Date: 2017-08-23

# Introduction to precrec

#### 2017-08-23

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 eight 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

#### 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))

    ##    user  system elapsed
    ##   1.041   0.072   1.156
    ##    user  system elapsed
    ##  14.784   1.849  16.760

#### 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)

modnames | dsids | curvetypes | aucs
--- | --- | --- | ---
m1 | 1 | ROC | 0.7200000
m1 | 1 | PRC | 0.7397716

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

| modnames | dsids | curvetypes | aucs
--- | --- | --- | --- | ---
2 | m1 | 1 | PRC | 0.7397716

#### 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))

x | y | modname | dsid | type
--- | --- | --- | --- | ---
0.000 | 0.0 | m1 | 1 | ROC
0.000 | 0.1 | m1 | 1 | ROC
0.000 | 0.2 | m1 | 1 | ROC
0.001 | 0.2 | m1 | 1 | ROC
0.002 | 0.2 | m1 | 1 | ROC
0.003 | 0.2 | m1 | 1 | ROC

## 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))

x | y | modname | dsid | type
--- | --- | --- | --- | ---
0.000 | 0 | random | 1 | ROC
0.001 | 0 | random | 1 | ROC
0.002 | 0 | random | 1 | ROC
0.003 | 0 | random | 1 | ROC
0.004 | 0 | random | 1 | ROC
0.005 | 0 | random | 1 | ROC

## 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))

x | y | modname | dsid | type
--- | --- | --- | --- | ---
0.000 | 0.0 | m1 | 1 | ROC
0.000 | 0.1 | m1 | 1 | ROC
0.000 | 0.2 | m1 | 1 | ROC
0.000 | 0.3 | m1 | 1 | ROC
0.001 | 0.3 | m1 | 1 | ROC
0.002 | 0.3 | m1 | 1 | ROC

## 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))

x | y | ymin | ymax | modname | type
--- | --- | --- | --- | --- | ---
0.000 | 0.0 | 0.0000000 | 0.0000000 | random | ROC
0.000 | 0.1 | 0.0413733 | 0.1586267 | random | ROC
0.001 | 0.1 | 0.0413733 | 0.1586267 | random | ROC
0.002 | 0.1 | 0.0413733 | 0.1586267 | random | ROC
0.003 | 0.1 | 0.0413733 | 0.1586267 | random | ROC
0.004 | 0.1 | 0.0413733 | 0.1586267 | random | ROC

## 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))

score1 | score2 | label | fold
--- | --- | --- | ---
2.0606025 | 1.0689227 | pos | 1
0.3066092 | 0.1745491 | pos | 3
1.5597733 | -1.5666375 | pos | 1
-0.6044989 | 1.1572727 | pos | 3
-0.2229031 | 0.6070042 | pos | 5
-0.7679551 | -1.7908147 | pos | 5

#### 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))

x | y | ymin | ymax | modname | type
--- | --- | --- | --- | --- | ---
0.00 | NA | NA | NA | random | score
0.05 | 1.7987698 | 1.6044863 | 1.993053 | random | score
0.10 | 1.2707917 | 1.1117231 | 1.429860 | random | score
0.15 | 1.0325857 | 0.9020354 | 1.163136 | random | score
0.20 | 0.8699837 | 0.7380831 | 1.001884 | random | score
0.25 | 0.7332653 | 0.6258377 | 0.840693 | random | score

## 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)

modnames | dsids | curvetypes | paucs | spaucs
--- | --- | --- | --- | ---
m1 | 1 | ROC | 0.1006250 | 0.4025000
m1 | 1 | PRC | 0.2345849 | 0.9383396

### 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)

modnames | dsids | aucs | ustats
--- | --- | --- | ---
m1 | 1 | 0.72 | 72

## 11. 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)

## 12. Citation

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

Takaya Saito; Marc Rehmsmeier

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

doi: 10.1093/bioinformatics/btw570

## 13. External links

- Classifier evaluation with imbalanced datasets - our web site that contains several pages with useful tips for performance evaluation on binary classifiers.

- The Precision-Recall Plot Is More Informative than the ROC Plot When Evaluating Binary Classifiers on Imbalanced Datasets - our paper that summarized potential pitfalls of ROC plots with imbalanced datasets and advantages of using precision-recall plots instead.