cv_method_corr: Formula-based method to calculate the PCC of a CV-based...
In HDDesign: Sample Size Calculation for High Dimensional Classification Study

Description Usage Arguments Details Value Author(s) References Examples

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.

1 2	cv_method_corr(mu0, p, m, n, alpha_list, nrep, p1 = 0.5, ss = F, pcorr, chol.rho,sampling.p=0.5)

`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.

Refer to Sanchez, Wu, Song, Wang 2015, Section 3 and Supplementary materials.

If ss=FALSE, the function returns the expected PCC. If ss=TRUE, the function returns a vector containing the expected PCC, sensitivity and specificity.

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>

Sanchez, B.N., Wu, M., Song, P.X.K., and Wang W. (2016). "Study design in high-dimensional classification analysis." Biostatistics, in press.

	## 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