R: Sample size computation in simultaneous tests for ratios of...

n.ratio {mratios} | R Documentation

## Sample size computation in simultaneous tests for ratios of means

### 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)

[Package mratios version 1.3.17 Index]