# Introduction to precrec In precrec: Calculate Accurate Precision-Recall and ROC (Receiver Operator Characteristics) Curves

The `precrec` package provides accurate computations of ROC and Precision-Recall curves.

## 1. Basic functions

The `evalmod` function calculates ROC and Precision-Recall curves and returns an S3 object.

```library(precrec)

# Load a test dataset
data(P10N10)

# Calculate ROC and Precision-Recall curves
sscurves <- evalmod(scores = P10N10\$scores, labels = P10N10\$labels)
```

### S3 generics

The R language specifies S3 objects and S3 generic functions as part of the most basic object-oriented system in R. The `precrec` package provides nine S3 generics for the S3 object created by the `evalmod` function.

S3 generic Package Description

```     print   base      Print the calculation results and the summary of the test data
```

as.data.frame base Convert a precrec object to a data frame plot graphics Plot performance evaluation measures autoplot ggplot2 Plot performance evaluation measures with ggplot2 fortify ggplot2 Prepare a data frame for ggplot2 auc precrec Make a data frame with AUC scores part precrec Set partial curves and calculate AUC scores pauc precrec Make a data frame with pAUC scores auc_ci precrec Calculate confidence intervals of AUC scores

#### Example of the plot function

The `plot` function outputs ROC and Precision-Recall curves

```# Show ROC and Precision-Recall plots
plot(sscurves)

# Show a Precision-Recall plot
plot(sscurves, "PRC")
```

#### Example of the autoplot function

The `autoplot` function outputs ROC and Precision-Recall curves by using the `ggplot2` package.

```# The ggplot2 package is required
library(ggplot2)

# Show ROC and Precision-Recall plots
autoplot(sscurves)

# Show a Precision-Recall plot
autoplot(sscurves, "PRC")
```

Reduced supporting points make the plotting speed faster for large data sets.

```# 5 data sets with 50000 positives and 50000 negatives
samp1 <- create_sim_samples(5, 50000, 50000)

# Calculate curves
eval1 <- evalmod(scores = samp1\$scores, labels = samp1\$labels)

# Reduced supporting points
system.time(autoplot(eval1))

# Full supporting points
system.time(autoplot(eval1, reduce_points = FALSE))
```

#### Example of the auc function

The `auc` function outputs a data frame with the AUC (Area Under the Curve) scores.

```# Get a data frame with AUC scores
aucs <- auc(sscurves)

# Use knitr::kable to display the result in a table format
knitr::kable(aucs)

# Get AUCs of Precision-Recall
aucs_prc <- subset(aucs, curvetypes == "PRC")
knitr::kable(aucs_prc)
```

#### Example of the as.data.frame function

The `as.data.frame` function converts a precrec object to a data frame.

```# Convert sscurves to a data frame
sscurves.df <- as.data.frame(sscurves)

# Use knitr::kable to display the result in a table format
knitr::kable(head(sscurves.df))
```

## 2. Data preparation

The `precrec` package provides four functions for data preparation.

Function Description

```   join_scores Join scores of multiple models into a list
join_labels Join observed labels of multiple test datasets into a list
mmdata Reformat input data for performance evaluation calculation
```

create_sim_samples Create random samples for simulations

### Example of the join_scores function

The `join_scores` function combines multiple score datasets.

```s1 <- c(1, 2, 3, 4)
s2 <- c(5, 6, 7, 8)
s3 <- matrix(1:8, 4, 2)

# Join two score vectors
scores1 <- join_scores(s1, s2)

# Join two vectors and a matrix
scores2 <- join_scores(s1, s2, s3)
```

### Example of the join_labels function

The `join_labels` function combines multiple score datasets.

```l1 <- c(1, 0, 1, 1)
l2 <- c(1, 0, 1, 1)
l3 <- c(1, 0, 1, 0)

# Join two label vectors
labels1 <- join_labels(l1, l2)
labels2 <- join_labels(l1, l3)
```

### Example of the mmdata function

The `mmdata` function makes an input dataset for the `evalmod` function.

```# Create an input dataset with two score vectors and one label vector
msmdat <- mmdata(scores1, labels1)

# Specify dataset IDs
smmdat <- mmdata(scores1, labels2, dsids = c(1, 2))

# Specify model names and dataset IDs
mmmdat <- mmdata(scores1, labels2, modnames = c("mod1", "mod2"), dsids = c(1, 2))
```

### Example of the create_sim_samples function

The `create_sim_samples` function is useful to make a random sample dataset with different performance levels.

