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Title: "R2ROC" Author: "Md Moksedul Momin and Hong Lee" Date: "25/06/23" #to be updated

R2ROC

The ‘R2ROC’ package can be used to derive test statistics for AUC values from polygenic risk score (PRS) models (variance and covariance of AUC values, p-value, and 95% confidence intervals (CI)). For example, it can test if two sets of AUC values from two different PRS models are significantly different from each other and whether the two sets of PGS are independent or dependent.

INSTALLATION

To use R2ROC:

install.packages("devtools")
library(devtools)
# devtools::install_github("mommy003/R2ROC")
install.packages("R2ROC", repos = c('https://mommy003.r-universe.dev', 'https://cloud.r-project.org'))
library(R2ROC)

or from CRAN

install.packages("R2ROC") 
library(R2ROC)

QUICK START

We illustrate the usage of R2ROC using multiple sets of PRS estimated based on GWAS summary statistics from the UK Biobank or Biobank Japan (reference datasets). In a target dataset, the phenotypes of target samples (y) can be predicted with PRS (a PRS model, e.g. y=PRS+e, where y and PRS are column-standardized 1 for the pre-adjusted phenotype. But for raw case-control data, phenotypes are assigned as 0 and 1. Note that the target individuals should be independent of reference individuals. We can test the significant differences in the AUC between a pair of PRS (see auc_var and auc_diff function and example in the manual).

DATA PREPARATION

Estimation of AUC and statistical testing of significant differences between AUC values of two PRS:

R2ROC requires only phenotype and estimated PRS (from PLINK or any other software). Note that any missing value in the phenotypes and PRS tested in the model should be removed. If we want to test the significant difference of AUC values for two independent PRS, the auc_diff function can be used with an input file that includes the following fields (please see the dat1 and dat2 file embedded within the package and auc_diff function in the manual).

• Phenotype (y)
• PRS for discovery population 1 (x1)
• PRS for discovery population 2 (x2)

To get the AUC value for AUC(y=x[,v1]).(here we define AUC= AUC(y=x[,v1]))

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$p (two-tailed P-value for the AUC is significantly different from 0.5)
• 9.28062e-175
• output$p_one_tail (one-tailed P-value for the AUC is significantly different from 0.5)
• 4.64031e-175

To get the test statistics for the difference between AUC(y=x[,v1]) and AUC(y=x[,v2]).(here we define AUC= AUC(y=x[,v1])) and AUC=AUC(y=x[,v2])))

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[,v1]+x[,v2]) and AUC(y=x[,v2]).

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$heller_p (two-tailed P-value based on Heller's test for the differences is significantly different from zero)
• 4.2085e-237
• output$heller_upper_diff (upper limit of 95% CI for difference based on Heller's test)
• 0.2013899
• output$heller_lower_diff (lower limit of 95% CI for difference based on Heller's test)
• 0.1586212

To get the transformed AUC from predictive ability (R2)

output=auc_trf(0.04, 0.002, 0.05)

• R2ROC output
• output$auc (transformed AUC)
• 0.7522887
• output$se (se of transformed AUC)
• 0.005948364

References

1. Olkin, I. and Finn, J.D. Correlations redux. Psychological Bulletin, 1995. 118(1): p. 155.
2. DeLong, E.R., D.M. DeLong, and D.L. Clarke-Pearson, Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach. Biometrics, 1988: p. 837-845.
3. Heller, G., et al., Inference for the difference in the area under the ROC curve derived from nested binary regression models. Biostatistics, 2017. 18(2): p. 260-274.
4. Momin, M.M., Lee, S., Wray, N.R. and Lee S.H. 2023. Significance tests for R2 of out-of-sample prediction using polygenic scores. The American Journal of Human Genetics, 2023. 110: p. 349-358.
5. Momin, M.M., Wray, N.R. and Lee S.H. 2023. R2ROC: an efficient method of comparing two or more correlated AUC from out-of-sample prediction using polygenic scores. Human Genetics. 2024 Jun 20. doi: 10.1007/s00439-024-02682-1. PMID: 38902498.

Contact information

Please contact Md Moksedul Momin (cvasu.momin@gmail.com) or Hong Lee (hong.lee@unisa.edu.au) if you have any queries.