Minimum sample size for continuous‐outcome prediction models

Compute the minimum sample size required to develop a prediction model with a continuous outcome. This wraps the same simulation engine as simulate_binary(), combining bisection search with Gaussian-process learning-curve modelling. From user inputs (maximum achievable performance, target performance, etc.) it constructs a data-generating function, model-fitting function, and metric function, then searches for the smallest $n$ meeting the chosen criterion.

Usage

simulate_continuous(
  signal_parameters,
  noise_parameters = 0,
  complexity = 1,
  data_control = NULL,
  maximum_achievable_rsquared,
  model = c("lm", "lasso", "ridge", "rf", "xgboost"),
  metric = "calibration_slope",
  target_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.
complexity: Integer in 1:4 selecting the data-generating signal structure (see Data control). Default 1.
data_control: Optional named list controlling the predictors (see Data control). Default NULL (generator defaults).
maximum_achievable_rsquared: Numeric in (0, 1). Maximum achievable $R^2$ with effectively unlimited data. This is used to calibrate the data-generating mechanism and is not the minimum acceptable threshold.
model: Character string specifying the modelling algorithm. One of "lm" (linear regression), "lasso", "ridge", "rf" (random forest), or "xgboost" (gradient-boosted trees). The machine-learning options are experimental.
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.)
target_performance: Numeric. Minimum acceptable value of the selected performance metric $M^*$; 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.

Data control

complexity selects the signal structure of the data-generating mechanism: 1 purely linear, 2 linear + quadratic, 3 linear + quadratic + interaction, 4 the Friedman function. data_control is an optional list fine-tuning the predictors:

nonlinear_strength: Numeric in [0, 1). Fraction of the signal variance carried by the nonlinear, linearly-inaccessible component. Applies to complexity 2 and 3 only; ignored (with a warning) for 1 and 4. If omitted, the generator's per-complexity default is used.
correlation: Numeric in [-1, 1]. Pairwise correlation among the candidate predictors. Default 0.3.
predictor_distribution: One of "normal", "uniform", "binary", "exponential", "lognormal", "t", "laplace". "binary" selects 0/1 predictors and requires binary_predictor_prevalence; any other value selects continuous predictors from that family. Default "normal".
binary_predictor_prevalence: Numeric in (0, 1). Prevalence of the binary predictors; required when predictor_distribution = "binary", ignored (with a warning) otherwise. Note: binary predictors are incompatible with complexity 2/3 because squaring a 0/1 variable returns itself.

Examples

if (FALSE) { # \dontrun{
est <- simulate_continuous(
  signal_parameters = 8,
  noise_parameters = 8,
  complexity = 3,
  maximum_achievable_rsquared = 0.50,
  model = "lm",
  metric = "calibration_slope",
  target_performance = 0.9,
  n_reps_total = 1000,
  mean_or_assurance = "assurance"
)
est
} # }