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",
low_psi = -1,
hi_psi = 1,
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
)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 applied to counterfactual unswitched survival times.
If boot is TRUE, this value represents the
bootstrap p-value.
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.
The variables include id, stratum,
"t_star", "d_star", "treated", and treat.
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. The variables include id, stratum,
"t_star", "d_star", "treated", base_cov,
and treat.
fit_aft: The fitted AFT model for estimating psi.
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.
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.
low_psi: The lower limit of the causal parameter.
hi_psi: The upper limit of the causal parameter.
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.
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).
The name of the id variable in the input data.
The name(s) of the stratum variable(s) in the input data.
The name of the time variable in the input data.
The name of the event variable in the input data.
The name of the treatment variable in the input data.
The name of the rx variable in the input data.
The name of the censor_time variable in the input data.
The names of baseline covariates (excluding treat) in the input data for the causal AFT model and the outcome Cox model.
The assumed distribution for time to event for the AFT model. Options include "exponential", "weibull" (default), "loglogistic", and "lognormal".
The lower limit of the causal parameter.
The upper limit of the causal parameter.
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.
The optional sensitivity parameter for the constant treatment effect assumption.
Whether to apply recensoring to counterfactual
survival times. Defaults to TRUE.
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.
Whether to exclude recensoring for treatment arms
with no switching. Defaults to TRUE.
The significance level to calculate confidence intervals.
The method for handling ties in the Cox model, either "breslow" or "efron" (default).
The desired accuracy (convergence tolerance) for psi
for the root finding algorithm.
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.
The number of bootstrap samples.
The seed to reproduce the bootstrap results. The default is missing, in which case, the seed from the environment will be used.
Kaifeng Lu, kaifenglu@gmail.com
We use the following steps to obtain the hazard ratio estimate and confidence interval had there been no treatment switching:
Use IPE to estimate the causal parameter \(\psi\) based on the AFT model for the observed survival times for the experimental arm and the counterfactual survival times for the control arm, $$U_{i,\psi} = T_{C_i} + e^{\psi}T_{E_i}$$
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.
Use either the log-rank test p-value for the intention-to-treat (ITT)
analysis or bootstrap to construct the confidence interval for
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.
Michael Branson and John Whitehead. Estimating a treatment effect in survival studies in which patients switch treatment. Statistics in Medicine. 2002;21(17):2449-2463.
Ian R White. Letter to the Editor: Estimating treatment effects in randomized trials with treatment switching. Statistics in Medicine. 2006;25(9):1619-1622.
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)
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