powertools (version 1.0.0)

altprimary: Power calculation for multiple alternative (at least one) primary continuous endpoints assuming known covariance matrix

Description

Calculates power and sample size for the case of comparing two groups on the means of K continuous endpoints and concluding that the trial is a 'success' if the null hypothesis is rejected for at least one of the K endpoints. All mean differences must be specified as positive; the scale for some outcomes may need to be reversed to meet this condition. All tests are assumed to be upper-tailed, one-sided tests. Can solve for power, n1, n.ratio or alpha.

To use a Bonferroni correction for multiple comparisons, specify alpha as the desired familywise error rate (FWER) divided by K. For example, for one-sided FWER of 0.025 and K = 2 endpoints, specify alpha as 0.0125.

Either sd and rho or Sigma must be specified.

A known covariance matrix is assumed, which can result in a slight overestimate of power and underestimate of required sample size.

Usage

altprimary(
  K,
  n1 = NULL,
  n.ratio = 1,
  delta = NULL,
  Sigma,
  sd,
  rho,
  alpha = 0.025,
  power = NULL,
  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 (type 1 error rate) for each test; defaults to 0.025. A one-sided test is assumed.

power

The specified level of power.

v

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

Details

Sozu T, Sugimoto T, Hamasaki T, Evans SR (2015) Sample Size Determination in Clinical Trials with Multiple Endpoints. Springer International Publishing, Switzerland.

Examples

altprimary(K = 2, n1 = 100, delta = c(0.4, 0.5), sd = c(1, 1), rho = 0.3,
alpha = 0.025 / 2, power = NULL)

Sigma <- matrix(c(1, 0.3, 0.3, 0.3, 1, 0.3, 0.3, 0.3, 1), nrow = 3, ncol = 3)
altprimary(K = 3, n1 = 100, delta = c(0.2, 0.2, 0.4), Sigma = Sigma,
   alpha = 0.025 / 3, power = NULL)