| Title: | AUC Statistics |
|---|---|
| Description: | Area under the receiver operating characteristic curves (AUC) statistic for significance test. Variance and covariance of AUC values used to assess the 95% Confidence interval (CI) and p-value of the AUC difference for both nested and non-nested model. |
| Authors: | Hong Lee [aut, cph], Moksedul Momin [aut, cre, cph] |
| Maintainer: | Moksedul Momin <[email protected]> |
| License: | GPL (>=3) |
| Version: | 1.0.1 |
| Built: | 2024-10-31 22:13:13 UTC |
| Source: | https://github.com/mommy003/r2roc |
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)
auc_diff(dat, v1, v2, nv, kv)auc_diff(dat, v1, v2, nv, kv)
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 |
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 |
#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$heller_lower_diff (lower limit of 95% CI for #difference based on Hellers test) #0.1586212#To get the test statistics for the difference between AUC(y=x[,1]) #and AUC(y=x[,2]) dat=dat1 #(this example embedded within the package) nv=length(dat$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
This function transforms the observed scale predictive ability (R2) and its standard error (SE) to AUC with its SE
auc_trf(R2, se, kv)auc_trf(R2, se, kv)
R2 |
R2 or coefficient of determination on the observed scale |
se |
Standard error of R2 |
kv |
Population prevalence |
This function will transform the observed R2 and its s.e between to AUC. Output from the command is the lists of outcomes.
auc |
Transformed AUC |
se |
SE of transformed AUC |
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.
#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#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
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)
auc_var(dat, v1, nv, kv)auc_var(dat, v1, nv, kv)
dat |
N by (M+1) matrix having variables in the order of cbind(y,x) |
v1 |
This can be set as v1=c(1), v1=c(1,2) or possibly with more values |
nv |
Sample size |
kv |
Population prevalence |
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.
auc |
AUC |
var |
Variance of AUC |
upper_auc |
Upper limit of 95% CI for AUC |
lower_auc |
Lower limit of 95% CI for AUC |
#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$$p_one_tail (one-tailed P-value for the AUC is significantly different from 0.5) 4.64031e-175#To get the AUC for AUC(y=x[,1]) dat=dat1 #(this example embedded within the package) nv=length(dat$V1) kv=sum(dat$V1)/length(dat$V1)# pop. prevalence estimated from data #R2ROC also allows users to estimate AUC using pre-adjusted phenotype #In that case, users need to specify kv #eg. kv=0.10 for dat2 (dat2 embedded within the package) v1=c(1) output=auc_var(dat,v1,nv,kv) #R2ROC output #output$auc (AUC) #0.7390354 #output$var (variance of AUC) #7.193337e-05 #output$upper_auc (upper limit of 95% CI for AUC) #0.7556589 #output$lower_auc (lower limit of 95% CI for AUC) #0.7224119 #output$p 9.28062e-175 (two-tailed P-value for the AUC is significantly different from 0.5) #output$$p_one_tail (one-tailed P-value for the AUC is significantly different from 0.5) 4.64031e-175
A dataset containing raw phenotypes and multiple PGSs estimated two independent discovery population
dat1dat1
A data frame with 10000 rows and 3 variables:
Phenotype, raw case-caontrol data
PGS1, for discovery population 1
PGS2, for discovery population 2
A dataset containing preadjusted phenotypes and multiple PGSs estimated two independent discovery population
dat2dat2
A data frame with 10000 rows and 3 variables:
Phenotype, preadjustde case-caontrol data
PGS1, for discovery population 1
PGS2, for discovery population 2
olkin_auc1 function
olkin_auc1(omat, nv, kv)olkin_auc1(omat, nv, kv)
omat |
3 by 3 matrix having the correlation coefficients between y, x1 and x2, i.e. omat=cor(dat) where dat is N by 3 matrix having variables in the order of cbind (y,x1,x2) |
nv |
Sample size |
kv |
Population prevalance |
This function will be used as source code
olkin_auc1_2 function
olkin_auc1_2(omat, nv, kv)olkin_auc1_2(omat, nv, kv)
omat |
3 by 3 matrix having the correlation coefficients between y, x1 and x2, i.e. omat=cor(dat) where dat is N by 3 matrix having variables in the order of cbind (y,x1,x2) |
nv |
Sample size |
kv |
Population prevalance |
This function will be used as source code
olkin_auc12 function
olkin_auc12(omat, nv, kv)olkin_auc12(omat, nv, kv)
omat |
3 by 3 matrix having the correlation coefficients between y, x1 and x2, i.e. omat=cor(dat) where dat is N by 3 matrix having variables in the order of cbind (y,x1,x2) |
nv |
Sample size |
kv |
Population prevalance |
This function will be used as source code
olkin_auc12_1 function
olkin_auc12_1(omat, nv, kv)olkin_auc12_1(omat, nv, kv)
omat |
3 by 3 matrix having the correlation coefficients between y, x1 and x2, i.e. omat=cor(dat) where dat is N by 3 matrix having variables in the order of cbind (y,x1,x2) |
nv |
Sample size |
kv |
Population prevalance |
This function will be used as source code
olkin_auc12_13 function
olkin_auc12_13(omat, nv, kv)olkin_auc12_13(omat, nv, kv)
omat |
3 by 3 matrix having the correlation coefficients between y, x1 and x2, i.e. omat=cor(dat) where dat is N by 3 matrix having variables in the order of cbind (y,x1,x2) |
nv |
Sample size |
kv |
Population prevalance |
This function will be used as source code
olkin_auc12_3 function
olkin_auc12_3(omat, nv, kv)olkin_auc12_3(omat, nv, kv)
omat |
3 by 3 matrix having the correlation coefficients between y, x1 and x2, i.e. omat=cor(dat) where dat is N by 3 matrix having variables in the order of cbind (y,x1,x2) |
nv |
Sample size |
kv |
Population prevalance |
This function will be used as source code
olkin_auc12_34 function
olkin_auc12_34(omat, nv, kv)olkin_auc12_34(omat, nv, kv)
omat |
3 by 3 matrix having the correlation coefficients between y, x1 and x2, i.e. omat=cor(dat) where dat is N by 3 matrix having variables in the order of cbind (y,x1,x2) |
nv |
Sample size |
kv |
Population prevalance |
This function will be used as source code