Description Usage Arguments Details Value References See Also Examples
View source: R/power.unknown.var.R
The function calculates either sample size or power for continuous multiple co-primary endpoints with unknown covariance.
1 2 3 |
K |
number of co-primary endpoints |
n |
optional: sample size |
delta |
expected effect size (length |
Sigma |
unknown covariance matrix (dimension |
SD |
unknown standard deviations (length |
rho |
unknown correlations (length |
sig.level |
significance level (Type I error probability) |
power |
optional: power of test (1 minus Type II error probability) |
M |
Number of replications for the required simulations. |
min.n |
Starting point of search interval for sample size |
max.n |
End point of search interval for sample size, must be larger than |
tol |
the desired accuracy for |
use.uniroot |
Finds one root of one equation |
The function can be used to either compute sample size or power for continuous multiple co-primary endpoints with unknown covariance. The implementation is based on the formulas given in the references below.
The null hypothesis reads mu_Tk-mu_Ck <= 0 for at least one k in {1,...,K} where Tk is treatment k, Ck is control k and K is the number of co-primary endpoints.
One has to specify either n
or power
, the other parameter is
determined. An approach to calculate sample size n
, is to first call
power.known.var
and use the result as min.n
. The input for
max.n
must be larger then min.n
. Moreover, either covariance
matrix Sigma
or standard deviations SD
and correlations rho
must be given.
The sample size is calculated by simulating Wishart distributed random matrices, hence the results include a certain random variation.
Object of class power.mpe.test
, a list of arguments (including the
computed one) augmented with method and note elements.
Sugimoto, T. and Sozu, T. and Hamasaki, T. (2012). A convenient formula for sample size calculations in clinical trials with multiple co-primary continuous endpoints. Pharmaceut. Statist., 11: 118-128. doi:10.1002/pst.505
Sozu, T. and Sugimoto, T. and Hamasaki, T. and Evans, S.R. (2015). Sample Size Determination in Clinical Trials with Multiple Endpoints. Springer Briefs in Statistics, ISBN 978-3-319-22005-5.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | ## compute power
## Not run:
power.unknown.var(K = 2, n = 20, delta = c(1,1), Sigma = diag(c(1,1)))
## To compute sample size, first assume covariance as known
power.known.var(K = 2, delta = c(1,1), Sigma = diag(c(2,2)), power = 0.9,
sig.level = 0.025)
## The value of n, which is 51, is used as min.n and max.n must be larger
## then min.n so we try 60.
power.unknown.var(K = 2, delta = c(1,1), Sigma = diag(c(2,2)), power = 0.9,
sig.level = 0.025, min.n = 51, max.n = 60)
## More complex example with unknown covariance matrix assumed to be
Sigma <- matrix(c(1.440, 0.840, 1.296, 0.840,
0.840, 1.960, 0.168, 1.568,
1.296, 0.168, 1.440, 0.420,
0.840, 1.568, 0.420, 1.960), ncol = 4)
## compute power
power.unknown.var(K = 4, n = 90, delta = c(0.5, 0.75, 0.5, 0.75), Sigma = Sigma)
## equivalent: unknown SDs and correlation rho
power.unknown.var(K = 4, n = 90, delta = c(0.5, 0.75, 0.5, 0.75),
SD = c(1.2, 1.4, 1.2, 1.4),
rho = c(0.5, 0.9, 0.5, 0.1, 0.8, 0.25))
## End(Not run)
|
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.