20.1 – Area under the curve

[under construction]

Introduction

Area under the curve, AUC, represents the total change in y given change in x. For example, if x is time, and y is oxygen consumption, an AUC would be appropriate to quantify the total oxygen consumption following strenuous exercise (Excess post-exercise oxygen consumption, EPOC) or following a large meal (Specific Dynamic Action, SDA).

In biostatistics, area under the relative (receiver) operating carrier, AUROC, shows characteristics of a diagnostic model, a graphic used to show trade off between sensitivity and specificity. Classifier performance. Used to find the appropriate cut-off. Plot true positive rates against false positive rates as cumulative functions, shows the relationship between sensitivity and specificity for every possible cut off value. Can then calculate AUC to get a measure of the intervention’s ability to discriminate between true and false positive rates.

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Related, area under precision-recall curve, AUPRC,

estimate area (1) trapezoid method, (2) average precision score

 

Area under the curve

Download and install R package MESS; requires geepack, geeM, and Matrix packages

R code

x <- seq(1:10) 
y <- c(1,4,5,2,11,22,9,7,5,1) 
#length(x)==length(y)
#smooth the data 
loxy <- loess(y~x)
#Make a plot (Fig. 1)
plot(x,y, pch=19, cex=2, col="blue") 
lines(predict(loxy), type="l", col="red")

where == is an R comparison operator.

And R output

area under the curve, AOC, example

Figure 1. Area under the curve example.

library(MESS) 
auc(x,y,from=0,rule=2) 
auc(x,loxy$fitted,from=0,rule=2)

And R output

#area under curve for raw data
[1] 67
#area under curve for smoothed data
[1] 66.77616

Area under the receiver operating carrier curve

Download and install ROCR

R code

#modified from https://rviews.rstudio.com/2019/03/01/some-r-packages-for-roc-curves/

library(ROCR)
data(ROCR.simple) 
df <- data.frame(ROCR.simple) 
pred <- prediction(df$predictions, df$labels) 
perf <- performance(pred,"tpr","fpr") 
plot(perf,colorize=TRUE)

R output

ROC plot

Figure 2. Example ROC curve

The right-hand axes is color codes by AUC values: good tests AUC between 0.8 and 0.9, very good tests greater than 0.9.

Area under the precision recall curve

— under construction

Questions

[pending]

Chapter 20 contents

/MD