Level name Description

``` random Random
poor_er Poor early retrieval
good_er Good early retrieval
excel Excellent
perf Perfect
all All of the above
```
```# A dataset with 10 positives and 10 negatives for the random performance level
samps1 <- create_sim_samples(1, 10, 10, "random")

#  A dataset for five different performance levels
samps2 <- create_sim_samples(1, 10, 10, "all")

# A dataset with 20 samples for the good early retrieval performance level
samps3 <- create_sim_samples(20, 10, 10, "good_er")

# A dataset with 20 samples for five different performance levels
samps4 <- create_sim_samples(20, 10, 10, "all")
```

## 3. Multiple models

The `evalmod` function calculate performance evaluation for multiple models when multiple model names are specified with the `mmdata` or the `evalmod` function.

### Data preparation

There are several ways to create a dataset with the `mmdata` function for multiple models.

```# Use a list with multiple score vectors and a list with a single label vector
msmdat1 <- mmdata(scores1, labels1)

# Explicitly specify model names
msmdat2 <- mmdata(scores1, labels1, modnames = c("mod1", "mod2"))

# Use a sample dataset created by the create_sim_samples function
msmdat3 <- mmdata(samps2[["scores"]], samps2[["labels"]], modnames = samps2[["modnames"]])
```

### ROC and Precision-Recall calculations

The `evalmod` function automatically detects multiple models.

```# Calculate ROC and Precision-Recall curves for multiple models
mscurves <- evalmod(msmdat3)
```

### S3 generics

All the S3 generics are effective for the S3 object generated by this approach.

```# Show ROC and Precision-Recall curves with the ggplot2 package
autoplot(mscurves)
```

#### Example of the as.data.frame function

The `as.data.frame` function also works with this object.

```# Convert mscurves to a data frame
mscurves.df <- as.data.frame(mscurves)

# Use knitr::kable to display the result in a table format
knitr::kable(head(mscurves.df))
```

## 4. Multiple test sets

The `evalmod` function calculate performance evaluation for multiple test datasets when different test dataset IDs are specified with the `mmdata` or the `evalmod` function.

### Data preparation

There are several ways to create a dataset with the `mmdata` function for multiple test datasets.

```# Specify test dataset IDs names
smmdat1 <- mmdata(scores1, labels2, dsids = c(1,2))

# Use a sample dataset created by the create_sim_samples function
smmdat2 <- mmdata(samps3[["scores"]], samps3[["labels"]], dsids = samps3[["dsids"]])
```

### ROC and Precision-Recall calculations

The `evalmod` function automatically detects multiple test datasets.

```# Calculate curves for multiple test datasets and keep all the curves
smcurves <- evalmod(smmdat2, raw_curves = TRUE)
```

### S3 generics

All the S3 generics are effective for the S3 object generated by this approach.

```# Show an average Precision-Recall curve with the 95% confidence bounds
autoplot(smcurves, "PRC", show_cb = TRUE)

# Show raw Precision-Recall curves
autoplot(smcurves, "PRC", show_cb = FALSE)
```

#### Example of the as.data.frame function

The `as.data.frame` function also works with this object.

```# Convert smcurves to a data frame
smcurves.df <- as.data.frame(smcurves)

# Use knitr::kable to display the result in a table format
knitr::kable(head(smcurves.df))
```

## 5. Multiple models and multiple test sets

The `evalmod` function calculates performance evaluation for multiple models and multiple test datasets when different model names and test dataset IDs are specified with the `mmdata` or the `evalmod` function.

### Data preparation

There are several ways to create a dataset with the `mmdata` function for multiple models and multiple datasets.

```# Specify model names and test dataset IDs names
mmmdat1 <- mmdata(scores1, labels2, modnames= c("mod1", "mod2"), dsids = c(1, 2))

# Use a sample dataset created by the create_sim_samples function
mmmdat2 <- mmdata(samps4[["scores"]], samps4[["labels"]],
modnames = samps4[["modnames"]], dsids = samps4[["dsids"]])
```

### ROC and Precision-Recall calculations

The `evalmod` function automatically detects multiple models and multiple test datasets.

```# Calculate curves for multiple models and multiple test datasets
mmcurves <- evalmod(mmmdat2)
```

### S3 generics

All the S3 generics are effective for the S3 object generated by this approach.

```# Show average Precision-Recall curves
autoplot(mmcurves, "PRC")

# Show average Precision-Recall curves with the 95% confidence bounds
autoplot(mmcurves, "PRC", show_cb = TRUE)
```

#### Example of the as.data.frame function

The `as.data.frame` function also works with this object.

```# Convert smcurves to a data frame
mmcurves.df <- as.data.frame(mmcurves)

# Use knitr::kable to display the result in a table format
knitr::kable(head(mmcurves.df))
```

## 6. Confidence interval bands

The `evalmod` function automatically calculates confidence bands when a model contains multiple test sets in provided dataset. Confidence intervals are calculated for additional supporting points, which are specified by the 'x_bins' option of the `evalmod` function.

