20.1: Area under the curve
- Page ID
- 45270
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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 tradeoff 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. 20.1.1) plot(x,y, pch=19, cex=2, col="blue") lines(predict(loxy), type="l", col="red")
where == is an R comparison operator.
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:
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
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