powertools (version 1.0.0)

coprimary.t: Power calculations for multiple co-primary continuous endpoints assuming unknown covariance matrix

Description

Computes power for test involving multiple co-primary continuous endpoints, assuming that the covariance matrix (variances and covariances between endpoints) is unknown and therefore t-based test statistics will be used. Studies with co-primary endpoints use “all-or-none” testing procedures and only declare the trial to be a “success” if all endpoints are affirmed. All true mean differences must be positive (the scale for some outcomes may need to be reversed to meet this condition) and upper-tailed one-sided tests are assumed. For known covariance matrix, see coprimary.z.

Either sd and rho or Sigma must be specified.

Usage

coprimary.t(
  K,
  n1 = NULL,
  n.ratio = 1,
  delta = NULL,
  Sigma,
  sd,
  rho,
  alpha = 0.025,
  power = NULL,
  M = 10000,
  v = FALSE
)

Value

A list of the arguments (including the computed one).

Arguments

K

The number of endpoints.

n1

The sample size for group 1.

n.ratio

The ratio n2/n1 between the sample sizes of two groups; defaults to 1 (equal group sizes).

delta

A vector of length K of the true mean differences mu1k - mu2k; must all be positive.

Sigma

The covariance matrix of the K outcomes, of dimension K x K.

sd

A vector of length K of the standard deviations of the K outcomes.

rho

A vector of length 0.5K(K-1) of the correlations among the K outcomes.

alpha

The significance level or type 1 error rate; defaults to 0.025. A one-sided test is assumed.

power

The specified level of power.

M

Number of simulated values for the covariance matrix, simulated from Wishart distribution. Defaults to 10000.

v

Either TRUE for verbose output or FALSE to output computed argument only.

Details

See Crespi et al. (2025) for more details. This function is based on the power.unknown.var function from the mpe R package and material from Sozu T, Sugimoto T, Hamasaki T, Evans SR. (2015) Sample Size Determination in Clinical Trials with Multiple Endpoints. Springer International Publishing, Switzerland.

This function can be computationally intensive and slow when solving for sample size. Smaller M can descrease computation time. The function coprimary.z provides a close approximation and is much faster.

Examples

# M is set to 10 in these examples to reduce runtime;
# please increase M or do not specify M (defaults to M = 10000) for optimal results
coprimary.t(K = 2, n1 = 100, delta = c(0.4, 0.5), sd = c(1, 1), rho = 0.3, alpha = 0.025,
power = NULL, M = 10)

Sigma <- matrix(c(1, 0.3, 0.3, 0.3, 1, 0.3, 0.3, 0.3, 1), nrow = 3, ncol = 3)
coprimary.t(K = 3, n1 = 200, delta = c(0.2, 0.3, 0.4), Sigma = Sigma, alpha = 0.025,
power = NULL, M = 10)