### Example of confidence bands when x_bins is 2

The dataset `smmdat2` contains 20 samples for a single model/classifier.

```# Show all curves
smcurves_all <- evalmod(smmdat2, raw_curves = TRUE)
autoplot(smcurves_all)
```

Additional supporting points are calculated for `x = (0, 0.5, 1.0)` when `x_bins` is set to 2.

```# x_bins: 2
smcurves_xb2 <- evalmod(smmdat2, x_bins = 2)
autoplot(smcurves_xb2)
```

### Example of confidence bands when x_bins is 10

Additional supporting points are calculated for `x = (0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0)` when `x_bins` is set to 10.

```# x_bins: 10
smcurves_xb10 <- evalmod(smmdat2, x_bins = 10)
autoplot(smcurves_xb10)
```

### Example of the alpha value

The `evalmod` function accepts the `cb_alpha` option to specify the alpha value of the point-wise confidence bounds calculation. For instance, 95\% confidence bands are calculated when `cb_alpha` is 0.05.

```# cb_alpha: 0.1 for 90% confidence band
smcurves_cb1 <- evalmod(smmdat2, x_bins = 10, cb_alpha = 0.1)
autoplot(smcurves_cb1)

# cb_alpha: 0.01 for 99% confidence band
smcurves_cb2 <- evalmod(smmdat2, x_bins = 10, cb_alpha = 0.01)
autoplot(smcurves_cb2)
```

## 7. Cross validation

The `format_nfold` function takes a data frame with scores, label and n-fold columns and convert it to a list for `evalmod` and `mmdata`.

#### Example of a data frame with 5-fold data

```# Load data
data(M2N50F5)

# Use knitr::kable to display the result in a table format
knitr::kable(head(M2N50F5))
```

#### Example of the format_nfold function with 5-fold datasets

```# Convert data frame to list
nfold_list1 = format_nfold(nfold_df = M2N50F5,  score_cols = c(1, 2),
lab_col = 3, fold_col = 4)

# Use column names
nfold_list2 = format_nfold(nfold_df = M2N50F5, score_cols = c("score1", "score2"),
lab_col = "label", fold_col = "fold")

# Use the result for evalmod
cvcurves <- evalmod(scores = nfold_list2\$scores, labels = nfold_list2\$labels,
modnames = rep(c("m1", "m2"), each = 5), dsids = rep(1:5, 2))
autoplot(cvcurves)
```

### evalmod and mmdata with cross validation datasets

Both `evalmod` and `mmdata` function can directly take the arguments of the `format_nfold` function.

#### Example of evalmod and mmdata with 5-fold data

```# mmdata
cvcurves2 <- mmdata(nfold_df = M2N50F5, score_cols = c(1, 2), lab_col = 3, fold_col = 4,
modnames = c("m1", "m2"), dsids = 1:5)

# evalmod
cvcurves3 <- evalmod(nfold_df = M2N50F5, score_cols = c(1, 2), lab_col = 3, fold_col = 4,
modnames = c("m1", "m2"), dsids = 1:5)
autoplot(cvcurves3)
```

## 8. Basic performance measures

The `evalmod` function also calculates basic evaluation measures - error, accuracy, specificity, sensitivity, and precision.

Measure Description

```  error Error rate
```

accuracy Accuracy specificity Specificity, TNR, 1 - FPR sensitivity Sensitivity, TPR, Recall precision Precision, PPV mcc Matthews correlation coefficient fscore F-score

### Basic measure calculations

The `mode = "basic"` option makes the `evalmod` function calculate the basic evaluation measures instead of performing ROC and Precision-Recall calculations.

```# Calculate basic evaluation measures
mmpoins <- evalmod(mmmdat2, mode = "basic")
```

### S3 generics

All the S3 generics except for `auc`, `part` and `pauc` are effective for the S3 object generated by this approach.

```# Show normalized ranks vs. error rate and accuracy
autoplot(mmpoins, c("error", "accuracy"))

# Show normalized ranks vs. specificity, sensitivity, and precision
autoplot(mmpoins, c("specificity", "sensitivity", "precision"))

# Show normalized ranks vs. Matthews correlation coefficient and F-score
autoplot(mmpoins, c("mcc", "fscore"))
```

#### Normalized ranks and predicted scores

In addition to the basic measures, the `autoplot` function can plot normalized ranks vs. scores and labels.

```# Show normalized ranks vs. scores and labels
autoplot(mmpoins, c("score", "label"))
```

#### Example of the as.data.frame function

The `as.data.frame` function also works for the precrec objects of the basic measures.

```# Convert mmpoins to a data frame
mmpoins.df <- as.data.frame(mmpoins)

# Use knitr::kable to display the result in a table format
knitr::kable(head(mmpoins.df))
```

## 9. Partial AUCs

The `part` function calculates partial AUCs and standardized partial AUCs of both ROC and precision-recall curves. Standardized pAUCs (spAUCs) are standardized to the score range between 0 and 1.

