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Rank Preserving Structural Failure Time Model (RPSFTM) for Treatment Switching

Source: R/rpsftm.R
rpsftm.Rd

Estimates the causal treatment effect parameter using g-estimation based on the log-rank test, Cox model, or parametric survival/accelerated failure time (AFT) model. The method uses counterfactual untreated survival times to estimate the causal parameter and derives the adjusted hazard ratio from the Cox model using counterfactual unswitched survival times.

Usage

rpsftm(
  data,
  id = "id",
  stratum = "",
  time = "time",
  event = "event",
  treat = "treat",
  rx = "rx",
  censor_time = "censor_time",
  base_cov = "",
  psi_test = "logrank",
  aft_dist = "weibull",
  strata_main_effect_only = TRUE,
  low_psi = -2,
  hi_psi = 2,
  n_eval_z = 101,
  treat_modifier = 1,
  recensor = TRUE,
  admin_recensor_only = TRUE,
  autoswitch = TRUE,
  gridsearch = 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 outcome Cox model. These covariates will also be used in the Cox model for estimating psi when psi_test = "phreg" and in the parametric survival regression/AFT model for estimating psi when psi_test = "lifereg".

psi_test

The survival function to calculate the Z-statistic, e.g., "logrank" (default), "phreg", or "lifereg".

aft_dist

The assumed distribution for time to event for the AFT model when psi_test = "lifereg". 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.

n_eval_z

The number of points between low_psi and hi_psi (inclusive) at which to evaluate the Z-statistics.

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.

gridsearch

Whether to use grid search to estimate the causal parameter psi. Defaults to TRUE, otherwise, a root finding algorithm will be used.

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_roots: Vector of psi values at which the Z-statistic is zero, identified using grid search and linear interpolation.

  • psi_CI: The confidence interval for psi.

  • psi_CI_type: The type of confidence interval for psi, i.e., "grid search", "root finding", 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.

  • eval_z: A data frame containing the Z-statistics for treatment effect 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.

  • 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_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 \(\psi\) using g-estimation based on the log-rank test (default), Cox model, or parametric survival/AFT model, using counterfactual untreated survival times for both arms: $$U_{i,\psi} = T_{C_i} + e^{\psi}T_{E_i}$$

  • 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.

If grid search is used to estimate \(\psi\), the estimated \(\psi\) is the one with the smallest absolute value among those at which the Z-statistic is zero based on linear interpolation. If root finding is used, the estimated \(\psi\) is the solution to the equation where the Z-statistic is zero.

References

James M. Robins and Anastasios A. Tsiatis. Correcting for non-compliance in randomized trials using rank preserving structural failure time models. Communications in Statistics. 1991;20(8):2609-2631.

Ian R. White, Adbel G. Babiker, Sarah Walker, and Janet H. Darbyshire. Randomization-based methods for correcting for treatment changes: Examples from the CONCORDE trial. Statistics in Medicine. 1999;18(19):2617-2634.

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples


library(dplyr)

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

data <- immdef %>% mutate(rx = 1-xoyrs/progyrs)

fit1 <- rpsftm(
  data, id = "id", time = "progyrs", event = "prog", treat = "imm",
  rx = "rx", censor_time = "censyrs", 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       -0.187   -0.347    0.004    
#> Causal survival time ratio 1.206    0.996     1.415    
#> Hazard ratio (HR)          0.759    0.572     1.007    
#> 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 <- rpsftm(
  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"),
  low_psi = -3, hi_psi = 3, 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          62          62.0
#>           bras.f
#> Control       CT
#> Treatment    MTA
#> 
#>                            Estimate Lower 95% Upper 95%
#> Causal parameter psi       1.013    -0.338    2.095    
#> Causal survival time ratio 0.363    0.123     1.401    
#> Hazard ratio (HR)          2.820    0.609     13.062   
#> P-value (log-rank)         0.1851