msm: Marginal Structural Model (MSM) for Treatment Switching

In trtswitch: Treatment Switching

Marginal Structural Model (MSM) for Treatment Switching

Description

Excludes data after treatment switching when fitting the switching model to estimate the probabilities of not switching and then switching. The inverse of these probabilities (inverse probability of treatment weights) are then used as weights in a Cox model including data after switching to estimate the adjusted hazard ratio.

Usage

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

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. base_cov: The baseline covariates (excluding treat) used in the outcome model. numerator: The baseline covariates (excluding treat) used in the numerator switching model for stabilized weights. denominator: The baseline (excluding treat) and time-dependent covariates used in the denominator switching model.
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.
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 (excluding treat) and time-dependent covariates in the input data for the denominator switching model.
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.
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 treatment switching times.
firth	Whether the Firth's bias reducing penalized likelihood should be used.
flic	Whether to apply intercept correction to obtain more accurate predicted probabilities.
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.
treat_alt_interaction	Whether to include an interaction between randomized and alternative treatments in the outcome model when both randomized arms can switch to alternative treatment.
alpha	The significance level to calculate confidence intervals.
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 FALSE.
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)

Details

The hazard ratio and confidence interval under a no-switching scenario are obtained as follows:

• Exclude observations after treatment switch when fitting the switching model.

• Define crossover indicators for the last time interval of each subject.

• Fit the denominator switching model (and numerator model for stabilized weights) using a pooled logistic regression model to estimate the inverse probability of treatment weights (IPTWs).

  • The probability of remaining unswitched is calculated as 1 - \hat{p}_{\text{switch}} and multiplied over time before treatment switch.

  • At the time of switching, this product is multiplied by the predicted probability of switching.

  • After treatment switch, the IPTW remains constant.

  • The inverse of the probability at the start of each interval is used as the interval weight.

• Fit a weighted Cox model to the outcome survival times, including data after treatment switch, to estimate the hazard ratio.

• Construct the p-value and confidence interval for the hazard ratio using either robust sandwich variance or bootstrapping. When bootstrapping is used, the confidence interval and p-value are based on a t-distribution with n_boot - 1 degrees of freedom.

Value

A list with the following components:

• pvalue: The two-sided p-value.

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

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

• data_switch: A list of input data for the switching models by treatment group. The variables include id, stratum, "tstart", "tstop", "cross", denominator, swtrt, and swtrt_time. In addition, stratum variables are converted to dummy variables, and natural cubic spline basis variables are created for the visit-specific intercepts.

• 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. The variables include id, stratum, "tstart", "tstop", "event", "treated", "crossed", "unstablized_weight", "stabilized_weight", base_cov, and treat. If treat_alt_interaction is TRUE, the data set also includes the "treated_crossed" variable.

• weight_summary: A data frame summarizing the weights by treatment arm.

• km_outcome: The Kaplan-Meier estimates of the survival functions for the treatment and control groups based on the weighted outcome data truncated at time of treatment switching.

• lr_outcome: The log-rank test results for the treatment effect based on the weighted outcome data truncated at time of treatment switching.

• fit_outcome: The fitted outcome Cox model.

• fail: Whether a model fails to converge.

• 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.

Author(s)

Kaifeng Lu, [e-mail]

References

James M. Robins, Miguel Angel Hernan, and Babette Brumback. Marginal structural models and causal inference in epidemiology. Epidemiology. 2000;11(5):550-560.

Miguel Angel Hernan, Babette Brumback, and James M. Robins. Marginal structural modesl to estimate the causual effect of zidovudine on the survival of HIV-positive men. Epidemiology. 2000;11(5):561-570.

Jing Xu, Guohui Liu, and Bingxia Wang. Bias and Type I error control in correcting treatment effect for treatment switching using marginal structural models in Phase III oncology trials. Journal of Biopharmaceutical Statistics. 2022;32(6):897-914.

Examples

library(dplyr)

sim1 <- tssim(
  tdxo = 1, coxo = 1, allocation1 = 1, allocation2 = 1,
  p_X_1 = 0.3, p_X_0 = 0.3, 
  rate_T = 0.002, beta1 = -0.5, beta2 = 0.3, 
  gamma0 = 0.3, gamma1 = -0.9, gamma2 = 0.7, gamma3 = 1.1, gamma4 = -0.8,
  zeta0 = -3.5, zeta1 = 0.5, zeta2 = 0.2, zeta3 = -0.4, 
  alpha0 = 0.5, alpha1 = 0.5, alpha2 = 0.4, 
  theta1_1 = -0.4, theta1_0 = -0.4, theta2 = 0.2,
  rate_C = 0.0000855, accrualIntensity = 20/30,
  fixedFollowup = FALSE, plannedTime = 1350, days = 30,
  n = 500, NSim = 100, seed = 314159)

fit1 <- msm(
  sim1[[1]], id = "id", tstart = "tstart", 
  tstop = "tstop", event = "event", treat = "trtrand", 
  swtrt = "xo", swtrt_time = "xotime", 
  base_cov = "bprog", numerator = "bprog", 
  denominator = c("bprog", "L"), 
  ns_df = 3, swtrt_control_only = TRUE, boot = FALSE)
  
fit1

trtswitch documentation built on Jan. 10, 2026, 5:08 p.m.