Iterative Parameter Estimation (IPE) for Treatment Switching
Obtains the causal parameter estimate from the accelerated failure-time (AFT) model and the hazard ratio estimate from the Cox model to adjust for treatment switching.
ipe( data, id = "id", stratum = "", time = "time", event = "event", treat = "treat", rx = "rx", censor_time = "censor_time", base_cov = "", aft_dist = "weibull", strata_main_effect_only = 1, treat_modifier = 1, recensor = TRUE, admin_recensor_only = TRUE, autoswitch = TRUE, alpha = 0.05, ties = "efron", tol = 1e-06, boot = FALSE, 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.rx: The proportion of time on active treatment.censor_time: The administrative censoring time. It should be provided for all subjects including those who had events.base_cov: The 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.
rx: The name of the rx variable in the input data.
censor_time: The name of the censor_time variable in the input data.
base_cov: The names of baseline covariates (excluding treat) in the input data for the outcome Cox model.
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.
treat_modifier: The optional sensitivity parameter for the constant treatment effect assumption.
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.
autoswitch: Whether to exclude recensoring for treatment arms with no switching. Defaults to TRUE.
alpha: The significance level to calculate confidence intervals.
ties: The method for handling ties in the Cox model, either "breslow" or "efron" (default).
tol: The desired accuracy (convergence tolerance) for psi.
boot: Whether to use bootstrap to obtain the confidence interval for hazard ratio. Defaults to FALSE, in which case, the confidence interval will be constructed to match the log-rank test p-value.
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.
psi_CI: The confidence interval for psi.
psi_CI_type: The type of confidence interval for psi, i.e., "log-rank p-value" or "bootstrap".
logrank_pvalue: The two-sided p-value of the log-rank test for the 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 "log-rank p-value" or "bootstrap".
Sstar: A data frame containing the counterfactual untreated survival times and event indicators for each treatment group.
kmstar: A data frame containing the Kaplan-Meier estimates based on the counterfactual untreated survival times by treatment arm.
data_aft: The input data for the AFT model for estimating psi.
fit_aft: The fitted AFT model for estimating psi.
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.treat_modifier: The sensitivity parameter for the constant treatment effect assumption.recensor: Whether to apply recensoring to counterfactual survival times.admin_recensor_only: Whether to apply recensoring to administrative censoring times only.autoswitch: Whether to exclude recensoring for treatment arms with no switching.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.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.
psi_boots: The bootstrap psi estimates if boot is TRUE.
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) # Example 1: one-way treatment switching (control to active) data <- immdef %>% mutate(rx = 1-xoyrs/progyrs) fit1 <- ipe( data, id = "id", time = "progyrs", event = "prog", treat = "imm", rx = "rx", censor_time = "censyrs", aft_dist = "weibull", boot = FALSE) c(fit1$hr, fit1$hr_CI) # Example 2: two-way treatment switching (illustration only) # the eventual survival time shilong1 <- shilong %>% arrange(bras.f, id, tstop) %>% group_by(bras.f, id) %>% slice(n()) %>% select(-c("ps", "ttc", "tran")) shilong2 <- shilong1 %>% mutate(rx = ifelse(co, ifelse(bras.f == "MTA", dco/ady, 1 - dco/ady), ifelse(bras.f == "MTA", 1, 0))) fit2 <- ipe( shilong2, id = "id", time = "tstop", event = "event", treat = "bras.f", rx = "rx", censor_time = "dcut", base_cov = c("agerand", "sex.f", "tt_Lnum", "rmh_alea.c", "pathway.f"), aft_dist = "weibull", boot = FALSE) c(fit2$hr, fit2$hr_CI)
Michael Branson and John Whitehead. Estimating a treatment effect in survival studies in which patients switch treatment. Statistics in Medicine. 2002;21:2449-2463.
Ian R White. Letter to the Editor: Estimating treatment effects in randomized trials with treatment switching. Statistics in Medicine. 2006;25:1619-1622.
Kaifeng Lu, kaifenglu@gmail.com
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