Simulate Event Times for Each Participant from a Weibull Proportional Hazards Regression Model

sim_weib_ph(weibull_ph_mod, samp_df, cond_drift = 0, cond_trt_effect = 0)

Arguments

weibull_ph_mod: survreg object corresponding to a Weibull proportional hazards model fit using the external data
samp_df: Data frame of covariates corresponding to the sample arm (control or treated) for which event times should be simulated. The column names should correspond to the covariate names in the survreg object.
cond_drift: Optional value of the conditional drift by which the intercept in the Weibull proportional hazards regression model should be increased/decreased to incorporate the impact of unmeasurable sources of drift. Default is 0.
cond_trt_effect: Optional value of the conditional treatment effect by which the intercept in the Weibull proportional hazards regression model should be increased/decreased if simulating event data for a treated arm. Default is 0.

Value

Vector of simulated event times from a Weibull proportional hazards regression model

Details

Simulate the event times for each participant using a Weibull proportional hazards (PH) regression model. The "true" parameter values for the Weibull shape $\alpha$ and the regression coefficients $\boldsymbol{\beta}$ are assumed to be equal to the parameter estimates from a survreg object (weibull_ph_mod) fit using external data (note that the Weibull shape parameter $\alpha$ is defined as the inverse of the scale parameter reported by survreg).

For participant $i$, let $y_i$ denote the time-to-event random variable and $\boldsymbol{x}_i = \{x_{i,1}, \ldots, x_{i,p}\}$ the vector of $p$ covariates (row $i$ of samp_df) that correspond to the $(p+1)$-dimensional vector of regression coefficients $\boldsymbol{\beta}$. The density function of the Weibull PH regression model is

$$f(y_i \mid \boldsymbol{x}_i, \alpha, \boldsymbol{\beta}, \delta, \gamma) = \left( \frac{\alpha}{\sigma_i} \right) \left( \frac{y_i}{\sigma_i} \right)^{\alpha - 1} \exp \left( -\left( \frac{y_i}{\sigma_i} \right)^\alpha \right),$$

where $-\log(\sigma_i) = \beta_0 + \beta_1 x_{i,1} + \ldots + \beta_p x_{i,p} + \delta + \gamma$. Here, $\delta$ and $\gamma$ denote the conditional drift (cond_drift) and conditional treatment effect (cond_trt_effect), respectively, that can be calculated using calc_cond_weibull() for desired values of the marginal drift and marginal treatment effect.

Examples

library(dplyr)
library(survival)
# Model "true" regression coefficients and shape parameter using the external data
weibull_ph_mod <- survreg(Surv(y, event) ~ cov1 + cov2 + cov3 + cov4, data = ex_tte_df,
                          dist = "weibull")

# Sample covariates for internal control arm via bootstrap from external data
samp_int_ctrl <- bootstrap_cov(ex_tte_df, n = 100) |>
  select(c(cov1, cov2, cov3, cov4))     # keep only covariate columns
tte_dat <- sim_weib_ph(weibull_ph_mod, samp_df = samp_int_ctrl)