### partial AUC calculations

It requires an S3 object produced by the `evalmod` function and uses `xlim` and `ylim` to specify the partial area of your choice. The `pauc` function outputs a data frame with the pAUC scores.

```# Calculate ROC and Precision-Recall curves
curves <- evalmod(scores = P10N10\$scores, labels = P10N10\$labels)

# Calculate partial AUCs
curves.part <- part(curves, xlim = c(0.0, 0.25))

# Retrieve a dataframe of pAUCs
paucs.df <- pauc(curves.part)

# Use knitr::kable to display the result in a table format
knitr::kable(paucs.df)
```

### S3 generics

All the S3 generics are effective for the S3 object generated by this approach.

```# Show ROC and Precision-Recall curves
autoplot(curves.part)
```

## 10. Fast AUC (ROC) calculation

The area under the ROC curve can be calculated from the U statistic, which is the test statistic of the Mann–Whitney U test.

### AUC calculation with the U statistic

The `evalmod` function calculates AUCs with the U statistic when mode = 'aucroc'.

```# Calculate AUC (ROC)
aucs <- evalmod(scores = P10N10\$scores, labels = P10N10\$labels, mode = 'aucroc')

# Convert to data.frame
aucs.df <- as.data.frame(aucs)

# Use knitr::kable to display the result in a table format
knitr::kable(aucs.df)
```

## 11. Confidence intervals of AUCs

The `auc_ci` function calculates confidence intervals of the calculated ROCs by the `evalmod` function.

### Default CI calculation with normal distribution and alpha=0.05

The `auc_ci` function calculates CIs for both ROC and precision-recall AUCs. The specified data must contain multiple datasets, such as cross-validation data.

```# Calculate CI of AUCs with normal distibution
auc_ci <- auc_ci(smcurves)

# Use knitr::kable to display the result in a table format
knitr::kable(auc_ci)
```

### CI calculation with a different alpha (0.01)

The `auc_ci` function accepts a different significance level.

```# Calculate CI of AUCs with alpha = 0.01
auc_ci_a <- auc_ci(smcurves, alpha = 0.01)

# Use knitr::kable to display the result in a table format
knitr::kable(auc_ci_a)
```

### CI calculation with t-distribution

The `auc_ci` function accepts either normal or t-distribution for CI calculation.

```# Calculate CI of AUCs t-distribution
auc_ci_t <- auc_ci(smcurves, dtype = "t")

# Use knitr::kable to display the result in a table format
knitr::kable(auc_ci_t)
```

## 12. Balanced and imbalanced datasets

It is easy to simulate various scenarios, such as balanced vs. imbalanced datasets, by using the `evalmod` and `create_sim_samples` functions.

### Data preparation

```# Balanced dataset
samps5 <- create_sim_samples(100, 100, 100, "all")
simmdat1 <- mmdata(samps5[["scores"]], samps5[["labels"]],
modnames = samps5[["modnames"]], dsids = samps5[["dsids"]])

# Imbalanced dataset
samps6 <- create_sim_samples(100, 25, 100, "all")
simmdat2 <- mmdata(samps6[["scores"]], samps6[["labels"]],
modnames = samps6[["modnames"]], dsids = samps6[["dsids"]])
```

### ROC and Precision-Recall calculations

The `evalmod` function automatically detects multiple models and multiple test datasets.

```# Balanced dataset
simcurves1 <- evalmod(simmdat1)

# Imbalanced dataset
simcurves2 <- evalmod(simmdat2)
```

### Balanced vs. imbalanced datasets

ROC plots are unchanged between balanced and imbalanced datasets, whereas Precision-Recall plots show a clear difference between them. See our article or website for potential pitfalls by using ROC plots with imbalanced datasets.

```# Balanced dataset
autoplot(simcurves1)

# Imbalanced dataset
autoplot(simcurves2)
```

## 13. Citation

Precrec: fast and accurate precision-recall and ROC curve calculations in R

Takaya Saito; Marc Rehmsmeier

Bioinformatics 2017; 33 (1): 145-147.

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precrec documentation built on April 6, 2021, 5:07 p.m.