Sensitivity and specificity changes using a single threshold and a gradient of thresholds at 0.5 using pROC in R

问题

I am trying to calculate ROC for a model of multi-class image. But since I didn't find any best way for multi-class classification, I have converted it to binary class. I have 31 classes of image. Using binary methods I am trying to find ROC of each 31 classes individually.

    df <- read.xlsx("data.xlsx",sheetName = 1,header = F)
    dn <- as.vector(df$X1) # 31 class 
    model_info <- read.csv("all_new.csv",stringsAsFactors = F) # details of 
    model output (Actual labels, Model labels, probabablity values)

head(model_info)

           Actual_labels             App_labels                      X1st
1 tinea cruris and corporis tinea cruris and corporis tinea cruris and corporis
2 tinea cruris and corporis tinea cruris and corporis tinea cruris and corporis
3 tinea cruris and corporis              no diagnosis             acne vulgaris
4                    eczema                    eczema                    eczema
5                    eczema              no diagnosis                 psoriasis
6              folliculitis    impetigo and pyodermas    impetigo and pyodermas
                       X2nd                      X3rd X.st.. X2nd.. X3rd..
1                 psoriasis             herpes zoster   0.89   0.05   0.03
2                 psoriasis                    eczema   0.89   0.03   0.02
3                 psoriasis     molluscum contagiosum   0.29   0.16   0.14
4 tinea cruris and corporis                 psoriasis   0.62   0.09   0.08
5                   melasma tinea cruris and corporis   0.27   0.27   0.25
6             acne vulgaris                 psoriasis   0.73   0.07   0.03

head(dn)

[1] "acne vulgaris"      "alopecia areata"    "anogenital warts"  
[4] "bullous pemphigoid" "candidiasis"        "chicken pox"   

App_call function basically converts the probability values to 0 or 1 based on whether model call is true or not

app_call <- function(cut_off, category){
            labels_thr <- rep(0,nrow(app_res))
            ind <- which(model_info$X.st.. >= cut_off) # index of instances 
             above threshold
            true_val <- which(app_res$App.Diagnosis[ind] == category) # index of instances where actual labels are similar to model labels for 1st class out of 31 class. 
            labels_thr[ind[true_val]] <- 1
            return(labels_thr)}

    index0 <- grep(pattern = paste0("^",dn[i],"$"),x = model_info$Actual_labels)

    actual_labels <- rep(0,nrow(model_info))

    if(length(index)>= 1){
        actual_labels[index0] <- 1
        actual_labels[-index0] <- 0} 

    app_labels <- app_call(cut_off = 0.5,category  = dn[i])
    res <- roc(actual_labels,app_labels)
    res1 <-   roc(actual_labels,model_info$X.st..)

