Comparing multiple AUCs in parallel (R)

The following should work, please check it. I didn't write all the details, but you can ask me other questions if you don't understand the code.

#load pROC
library(pROC)
#> Type 'citation("pROC")' for a citation.
#> 
#> Attaching package: 'pROC'
#> The following objects are masked from 'package:stats':
#> 
#>     cov, smooth, var

#generate df with random numbers
set.seed(123)
df <- data.frame(disease_status = rbinom(n=100, size=1, prob=0.20),
                 test1 = rnorm(100, mean=15, sd=4),
                 test2 = rnorm(100, mean=30, sd=2),
                 test3 = rnorm(100, mean=50, sd=3))

#create roc object for test1, test2, test3
roc.out_test1<-roc(df$disease_status, df$test1, plot=TRUE, smooth = FALSE)
#> Setting levels: control = 0, case = 1
#> Setting direction: controls < cases

roc.out_test2<-roc(df$disease_status, df$test2, plot=TRUE, smooth = FALSE)
#> Setting levels: control = 0, case = 1
#> Setting direction: controls < cases

roc.out_test3<-roc(df$disease_status, df$test3, plot=TRUE, smooth = FALSE)
#> Setting levels: control = 0, case = 1
#> Setting direction: controls < cases

# compare the AUC of test1 and test 2
roc.test(roc.out_test1, roc.out_test2, reuse.auc = TRUE, method = "delong", na.rm = TRUE)
#> 
#>  DeLong's test for two correlated ROC curves
#> 
#> data:  roc.out_test1 and roc.out_test2
#> Z = 0.60071, p-value = 0.548
#> alternative hypothesis: true difference in AUC is not equal to 0
#> sample estimates:
#> AUC of roc1 AUC of roc2 
#>   0.5840108   0.5216802

Now we generate a list of all possible combinations of the three tests and run the roc.test function using the same parameters that you set.

all_tests <- combn(
  list(
    "test1" = roc.out_test1,
    "test2" = roc.out_test2,
    "test3" = roc.out_test3
  ),
  FUN = function(x, ...) roc.test(x[[1]], x[[2]]),
  m = 2,
  simplify = FALSE, 
  reuse.auc = TRUE, 
  method = "delong", 
  na.rm = TRUE
)

The output is a list of choose(3, 2) = 3 elements (i.e. the number of combinations of n elements taken 2 at a time) and each element of the list is a test. For example this is the same as your previous test:

all_tests[[1]]
#> 
#>  DeLong's test for two correlated ROC curves
#> 
#> data:  x[[1]] and x[[2]]
#> Z = 0.60071, p-value = 0.548
#> alternative hypothesis: true difference in AUC is not equal to 0
#> sample estimates:
#> AUC of roc1 AUC of roc2 
#>   0.5840108   0.5216802

The only problem here is that it's difficult to recognise which tests are used in the comparisons, so we can also add a list of names:

tests_names <- combn(
  list("test1", "test2", "test3"), 
  m = 2, 
  FUN = paste, 
  simplify = TRUE, 
  collapse = "_"
)
all_tests <- setNames(all_tests, tests_names)

This is the result.

names(all_tests)
#> [1] "test1_test2" "test1_test3" "test2_test3"

The names of the objects flag the tests that are used in the comparison.

all_tests$test1_test2
#> 
#>  DeLong's test for two correlated ROC curves
#> 
#> data:  x[[1]] and x[[2]]
#> Z = 0.60071, p-value = 0.548
#> alternative hypothesis: true difference in AUC is not equal to 0
#> sample estimates:
#> AUC of roc1 AUC of roc2 
#>   0.5840108   0.5216802

^{Created on 2020-03-14 by the reprex package (v0.3.0)}

The roc.test() function expects a roc object as input. The list test is just character strings of all the arguments, which the function does not know what to do with. The list also includes comparisons of the tests with themselves i.e. "roc.out_test1,roc.out_test1,reuse.auc=TRUE" I assume you don't actually need to do this and that there are only 3 comparisons that you need 1v2, 1v3, 2v3. The purrr package provides map functions similar to lapply and map2 allows you to iterate of 2 lists at the same time. You need to create 2 lists of the actually roc objects and iterate over these.

#load pROC
library(pROC)
library(dplyr)
library(purrr) #For map2 function

#generate df with random numbers
set.seed(123)
df <- data.frame(disease_status = rbinom(n=100, size=1, prob=0.20),
                 test1 = rnorm(100, mean=15, sd=4),
                 test2 = rnorm(100, mean=30, sd=2),
                 test3 = rnorm(100, mean=50, sd=3))

#create roc object for test1, test2, test3
roc.out_test1<-roc(df$disease_status, df$test1, plot=TRUE, smooth = FALSE)
roc.out_test2<-roc(df$disease_status, df$test2, plot=TRUE, smooth = FALSE)
roc.out_test3<-roc(df$disease_status, df$test3, plot=TRUE, smooth = FALSE)

#compare the AUC of test1 and test 2
roc.test(roc.out_test1, roc.out_test2, reuse.auc=TRUE, method="delong", na.rm=TRUE)

roc_new <- function(test1,  test2){
  roc.test(test1, test2, reuse.auc=TRUE, method="delong", na.rm=TRUE)
}

#List of all tests
all_tests <- list(roc.out_test1,
                  roc.out_test2,
                  roc.out_test3) 

#Create unique combos of tests
unique_combos <- expand.grid(1:3, 1:3) %>% 
  filter(Var1 < Var2) %>% #exludes duplicate comparisons, 
                      #each col provides the index for the 2 lists to iterate over
  mutate(names = paste(Var1, " V ",  Var2)) #Create col to name final output list


#Create 2 lists to iterate over
#Create list 1
(test1 <- all_tests[as.numeric(unique_combos$Var1)])
#Create list 2
(test2 <- all_tests[as.numeric(unique_combos$Var2)])

#Iterate over both lists
output <- map2(test1, test2, roc_new)
names(output) <- unique_combos$names