Uses the marginal structural model (MSM) method to obtain the hazard ratio estimate of the Cox model to adjust for treatment switching.
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,
firth = FALSE,
flic = FALSE,
ns_df = 3,
stabilized_weights = TRUE,
trunc = 0,
trunc_upper_only = TRUE,
swtrt_control_only = TRUE,
treat_alt_interaction = FALSE,
alpha = 0.05,
ties = "efron",
boot = TRUE,
n_boot = 1000,
seed = NA
)A list with the following components:
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 "Cox model" or "bootstrap".
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.
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",
"unstablized_weight", "stabilized_weight",
base_cov, and treat.
fit_outcome: The fitted outcome Cox model.
fail: Whether a model fails to converge.
settings: A list with the following components:
strata_main_effect_only: Whether to only include the
strata main effects in the logistic regression switching model.
firth: Whether the Firth's bias reducing penalized likelihood
should be used.
flic: Whether to apply intercept correction to obtain more
accurate predicted probabilities.
ns_df: Degrees of freedom for the natural cubic spline.
stabilized_weights: Whether to use the stabilized weights.
trunc: The truncation fraction of the weight distribution.
trunc_upper_only: Whether to truncate the weights from the
upper end of the distribution only.
swtrt_control_only Whether treatment switching occurred only
in the control group.
treat_alt_interaction Whether to include an interaction
between randomized and alternative treatment in the outcome model.
alpa: The significance level to calculate confidence
intervals.
ties: The method for handling ties in the Cox model.
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.
fail_boots: The indicators for failed bootstrap samples
if boot is TRUE.
hr_boots: The bootstrap hazard ratio estimates if boot is
TRUE.
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.
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 tstart variable in the input data.
The name of the tstop 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 swtrt variable in the input data.
The name of the swtrt_time variable in the input data.
The names of baseline covariates (excluding treat) in the input data for the Cox model.
The names of baseline covariates (excluding treat) in the input data for the numerator switching model for stabilized weights.
The names of baseline (excluding treat) and time-dependent covariates in the input data for the denominator switching model.
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.
Whether the Firth's bias reducing penalized likelihood should be used.
Whether to apply intercept correction to obtain more accurate predicted probabilities.
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 artificial censoring times due to treatment switching.
Whether to use the stabilized weights.
The default is TRUE.
The truncation fraction of the weight distribution. Defaults to 0 for no truncation in weights.
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.
Whether treatment switching occurred only in
the control group. The default is TRUE.
Whether to include an interaction between randomized and alternative treatment in the outcome model when both randomized arms can switch to alternative treatment.
The significance level to calculate confidence intervals. The default value is 0.05.
The method for handling ties in the Cox model, either "breslow" or "efron" (default).
Whether to use bootstrap to obtain the confidence
interval for hazard ratio. Defaults to TRUE.
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:
Exclude observations after treatment switch for the switch model.
Set up the crossover indicators for the last time interval for each subject.
Fit the denominator switching model (and the numerator switching model for stabilized weights) to obtain the inverse probability of censoring weights using a pooled logistic regression model. The probability of remaining uncensored (i.e., not switching) will be calculated by subtracting the predicted probability of switching from 1. The probabilities of remaining unswitched will be multiplied over time before treatment switching, at which time point, it will be multiplied by the probability of treatment switching. The inverse probability of treatment weighting will not change after treatment switching.
Fit the weighted Cox model to the censored outcome survival times to obtain the hazard ratio estimate.
Use either robust sandwich variance or bootstrapping to construct the
p-value and confidence interval for the 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.
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.
sim1 <- tssim(
tdxo = 0, coxo = 0, p_R = 0.5, 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, followup = 20, days = 30,
n = 500, NSim = 100, seed = 314159)
fit1 <- msm(
sim1[[1]], id = "id", tstart = "tstart",
tstop = "tstop", event = "Y", 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)
c(fit1$hr, fit1$hr_CI)
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