sign_Mielke: Simulated Test Statistic for Noninferiority/Equivalence...

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

Simulated Test Statistic for Noninferiority/Equivalence Trials

Description

Simulates test statistics for multiple hypothesis testing in biosimilar development, following the approach described by Mielke et al. (2018). It calculates the necessary sample size for meeting equivalence criteria across multiple endpoints while considering correlation structures and applying multiplicity adjustments.

Usage

sign_Mielke(
  N,
  m,
  k,
  R,
  sigma,
  true.diff,
  equi.tol = log(1.25),
  design,
  alpha = 0.05,
  adjust = "no"
)

Arguments

N	Integer specifying the number of subjects per sequence.
m	Integer specifying the number of endpoints.
k	Integer specifying the number of endpoints that must meet equivalence to consider the test successful.
R	Matrix specifying the correlation structure between endpoints. This should be an m x m matrix, e.g., generated using variance.const.corr().
sigma	Numeric specifying the standard deviation of endpoints. Can be a vector of length m (one per endpoint) or a single value. In a 2x2 crossover design, this represents within-subject variance. In a parallel-group design, it represents the treatment group standard deviation.
true.diff	Numeric specifying the assumed true difference between test and reference. Can be a vector of length m or a single value.
equi.tol	Numeric specifying the equivalence margins. The interval is defined as (-equi.tol, +equi.tol).
design	Character specifying the study design. Options are "22co" for a 2x2 crossover design or "parallel" for a parallel-group design.
alpha	Numeric specifying the significance level.
adjust	Character specifying the method for multiplicity adjustment. Options include "no" for no adjustment, "bon" for Bonferroni correction, "k" for Mielke's weak k-adjustment, and "t" for the strong k-out-of-m adjustment. Legacy "pc" and "partial-conjunction" labels are accepted as aliases for "t".

Details

This function is designed for multiple-endpoint clinical trials, where success is defined as meeting equivalence criteria for at least a subset of tests. Simulated test statistics are based on multivariate normal distribution assumptions, and the function supports k-out-of-m success criteria for regulatory approval.

The adjustment options follow the multiple-endpoint framework of Mielke et al. (2018). In particular, adjust = "k" uses the weak k-adjustment k * alpha / m, whereas adjust = "t" uses the strong k-out-of-m adjustment alpha / (m - k + 1) for partial null configurations. This distinction is particularly relevant for biosimilar studies, where sample size estimation must account for multiple comparisons across endpoints, doses, or populations.

Value

An object of class simss_mielke. It contains the legacy fields SS and power.a, together with n_per_sequence, n_total, power, and the target and input parameters. Use summary() for a data-frame summary, print() for a concise report, or as.numeric() to extract SS.

References

Kong, L., Kohberger, R. C., & Koch, G. G. (2004). Type I Error and Power in Noninferiority/Equivalence Trials with Correlated Multiple Endpoints: An Example from Vaccine Development Trials. Journal of Biopharmaceutical Statistics, 14(4), 893–907.

Lehmann, E. L., & Romano, J. P. (2005). Generalizations of the Familywise Error Rate. The Annals of Statistics, 33(2), 1138–1154.

Mielke, J., Jones, B., Jilma, B., & König, F. (2018). Sample Size for Multiple Hypothesis Testing in Biosimilar Development. Statistics in Biopharmaceutical Research, 10(1), 39–49.

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