dput(actual_labels)
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    dput(app_labels)
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dput(model_info$X.st..)
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0.25, 0.91, 0.28, 0.4, 0.73, 0.32, 0.49, 0.37, 0.19, 0.35, 0.29, 
0.77, 0.36, 0.31, 0.85, 0.33, 0.61, 0.63, 0.41, 0.98, 0.28, 0.31, 
0.91, 0.34, 0.24, 0.82, 0.46, 0.5, 0.39, 0.72, 0.67, 0.51, 0.41, 
0.81, 0.74, 0.5, 0.97, 0.65, 0.44, 0.71, 0.35, 0.84, 0.97, 0.42, 
0.75, 0.91, 0.61, 0.94, 0.48, 0.42, 0.63, 0.81, 0.83, 0.66, 0.55, 
0.61, 0.41, 0.63, 1, 0.63, 0.41, 0.75, 0.27, 0.28, 0.24, 0.55, 
0.35, 0.85, 0.97, 0.64, 0.79, 0.92, 0.47, 0.81, 0.23, 0.16, 0.75, 
0.12, 0.43, 0.18, 0.69, 0.21, 0.39, 0.19, 0.85, 0.57, 0.97, 0.56, 
0.81, 0.13, 0.4, 0.47, 0.95, 0.43, 0.9, 0.67, 0.36, 0.38, 0.83, 
0.97, 0.48, 0.93, 0.67, 0.44, 0.34, 0.83, 0.77, 0.39, 0.56, 0.85, 
0.55, 0.22, 0.48, 0.46, 0.59, 0.89, 0.99, 0.57, 0.96, 0.97, 0.95, 
0.98, 0.24, 0.89, 0.5, 0.94, 0.6, 0.41, 0.71, 0.5, 0.2, 0.96, 
0.18, 0.93, 0.92, 0.85, 0.92, 0.82, 0.48, 0.62, 0.53, 0.59, 0.38, 
0.8, 0.49, 0.91, 0.58, 0.94, 0.68, 0.15, 0.96, 0.98, 0.89, 0.84, 
0.5, 0.88, 0.29, 0.24, 0.31, 0.29, 0.33, 0.49, 0.33, 0.76, 0.54, 
0.88, 0.78, 0.26, 0.52, 0.75, 0.97, 0.93, 0.27, 0.69, 0.19, 0.69, 
0.2, 0.21, 0.84, 0.31, 0.19, 0.8, 0.6, 0.19, 0.51, 0.98, 0.27, 
0.39, 0.77, 0.95, 0.73, 0.28, 0.79, 0.19, 0.98, 0.77, 0.31, 0.84, 
0.35, 0.19, 0.26, 0.82, 0.63, 0.38, 0.38, 0.26, 0.63, 0.65, 0.55, 
0.88, 0.6, 0.71, 0.85, 0.99, 0.28, 0.42, 0.65, 0.58, 0.97, 0.35, 
0.36, 0.32, 0.79, 0.68, 0.39, 0.45, 0.71, 0.98, 0.34, 0.62, 0.24, 
0.55, 0.43, 0.95, 0.32, 0.6, 0.63, 0.98, 0.2, 0.31, 0.9, 0.3, 
0.32, 0.37, 0.52, 0.64, 0.9, 0.22, 0.31, 0.39, 0.21, 0.93, 0.64, 
0.4, 0.96, 0.31, 0.46, 0.86, 0.56, 0.99, 0.83, 0.87, 0.36, 0.59, 
0.98, 0.72, 0.21, 0.52, 0.17, 0.21, 0.42, 0.97, 0.34, 0.96, 0.18, 
0.63, 0.45, 0.36, 0.31, 0.48, 0.94, 0.86, 0.16, 0.32, 0.97, 0.29, 
0.9, 0.38, 0.88, 0.6, 0.17, 0.19, 0.44, 0.98, 0.35, 0.36, 0.2, 
0.39, 0.53, 0.35, 0.57, 0.18, 0.26, 0.17, 0.77, 0.51, 1, 0.17, 
0.57, 0.48, 0.58, 0.25, 0.32, 0.33, 0.76, 0.16, 0.13, 0.46, 0.44, 
0.31, 0.56, 0.46, 0.6, 0.17, 0.36, 0.34, 0.44, 0.43, 0.86, 0.86, 
0.44, 0.34, 0.92, 0.32, 0.78, 0.21, 0.46, 0.92, 0.27, 0.98, 0.52, 
0.34, 0.27, 0.59, 0.45, 0.58, 0.27, 0.48, 0.21, 0.24, 0.29, 0.89, 
0.25, 0.33, 0.96, 0.56, 0.29, 0.97, 0.98, 0.59, 0.28, 0.22, 0.76, 
0.91, 0.92, 0.91, 0.94, 0.83, 0.48, 0.53, 0.56, 0.5, 0.75, 0.4, 
0.98, 0.6, 0.74, 0.66, 0.97, 0.62, 0.99, 0.39, 0.89, 0.86, 0.66, 
0.92, 0.34, 0.99, 0.69, 0.71, 0.8, 0.47, 0.5, 0.83, 0.83, 0.41, 
0.72, 0.98, 0.76, 0.65, 0.71, 0.9, 0.9, 1, 0.4, 0.46, 0.35, 0.72, 
0.92, 0.74, 0.44, 0.67, 0.97, 0.88, 0.84, 0.71, 0.45, 0.78, 0.9, 
0.72, 0.57, 0.68, 0.85, 0.84, 0.46, 0.91, 0.53, 0.96, 0.49, 0.93, 
0.49, 0.37, 0.95, 0.47, 0.87, 0.49, 0.58, 0.64, 0.84, 0.8, 0.49, 
0.67, 0.75, 0.44, 0.87, 0.71, 0.47, 0.46, 0.83, 0.74, 0.99, 0.86, 
0.64, 0.74, 0.43, 0.44, 0.57, 0.89, 0.67, 0.59, 0.89, 0.45, 0.62, 
