# indiv.1m.ssc: Sample size computation with an individual testing procedure... In rPowerSampleSize: Sample Size Computations Controlling the Type-II Generalized Family-Wise Error Rate

## Description

This function computes the sample size with an individual testing procedure in the context of multiple continuous endpoints. This method, based on the Union-Intersection testing procedure, allows one to take into account the correlation between the different endpoints in the computation of the sample size.

## Usage

 1 2 indiv.1m.ssc(method, ES, cor, power = 0.8, alpha = 0.05, alternative = "two.sided", tol = 1e-04, maxiter = 1000, tol.uniroot = 1e-04) 

## Arguments

 method description of the covariance matrix estimation. Two choices are possible: "Unknown" (normality assumption and unknown covariance matrix) and "Asympt" (asymptotic context). ES vector indicating the values of the effect size. The definition of the effect size is presented in the "Details" section. cor matrix indicating the correlation matrix between the endpoints. power value which corresponds to the chosen power. alpha value which correponds to the chosen Type-I error rate bound. alternative character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". tol the desired accuracy (convergence tolerance) for our algorithm. maxiter maximum number of iterations. tol.uniroot desired accuracy (convergence tolerance) for the uniroot.integer function.

## Details

ES: The effect size definition parameter for the k^{th} endpoint is defined as \frac{μ^{T}_{k}-μ^{C}_{k}}{σ^{*}_{k}}, where σ^{*}_{k} refers to the standard deviation of the population from which the different treatment groups were taken and μ^{T}_{k}-μ^{C}_{k} is the true mean difference between the test and the control group for the k^{th} group. We consider that: σ^{*}_{k}=\frac{σ^{2}_{k,T}+σ^{2}_{k,C}}{2}.

## Value

 Adjusted Type-I error rate adjusted Type-I error rate. 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.

global.1m.ssc, global.1m.analysis, indiv.1m.analysis, bonferroni.1m.ssc
  1 2 3 4 5 6 7 8 9 10 # Sample size computation for the individual method indiv.1m.ssc(method = "Known", ES = c(0.1, 0.2, 0.3), cor = diag(1, 3)) # 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 indiv.1m.ssc(method = "Known", ES = mu2 / sd2, cor = cor2)