global.1m.ssc {rPowerSampleSize}

Sample Size Computation Based on a Global Procedure in the Context of Multiple Continuous Endpoints

Description

This function computes the sample size with a global method in the context of m multiple continuous endpoints. Two groups are considered: C for control and T for treatment. The clinical aim is to be able to detect a mean difference between the test and the control product for at least one endpoint among m. This method is based on a multivariate model with co-variates taking into account the correlations between the endpoints.

Usage

global.1m.ssc(method, mean.diff, sd, cor, v = NULL, M = NULL, 
power = 0.8, alpha = 0.05)

Arguments

method

either "Model" if no co-variates are involved and "Adj.Model" for a model with co-variates.

mean.diff

vector of the mean differences of the m endpoints between both groups under the alternative hypothesis.

sd

vector of the standard deviations of the m endpoints. These are assumed identical for both groups.

cor

correlation matrix between the endpoints. These are assumed identical for both groups.

v

v is a p\times1 vector whose l^{th} component is v_{l}=\bar{a}_{l}^C-\bar{a}_l^T, where p is the number of adjustment variables, and \bar{a}_{l}^{i} is the mean of the adjustment variable a_{l} for the group i, i = C, T.

M

M is a p\times p matrix with general term M_{l,l'}=\left(\overline{a_la_{l'}}^C-\bar{a}_l^C\bar{a}_{l'}^C\right)+\left(\overline{a_{l}a_{l'}}^T-\bar{a}_l^T\bar{a}_{l'}^T\right).

power

value which corresponds to the chosen power.

alpha

value which correponds to the chosen Type-I error rate bound.

Value

Sample size

The required sample size.

Author(s)

P. Lafaye de Micheaux, B. Liquet and J. Riou

References

Lafaye de Micheaux P., Liquet B., Marque S., Riou J. (2014). Power and Sample Size Determination in Clinical Trials With Multiple Primary Continuous Correlated Endpoints, Journal of Biopharmaceutical Statistics, 24, 378–397.

See Also

global.1m.analysis, indiv.1m.ssc, indiv.1m.analysis, bonferroni.1m.ssc

Examples

# Sample size computation for the global method 
global.1m.ssc(method = "Adj.Model", mean.diff = c(0.1, 0.2, 0.3), sd =
c(1, 1, 1), cor = diag(1, 3), v = -0.2, M = 0.46)

# Table 2 in our 2014 paper:
Sigma2 <- matrix(c(5.58, 2, 1.24, 2, 4.29, 1.59, 1.24, 1.59, 4.09), ncol = 3)
sd2 <- sqrt(diag(Sigma2))
cor2 <- diag(1 / sd2) %*% Sigma2 %*% diag(1 / sd2)
mu2 <- c(0.35, 0.28, 0.46)
m <- 3
global.1m.ssc(method = "Model", mean.diff = mu2, sd = sd2, cor = cor2)