0.81, 0.93, 0.81, 0.98, 0.95, 0.63, 0.64, 0.96, 0.55, 0.49, 0.59, 
0.47, 0.42, 0.6, 0.51, 0.4, 0.3, 0.29, 0.45, 0.94, 0.29, 0.33, 
0.14, 0.71, 0.41, 0.6, 0.31, 0.95, 0.94, 0.87, 0.8, 0.53, 0.66, 
0.71, 0.19, 0.49, 0.97, 0.48, 0.43, 0.38, 0.4, 0.22, 0.38, 0.27, 
0.25, 0.45, 0.75, 0.38, 0.23, 0.92, 0.7, 0.68, 0.17, 0.39, 0.65, 
0.38, 0.39, 0.21, 0.28, 0.55, 0.89, 0.24, 0.34, 0.92, 0.31, 0.64, 
0.86, 0.94, 0.28, 0.43, 0.44, 0.82, 0.23, 0.81, 0.71, 0.53, 0.96, 
0.9, 0.55, 0.83, 0.64, 0.51, 0.32, 0.66, 0.45, 0.72, 0.28, 0.34, 
0.98, 0.76, 0.52, 0.95, 0.83, 0.47, 0.9, 0.31, 0.23, 0.61, 0.94, 
0.61, 0.42, 0.34, 0.55, 0.33, 0.93, 0.24, 0.51, 0.65, 0.17, 0.81, 
0.68, 0.51, 0.78, 0.37, 0.37, 0.99, 0.94, 0.64, 0.59, 0.61, 0.9, 
0.88, 0.64, 0.49, 0.09, 0.51, NA, 0.86, 0.45, 0.61, 0.24, 0.85, 
0.26, 0.29, 0.21, 0.66, 0.26, 0.47, 0.19, 0.99, 0.51, 0.91, 0.37, 
0.56, 0.71, 0.47, 0.44, 0.48, 0.52, 0.22, 0.52, 0.29, 0.46, 0.54, 
0.94, 0.24, 0.24, 0.47, 0.37, 0.9, 0.79, 0.81, 0.41, 0.38, 0.71, 
0.34, 0.46, 0.23, 0.54, 0.43, 0.85, 0.56, 0.26, 0.9, 0.25, 0.3, 
0.39, 0.89, 0.38, 0.18, 0.78, 0.37, 0.45, 0.51, 0.8, 0.61, 0.52, 
0.84, 0.4, 0.31, 0.28, 0.24, 0.23, 0.43, 0.77, 0.78, 0.95, 0.9, 
0.81, 0.15, 0.77, 0.77, 0.87, 0.75, 0.16, 0.49, 0.23, 0.93, 0.45, 
0.33, 0.75, 0.32, 0.75, 0.41, 0.24, 0.46, 0.17, 0.41, 0.45, 0.48, 
0.15, 0.66, 0.53, 0.75, 0.57, 0.46, 0.78, 0.24, 0.29, 0.95, 0.77, 
0.66, 0.94, 0.27, 0.29, 0.58, 0.6, 0.46, 0.58, 0.84, 0.69, 0.47, 
0.45, 0.48, 0.35, 0.89, 0.98, 0.93, 0.2, 0.94, 0.91, 0.75, 0.5, 
0.44, 0.69, 0.8, 0.76, 0.85, 0.84, 0.72, 0.25, 0.73, 0.26, 0.93, 
0.15, 0.33, 0.3, 0.6, 0.24, 0.21, 0.28, 0.51, 0.79, 0.77, 0.85, 
0.52, 0.39, 0.68, 0.83, 0.36, 0.15, 0.87, 0.55)

res1 = roc(actual_labels,app_labels)
res2= roc(actual_labels,model_info$X.st..)

The calls in the actual label class where it is "1" and have have a probablity threshold (model_info$X.st..) value more than 0.5 is named as "1" for app_labels and rest all zero

Both res1 and res2 have different values for sensitivitiy and specificity.

回答1:

A ROC curve shows the sensitivity and specificity tradeoff as the decision threshold of a classifier is varied. Typically ROC curve functions expect to get the prediction and the truth value as input.

This is exactly what you do when you run:

res2= roc(actual_labels,model_info$X.st..)

However your app_labels is of a very different nature: you have already merged in the "correct classification" aspect, which makes it more like a flattened contingency table than the "predictions" the ROC function expects. So you can no longer use a regular ROC function and need to calculate the sensitivity and specificity manually.

TP <- sum(app_labels & actual_labels)
TN <- sum(app_labels & !(actual_labels))
FP <- sum(!(app_labels) & !(actual_labels))
FN <- sum(!(app_labels) & actual_labels)

# Sensitivity:
TP / (TP+FN)

# Specificity:
TN / (TN + FP)

来源：https://stackoverflow.com/questions/57520855/sensitivity-and-specificity-changes-using-a-single-threshold-and-a-gradient-of-t