auc_diff {R2ROC}

auc_diff function

Description

This function estimates var(AUC(y~x[,v1]) - AUC(y~x[,v2])) where AUC is the Area Under ROC curve of the model, y is N by 1 matrix having the dependent variable, and x is N by M matrix having M explanatory variables. v1 or v2 indicates the ith column in the x matrix (v1 or v2 can be multiple values between 1 - M, see Arguments below)

Usage

auc_diff(dat, v1, v2, nv, kv)

Arguments

dat

N by (M+1) matrix having variables in the order of cbind(y,x)

v1

This can be set as v1=c(1) or v1=c(1,2)

v2

This can be set as v2=c(2), v2=c(3), v2=c(1,3) or v2=c(3,4)

nv

Sample size

kv

Population prevalence

Value

This function will estimate significant difference between two PRS (either dependent or independent and joint or single). To get the test statistics for the difference between AUC(y~x[,v1]) and AUC(y~x[,v2]) (here we define AUC1=AUC(y~x[,v1])) and AUC2=AUC(y~x[,v2]))). The outputs are listed as follows.

mean_diff

AUC differences between AUC1 and AUC2

var

Variances of AUC differences

upper_diff

Upper value of the differences

lower_diff

Upper value of the differences

p

Two tailed P-value for significant difference between AUC1 and AUC2

p_one_tail

One tailed P-value for significant difference

heller_p

P-value based on Heller's test for significant difference

heller_upper_diff

Upper limit of 95% CI for the difference basedon Heller's test

heller_lower_diff

Lower limit of 95% CI for the difference basedon Heller's test

Examples

#To get the test statistics for the difference between AUC(y=x[,1]) 
#and AUC(y=x[,2])
dat=dat1 #(this example embedded within the package)
nv=length(dat$V1)
kv=sum(dat$V1)/length(dat$V1)# pop. prevalence estimated from data
#R2ROC also allows users to estimate AUC using pre-adjusted phenotype
#In that case, users need to specify kv
#eg. kv=0.10 for dat2 (dat2 embedded within the package) 
v1=c(1)
v2=c(2)
output=auc_diff(dat,v1,v2,nv,kv)

#R2ROC output
#output$mean_diff (mean difference of AUC1 and AUC2)
#0.1756046

#output$var (variance of AUC difference)
#9.274356e-05

#output$upper_diff (upper limit of 95% CI for difference)
#0.1944801

#output$lower_diff (lower limit of 95% CI for difference)
#0.1567292

#output$p (two-tailed P-value for the differences is
#significantly different from zero)
#2.747031e-74

#output$p_one_tail (one-tailed P-value for the differences
#is significantly different from zero)
#1.373515e-74


#To get the test statistics for the difference between
#AUC(y=x[,1]+x[,2]) and AUC(y=x[,2])
dat=dat1 #(this example embedded within the package)
nv=length(dat$V1)
kv=sum(dat$V1)/length(dat$V1)# pop. prevalence estimated from data
#R2ROC also allows users to estimate AUC using pre-adjusted phenotype
#In that case, users need to specify kv
#eg. kv=0.10 for dat2 (dat2 embedded within the package) 
v1=c(1,2)
v2=c(2)
output=auc_diff(dat,v1,v2,nv,kv)

#R2ROC output
#output$mean_diff (mean difference of AUC1 and AUC2)
#0.1793682

#output$var (variance of AUC difference)
#0.0001190366

#output$upper_diff (upper limit of 95% CI for difference)
#0.2007526

#output$lower_diff (lower limit of 95% CI for difference)
#0.1579839

#output$p (two-tailed P-value for the differences is
#significantly different from zero)
#9.87014e-61

#output$p_one_tail (one-tailed P-value for the differences
#is significantly different from zero)
#4.93507e-61

#output$heller_p (two-tailed P-value based on Hellers test
#for the differences is significantly different from zero)
#4.2085e-237

#output$heller_upper_diff (upper limit of 95% CI for
#difference based on Hellers test)
#0.2013899

#output$heller_lower_diff (lower limit of 95% CI for
#difference based on Hellers test)
#0.1586212