Skip to contents

Iterative Parameter Estimation (IPE) for Treatment Switching

Source: R/ipe.R
ipe.Rd

Estimates the causal parameter by iteratively fitting an accelerated failure time (AFT) model to counterfactual unswitched survival times, and derives the adjusted hazard ratio from the Cox model using counterfactual unswitched survival times based on the estimated causal parameter.

Usage

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 = TRUE,
  low_psi = -2,
  hi_psi = 2,
  treat_modifier = 1,
  recensor = TRUE,
  admin_recensor_only = TRUE,
  autoswitch = TRUE,
  root_finding = "brent",
  alpha = 0.05,
  ties = "efron",
  tol = 1e-06,
  boot = FALSE,
  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.

  • 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 causal AFT model and 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.

low_psi

The lower limit of the causal parameter.

hi_psi

The upper limit of the causal parameter.

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.

root_finding

Character string specifying the univariate root-finding algorithm to use. Options are "brent" (default) for Brent's method, or "bisection" for the bisection method.

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 for the root finding algorithm.

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.

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.

  • 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".

  • pvalue: The two-sided p-value.

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

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

  • 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", base_cov, 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.

  • res_aft: The deviance residuals from the fitted AFT model.

  • 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.

  • 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.

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 iteratively fitting an AFT model to the observed survival times for the treatment arm and the counterfactual survival times for the control arm: $$U_{i,\psi} = T_{C_i} + e^{\psi}T_{E_i}$$

  • 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.

  • Obtain the confidence interval for the hazard ratio using either the ITT log-rank test p-value or bootstrap. When bootstrapping, the interval and p-value are derived from a t-distribution with n_boot - 1 degrees of freedom.

References

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.

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples


library(dplyr)
#> 
#> Attaching package: ‘dplyr’
#> The following objects are masked from ‘package:stats’:
#> 
#>     filter, lag
#> The following objects are masked from ‘package:base’:
#> 
#>     intersect, setdiff, setequal, union

# 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)

fit1
#>             n event_n event_pct switch_n switch_pct event_out_n event_out_pct
#> Control   500     169      33.8      189       37.8         142          28.4
#> Treatment 500     143      28.6        0        0.0         143          28.6
#>           imm
#> Control     0
#> Treatment   1
#> 
#>                            Estimate Lower 95% Upper 95%
#> Causal parameter psi       -0.183   -0.370    0.004    
#> Causal survival time ratio 1.201    0.996     1.448    
#> Hazard ratio (HR)          0.766    0.583     1.006    
#> P-value (log-rank)         0.0556                      

# 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)

fit2
#>             n event_n event_pct switch_n switch_pct event_out_n event_out_pct
#> Control    93      63      67.7       68       73.1          58          62.4
#> Treatment 100      67      67.0       25       25.0          63          63.0
#>           bras.f
#> Control       CT
#> Treatment    MTA
#> 
#>                            Estimate Lower 95% Upper 95%
#> Causal parameter psi       0.953    -0.457    2.363    
#> Causal survival time ratio 0.386    0.094     1.579    
#> Hazard ratio (HR)          2.716    0.620     11.900   
#> P-value (log-rank)         0.1851