time: The time from randomization to treatment switch.

• swtrt_time_lower: The lower bound of treatment switching time.

• swtrt_time_upper: The upper bound of treatment switching time.

• base_cov: The baseline covariates (excluding treat) used in the outcome model.

• numerator: The baseline covariates (excluding treat) used in the switching model for the numerator for stabilized weights.

• denominator: The baseline and time-dependent covariates (excluding treat) used in the switching model for the denominator.

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.

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_lower

The name of the swtrt_time_lower 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.

numerator

The names of baseline covariates (excluding treat) in the input data for the numerator switching model for stabilized weights.

denominator

The names of baseline and time-dependent covariates (excluding treat) in the input data for the denominator switching model.

logistic_switching_model

Whether a pooled logistic regression switching model is used.

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.

ns_df

Degrees of freedom for the natural cubic spline for visit-specific intercepts of the pooled logistic regression model. Defaults to 3 for two internal knots at the 33 and 67 percentiles of the artificial censoring times due to treatment switching.

relative_time

Whether to use the time relative to swtrt_time_lower as the intercepts for the pooled logistic regression model. The default is TRUE.

stabilized_weights

Whether to use the stabilized weights. The default is TRUE.

trunc

The truncation fraction of the weight distribution. Defaults to 0 for no truncation in weights.

trunc_upper_only

Whether to truncate the weights from the upper end of the weight distribution only. Defaults to TRUE, otherwise the weights will be truncated from both the lower and upper ends of the distribution.

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).

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:

• Exclude observations after treatment switch.

• Set up the crossover and event indicators for the last time interval for each subject.

• For time-dependent covariates Cox switching models, replicate unique event times across treatment arms within each subject.

• Fit the denominator switching model (and the numerator switching model for stabilized weights) to obtain the inverse probability of censoring weights. This can be a Cox model with time-dependent covariates or a pooled logistic regression model. For pooled logistic regression switching model, the probability of remaining uncensored (i.e., not switching) will be calculated by subtracting the predicted probability of switching from 1 and then multiplied over time up to the current time point.

• Fit the weighted Cox model to the censored outcome survival times to obtain the hazard ratio estimate.

• Use either robust sandwich variance or bootstrapping to construct the p-value and confidence interval for the hazard ratio. If bootstrapping is used, the confidence interval and corresponding p-value are calculated based on a t-distribution with n_boot - 1 degrees of freedom.

References

James M. Robins and Dianne M. Finkelstein. Correcting for noncompliance and dependent censoring in an AIDS clinical trial with inverse probability of censoring weighted (IPCW) log-rank tests. Biometrics. 2000;56:779-788.

Examples

# Example 1: pooled logistic regression switching model

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 <- ipcw(
  sim1$paneldata, id = "id", tstart = "tstart", 
  tstop = "tstop", event = "died", treat = "trtrand", 
  swtrt = "xo", swtrt_time = "xotime", 
  swtrt_time_lower = "timePFSobs",
  swtrt_time_upper = "xotime_upper", base_cov = "bprog", 
  numerator = "bprog", denominator = "bprog*catlag", 
  logistic_switching_model = TRUE, ns_df = 3,
  relative_time = TRUE, swtrt_control_only = TRUE, 
  boot = FALSE)
  
c(fit1$hr, fit1$hr_CI) 

# Example 2: time-dependent covariates Cox switching model

fit2 <- ipcw(
  shilong, id = "id", tstart = "tstart", tstop = "tstop", 
  event = "event", treat = "bras.f", swtrt = "co", 
  swtrt_time = "dco", 
  base_cov = c("agerand", "sex.f", "tt_Lnum", "rmh_alea.c", 
               "pathway.f"),
  numerator = c("agerand", "sex.f", "tt_Lnum", "rmh_alea.c", 
                "pathway.f"),
  denominator = c("agerand", "sex.f", "tt_Lnum", "rmh_alea.c",
                  "pathway.f", "ps", "ttc", "tran"),
  swtrt_control_only = FALSE, boot = FALSE)

c(fit2$hr, fit2$hr_CI)