rPowerlib

rPowerlib computes statistical power for general linear multivariate models with fixed predictors and one or more Gaussian covariates.

Key Features:

• Noncentral F power approximation: Implements a noncentral F power approximation for fixed predictors in general linear multivariate models accommodating one or more Gaussian covariates.
• Taylor series expansion: Uses a Taylor series expansion of the matrix-variate beta distribution of type I to approximate the noncentrality parameter under alternative hypotheses.
• Monte Carlo simulation validation: Validates approximation methods via Monte Carlo simulations that model randomness in predictors and errors and that vary number of outcomes, hypothesis parameters, per-treatment sample size, and correlations between random predictors and outcomes.
• Computational efficiency: Produces single power calculations in milliseconds, substantially faster than empirical simulation methods (~3 minutes per calculation).

Scientific Applications:

• Power and sample size calculation: Calculation of statistical power and sample size for studies using general linear multivariate models with Gaussian covariates.
• Design of multivariate studies: Design and planning of experiments and studies involving multiple outcomes and fixed predictors.
• Hypothesis evaluation: Evaluation of complex multivariate hypotheses about fixed predictors in the presence of Gaussian covariates, including assessment across multiple outcomes.

Methodology:

Implements a noncentral F power approximation using a Taylor series expansion of the matrix-variate beta distribution of type I to approximate the noncentrality parameter, with validation by Monte Carlo simulations that model randomness in predictors and errors and vary outcomes, hypothesis parameters, per-treatment sample size, and correlations.