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

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.

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

auc_trf function

Description

This function transforms the observed scale predictive ability (R2) and its standard error (SE) to AUC with its SE

Usage

auc_trf(R2, se, kv)

Arguments

Value

This function will transform the observed R2 and its s.e between to AUC. Output from the command is the lists of outcomes.

References

Wray, Naomi R., et al. "The genetic interpretation of area under the ROC curve in genomic profiling." PLoS genetics 6.2 (2010): e1000864.

Lee, Sang Hong, et al. "A better coefficient of determination for genetic profile analysis." Genetic epidemiology 36.3 (2012): 214-224.

Examples

#To get the transformed AUC

output=auc_trf(0.04, 0.002, 0.05)
output

#output$auc (transformed AUC)
#0.7522887

#output$se (se of transformed AUC)
#0.005948364

auc_var function

Description

This function estimates var(AUC(y~x[,v1])) 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 indicates the ith column in the x matrix (v1 can be multiple values between 1 - M, see Arguments below)

Usage

auc_var(dat, v1, nv, kv)

Arguments

Value

This function will test the null hypothesis for AUC. To get the test statistics for AUC(y~x[,v1]). The outputs are listed as follows.

Examples

#To get the AUC for AUC(y=x[,1]) 

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)
output=auc_var(dat,v1,nv,kv)

#R2ROC output
#output$auc (AUC)
#0.7390354

#output$var (variance of AUC)
#7.193337e-05

#output$upper_auc (upper limit of 95% CI for AUC)
#0.7556589

#output$lower_auc (lower limit of 95% CI for AUC)
#0.7224119

#output$p
#9.28062e-175 (two tailed P-value for the AUC is significantly
#different from 0.5)

#output$p_one_tail (one tailed P-value for the AUC is significantly 
#different from 0.5)
#4.64031e-175

Raw phenotypes and 2 sets of discovery PGSs

Description

A dataset containing raw phenotypes and multiple PGSs estimated two independent discovery population

Usage

dat1

Format

A data frame with 10000 rows and 3 variables:

V1

Phenotype, raw case-caontrol data

V2

PGS1, for discovery population 1

V3

PGS2, for discovery population 2

Pre-adjusted phenotypes and 2 sets of discovery PGSs

Description

A dataset containing preadjusted phenotypes and multiple PGSs estimated two independent discovery population

Usage

dat2

Format

A data frame with 10000 rows and 3 variables:

V1

Phenotype, preadjustde case-caontrol data

V2

PGS1, for discovery population 1

V3

PGS2, for discovery population 2

olkin_auc1 function

Description

olkin_auc1 function

Usage

olkin_auc1(omat, nv, kv)

Arguments

Value

This function will be used as source code

olkin_auc12 function

Description

olkin_auc12 function

Usage

olkin_auc12(omat, nv, kv)

Arguments

Value

This function will be used as source code

olkin_auc12_1 function

Description

olkin_auc12_1 function

Usage

olkin_auc12_1(omat, nv, kv)

Arguments

Value

This function will be used as source code

olkin_auc12_13 function

Description

olkin_auc12_13 function

Usage

olkin_auc12_13(omat, nv, kv)

Arguments

Value

This function will be used as source code

olkin_auc12_3 function

Description

olkin_auc12_3 function

Usage

olkin_auc12_3(omat, nv, kv)

Arguments

Value

This function will be used as source code

olkin_auc12_34 function

Description

olkin_auc12_34 function

Usage

olkin_auc12_34(omat, nv, kv)

Arguments

Value

This function will be used as source code

olkin_auc1_2 function

Description

olkin_auc1_2 function

Usage

olkin_auc1_2(omat, nv, kv)

Arguments

Value

This function will be used as source code