Getting Started with simtte

Weibull Model

The Weibull hazard function is:

\[h(t) = \lambda \cdot \gamma \cdot t^{\gamma - 1}\]

where \(\lambda = \exp(\mu + \mathbf{x}'\boldsymbol{\beta})\) is the scale and \(\gamma\) is the shape parameter. The survival function \(S(t) = \exp(-\lambda t^\gamma)\) has a closed form, so simtte evaluates it directly on the reported time grid rather than by numerically integrating the survival ODE; this is numerically robust across shape and parameter regimes.

M-Spline Model

For the flexible model, the baseline hazard is represented as a linear combination of M-spline basis functions, allowing complex hazard shapes. The hazard value reported at a given time applies from that time until the next reported time (a last-observation-carried-forward convention), giving a piecewise-constant hazard on the reported grid.

Inverse Transform Sampling

Given a survival function \(S(t)\) reported on the grid supplied via time, we draw \(U \sim \text{Uniform}(0, 1)\) and find the first reported time \(t^*\) such that \(S(t^*) \le U\) (event_time_method = "grid", the default). Setting event_time_method = "log_survival" instead refines a crossing that falls strictly between two reported points by linearly interpolating cumulative hazard between them; see “Event-Time Interpolation” below.

Weibull Example

set.seed(42)
lp <- matrix(rnorm(50, 0, 0.5), nrow = 50)
result <- sim_tte(
  pi = lp,
  mu = -1,
  coefs = 1.1,
  time = seq(0.1, 100, by = 0.1),
  type = "weibull",
  end_time = 100
)
head(result)

M-Splines Example

data("ms_data")
lp <- matrix(runif(nrow(ms_data$basis)), nrow = nrow(ms_data$basis))
result <- sim_tte(
  pi = lp,
  mu = ms_data$mu,
  basis = ms_data$basis,
  coefs = ms_data$coefs,
  time = ms_data$time,
  type = "ms"
)
head(result)

Event-Time Interpolation

event_time_method defaults to "grid", which preserves the original grid-based event-time resolution shown above. Setting it to "log_survival" refines a crossing that falls strictly between two reported time points; the underlying survival trajectory is unchanged, and so is event/censoring classification for the same seed:

set.seed(1)
result_grid <- sim_tte(
  pi = lp, mu = -1, coefs = 1.1,
  time = seq(0.1, 100, by = 0.1),
  type = "weibull", end_time = 100,
  event_time_method = "grid"           # default
)

set.seed(1)
result_interp <- sim_tte(
  pi = lp, mu = -1, coefs = 1.1,
  time = seq(0.1, 100, by = 0.1),
  type = "weibull", end_time = 100,
  event_time_method = "log_survival"   # sub-grid refinement
)

# Same seed and trajectory -> identical event/censoring classification.
identical(result_grid$sim_status, result_interp$sim_status)

# sim_time can differ only where the crossing falls strictly between
# two reported grid points.
head(cbind(grid = result_grid$sim_time, log_survival = result_interp$sim_time))