n.ratio {mratios} | R Documentation |
Computes the sample sizes required in simultaneous tests for non-inferiority (or superiority) based on relative margins in multiple comparisons with a control.
n.ratio(m, rho, Power, CV0, rho.star, alpha, Min.power = TRUE)
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 |
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 + rho^2)/((rho - dot(rho))^2))*(CV0^2), where C_1 is the lower 1-alpha equi-coordinate percentage point of an m-variate normal distribution and C_2 is 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, rho < dot(rho), where rho < 1 for non-inferiority and rho > 1 for superiority testing. Whereas, if small response values indicate better treatment benefit, dot(rho) < rho, where rho > 1 for non-inferiority and rho < 1 for superiority testing.
Gemechis Dilba
Dilba, G., Guiard, V., and Bretz, F.: On the efficiency of ratio formatted hypotheses (submitted).
# # Example 1: Sample size calculation in tests for non-inferiority (two-sample case) # (Laster and Johnson (2003), Statatistics 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), Statatistics 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)