n.ratio: Sample size computation in simultaneous tests for ratios of...

In mratios: Ratios of Coefficients in the General Linear Model

Description

Computes the sample sizes required in simultaneous tests for non-inferiority (or superiority) based on relative margins in multiple comparisons with a control.

Usage

n.ratio(m, rho, Power, CV0, rho.star, alpha, Min.power = TRUE)

Arguments

m	number of comparisons with a control group
rho	relative non-inferiority (or superiority) margin
Power	given power (1-beta)
CV0	coefficient of variation of the control group
rho.star	the percentage (of the mean of the control group) to be detected
alpha	familywise error rate
Min.power	if set to TRUE (by default), the minimal power will be controlled, otherwise complete power

Details

The sample sizes are computed at the least favourable configurations, based on the assumption of no prior information regarding the true configuration of the ratios under the alternative hypotheses. The formula is

n = ((C_1 + C_2)^2) (1 + ρ^2)/((ρ - ρ^*)^2) CV0^2 ,

where C_1 is the lower 1-α equi-coordinate percentage point of an m-variate normal distribution and C_2 is the quantile of univariate (multivariate) normal distribution depending on the type of power controlled. In tests for non-inferiority (or superiority) with large response values indicating better treatment benefit, ρ < ρ^* , where ρ < 1 for non-inferiority and ρ > 1 for superiority testing. Whereas, if small response values indicate better treatment benefit, ρ^* < ρ, where ρ > 1 for non-inferiority and ρ < 1 for superiority testing.

Author(s)

Gemechis Dilba Djira

References

Dilba, G., Bretz, F., Hothorn, L.A., and Guiard, V. (2006). Power and sample size computations in simultaneous tests for non-inferiority based on relative margins. Statistics in Medicine 25, 1131-1147.

Examples

  #
  #  Example 1: Sample size calculation in tests for non-inferiority
  #  (two-sample case)(Laster and Johnson (2003),
  #  Statistics in Medicine 22:187-200)

     n.ratio(m=1, rho=0.8, Power=0.8, CV0=0.75, rho.star=1,
     alpha=0.05)


  #
  #  Example 2: Sample size calculation in simultaneous tests for
  #  non-inferiority
  #  (Dilba et al. (2006), Statistics in Medicine 25:1131-1147)

     n.ratio(m=3, rho=0.7, Power=0.8, CV0=0.5, rho.star=0.95,
     alpha=0.05)


  #
  #  Example 3: Controlling complete power
  #

     n.ratio(m=5, rho=1.2, Power=0.8, CV0=0.2, rho.star=1.40,
         alpha=0.05, Min.power=FALSE)

mratios documentation built on July 8, 2020, 6:43 p.m.