cv_method_corr {HDDesign} | R Documentation |
Formula-based method to calculate the PCC of a CV-based classifier when features are correlated.
Description
Determine the probability of correct classification (PCC) for a high dimensional classification study employing Cross validation classifier. This is similar to cv_method, but features generated are correlated.
Usage
cv_method_corr(mu0, p, m, n, alpha_list, nrep, p1 = 0.5, ss = F, pcorr,
chol.rho,sampling.p=0.5)
Arguments
mu0 |
The effect size of the important features. |
p |
The number of the features in total. |
m |
The number of the important features. |
n |
The total sample size for the two groups. |
alpha_list |
The search grid for the p-value threshold. |
nrep |
The number of simulation replicates employed to compute the expected PCC and/or sensitivity and specificity. |
p1 |
The prevalence of the group 1 in the population, default to 0.5. |
ss |
Boolean variable, default to FALSE. The TRUE value instruct the program to compute the sensitivity and the specificity of the classifier. |
pcorr |
Number of correlated features. |
chol.rho |
Cholesky decomposition of the covariance of the pcorr features that are correlated. It is assumed that the m important features are part of the pcorr correlated features. |
sampling.p |
The assumed proportion of group 1 samples in the training data; default of 0.5 assumes groups are equally represented regardless of p1. |
Details
Refer to Sanchez, Wu, Song, Wang 2015, Section 3 and Supplementary materials.
Value
If ss=FALSE, the function returns the expected PCC. If ss=TRUE, the function returns a vector containing the expected PCC, sensitivity and specificity.
Author(s)
Meihua Wu <meihuawu@umich.edu> Brisa N. Sanchez <brisa@umich.edu> Peter X.K. Song <pxsong@umich.edu> Raymond Luu <raluu@umich.edu> Wen Wang <wangwen@umich.edu>
References
Sanchez, B.N., Wu, M., Song, P.X.K., and Wang W. (2016). "Study design in high-dimensional classification analysis." Biostatistics, in press.
Examples
## Sigma_1 in the paper
#first block is pcorr x pcorr of compound symmetry
#other diagonal block is Identity; off diagonal blocks are 0
pcorr=10
p=500
rho.cs=.8
#create first block
rho=diag(c((1-rho.cs)*rep(1,pcorr),rep(1,p-pcorr)))+ matrix(c(rho.cs*
rep(1,pcorr),rep(0,p-pcorr)),ncol=1) %*% c(rep(1,pcorr),rep(0,p-pcorr))
chol.rho1.500=chol(rho[1:pcorr,1:pcorr])
lmax= max(eigen(rho)$values)
print(lmax)
set.seed(1)
cv_method_corr(mu0=0.4,p=500,m=10,n=80,alpha_list=c(0.0000001,0.0001,0.01),
nrep=10,p1=0.6,ss=TRUE,pcorr=pcorr,chol.rho=chol.rho1.500,sampling.p=0.5)
#return 0.6689385 0.6806896 0.6513119
#alpha_list should be a dense grid of pvalue cut-offs;
#three values are used here for simplicity of the example