type1Error: Empirical Type I Error at the Least-Favorable Null

In SimTOST: Sample Size Estimation for Bio-Equivalence Trials Through Simulation

Empirical Type I Error at the Least-Favorable Null

Description

Generates a boundary-null configuration and estimates its empirical rejection probability using simPower(). The comparator convention is c(test, reference). For normal ROM and count RR, a lower-bound null sets mean(test) / mean(reference) = L. For log-normal ROM, the boundary is imposed on the log-analysis scale used by the test; this coincides with the arithmetic mean ratio when the two arms have the same coefficient of variation.

Usage

type1Error(
  null = c("lower", "upper", "both"),
  x = NULL,
  comparator = NULL,
  endpoint = NULL,
  joint = FALSE,
  conf.level = 0.95,
  ...
)

Arguments

null	Boundary to evaluate: "lower", "upper", or "both".
x	Optional existing simss or simpower object. When supplied, its design and outcome parameters are reused; arguments in ... override stored settings such as n or nsim.
comparator	Optional comparator name identifying the boundary scenario when joint = FALSE. It must be one of the names in list_comparator; by default, the first comparator is used. It is ignored when joint = TRUE, because joint mode evaluates all comparators.
endpoint	Optional endpoint identifying the boundary component when joint = FALSE. It is available for the all-endpoints-required case (k equal to the number of endpoints), where one endpoint is placed on the boundary. For k smaller than the number of endpoints, use joint = TRUE so that all composite boundary configurations are evaluated.
joint	Logical. If TRUE, evaluate every comparator and every endpoint partial-null configuration and return the joint Type I-error result for each complete-trial decision. For a comparator with m endpoints and an at-least-k rule, all boundary counts from m - k + 1 through m are evaluated. Defaults to FALSE for backward compatibility.
conf.level	Confidence level for the simultaneous one-sided Monte Carlo upper bound across the evaluated joint scenarios. Defaults to 0.95.
...	Arguments passed to simPower(). The call must include the outcome parameters, comparator definitions, and equivalence margins.

Details

Comparators use the convention c(test, reference). For ROM, the tested estimand is test / reference; for DOM it is test - reference. With log-normal ROM, the test is performed after converting the supplied original-scale means and variances to the log-analysis scale, so the boundary scenario is calibrated on that scale. For count rate ratios, the analogous midpoint is sqrt(L * U) on the rate-ratio scale because the test is performed on the log-rate-ratio scale. Absolute rates and dispersion remain nuisance parameters, so this midpoint should be supplemented by a grid or optimization when a global supremum is required. If a comparator has m endpoints and requires k endpoints to pass, a composite null configuration has at least m - k + 1 non-equivalent endpoints. With joint = TRUE, all endpoint subsets with boundary counts from m - k + 1 through m, and all lower/upper direction combinations, are evaluated, while the complete decision still requires the k-of-m rule for every comparator in the same simulated trial. The returned joint object includes a Bonferroni simultaneous one-sided Monte Carlo upper bound for the maximum scenario probability.

Value

For null = "lower" or "upper", an object of class type1error containing the empirical Type I error in type1_error and its Monte Carlo interval. For null = "both", a named list containing the lower- and upper-bound results. With joint = TRUE, a type1error_joint object containing one joint result for every valid comparator, endpoint-subset, boundary-direction combination is returned.

SimTOST documentation built on Oct. 9, 2026, 5:07 p.m.