Minimum sample size for survival‐outcome prediction models

Compute the minimum sample size required to develop a prediction model with a time-to-event (survival) outcome. As with the other wrappers, this uses a simulation-based learning-curve approach with Gaussian-process surrogate modelling to locate the smallest $n$ meeting the chosen performance criterion.

Usage

simulate_survival(
  signal_parameters,
  noise_parameters = 0,
  predictor_type = "continuous",
  binary_predictor_prevalence = NULL,
  large_sample_cindex,
  baseline_hazard = 1,
  censoring_rate,
  model = "coxph",
  metric = "calibration_slope",
  minimum_acceptable_performance,
  n_reps_total = 1000,
  mean_or_assurance = "assurance",
  ...
)

Arguments

signal_parameters: Integer. Number of candidate predictors associated with the outcome (i.e., true signal features).
noise_parameters: Integer. Number of candidate predictors not associated with the outcome (noise features). Default is 0.
predictor_type: Character string, either "continuous" or "binary". Specifies the type of simulated candidate predictors.
binary_predictor_prevalence: Optional numeric in (0, 1). Prevalence of the binary predictors when predictor_type = "binary". Ignored otherwise.
large_sample_cindex: Numeric in (0, 1). Expected large-sample C-index for the survival model (used to tune the data-generating mechanism so that the model attains this performance for very large $n$).
baseline_hazard: Numeric greater than 0. Baseline hazard level used by the data-generating mechanism (e.g., the constant hazard in an exponential baseline). Larger values imply shorter event times, all else equal.
censoring_rate: Numeric in [0, 1). Proportion of individuals expected to be censored in the simulated datasets (administrative or random censoring). Higher values imply fewer observed events for a fixed $n$.
model: Character string; currently "coxph" (Cox proportional hazards).
metric: Character string naming the performance metric used to assess the sample size; defaults to "calibration_slope". (Internally mapped to the engine's metric identifiers.)
minimum_acceptable_performance: Numeric. The target threshold $M^\\*$; the algorithm searches for the smallest $n$ meeting the chosen criterion with respect to this threshold.
n_reps_total: Integer. Total number of simulation replications used by the engine across the search.
mean_or_assurance: Character string, either "mean" or "assurance". Controls whether the minimum $n$ is defined by the mean-based criterion or the assurance-based criterion (with the assurance level $\delta$ controlled by the engine's defaults or additional arguments in ...).
...: Additional options passed to simulate_custom() (e.g., assurance level $\delta$, per-iteration settings).

Value

An object of class "pmsims" containing the estimated minimum sample size and simulation diagnostics (inputs, fitted GP curve, intermediate evaluations, and summary metrics).

Criteria

Two formulations are supported.

Mean-based: find the smallest $n$ such that the expected model performance exceeds the target $M^*$, i.e. $$\min_n \; \mathbb{E}_{D_n}\{ M \mid D_n \} \ge M^*.$$
Assurance-based: find the smallest $n$ such that the probability the performance exceeds $M^*$ is at least $\delta$ (e.g. 0.80), i.e. $$\min_n \; \mathbb{P}_{D_n}\!\left( M \mid D_n \ge M^* \right) \ge \delta.$$

Here, $M$ is the chosen performance metric and the probability/expectation is over repeated samples of training data of size $n$. The assurance criterion explicitly accounts for variability across training sets; models with higher variance typically require larger $n$ to satisfy it.

Examples

if (FALSE) { # \dontrun{
est <- simulate_survival(
  signal_parameters = 10,
  noise_parameters = 10,
  predictor_type = "continuous",
  large_sample_cindex = 0.70,
  baseline_hazard = 0.01,
  censoring_rate = 0.30,
  metric = "calibration_slope",
  minimum_acceptable_performance = 0.9,
  n_reps_total = 1000,
  mean_or_assurance = "assurance"
)
est
} # }