# Creating FFTs for heart disease

## Tutorial: Creating FFTs for heart disease

This tutorial on using the FFTrees package follows the examples presented in Phillips, Neth, Woike, & Gaissmaier (2017) (freely available in html | PDF):

• Phillips, N. D., Neth, H., Woike, J. K. & Gaissmaier, W. (2017). FFTrees: A toolbox to create, visualize, and evaluate fast-and-frugal decision trees. Judgment and Decision Making, 12 (4), 344–368.

In the following, we explain how to use FFTrees to create, evaluate and visualize FFTs in four simple steps.

### Step 1: Install and load the FFTrees package

We can install FFTrees from CRAN using install.packages(). (We only need to do this once.)

# Install the package from CRAN:
install.packages("FFTrees")

To use the package, we first need to load it into your current R session. We load the package using library():

# Load the package:
library(FFTrees)

The FFTrees package contains several vignettes that guide through the package’s functionality (like this one). To open the main guide, run FFTrees.guide():

# Open the main package guide:
FFTrees.guide()

### Step 2: Create FFTs from training data (and test on testing data)

In this example, we will create FFTs from a heart disease data set. The training data are in an object called heart.train, and the testing data are in an object called heart.test. For these data, we will predict diagnosis, a binary criterion that indicates whether each patent has or does not have heart disease (i.e., is at high-risk or low-risk).

To create an FFTrees object, we use the function FFTrees() with two main arguments:

1. formula expects a formula indicating a binary criterion variable as a function of one or more predictor variable(s) to be considered for the tree. The shorthand formula = diagnosis ~ . means to include all predictor variables.

2. data specifies the training data used to construct the FFTs (which must include the criterion variable).

Here is how we can construct our first FFTs:

# Create an FFTrees object:
heart.fft <- FFTrees(formula = diagnosis ~ .,           # Criterion and (all) predictors
data = heart.train,                # Training data
data.test = heart.test,            # Testing data
main = "Heart Disease",            # General label
decision.labels = c("Low-Risk", "High-Risk")  # Decision labels (False/True)
)

The resulting trees, decisions, and accuracy statistics are now stored in an FFTrees object called heart.fft.

#### Other arguments

• algorithm: There are two different algorithms available to build FFTs "ifan" (Phillips et al., 2017) and "dfan" (Phillips et al., 2017). ("max" (Martignon, Katsikopoulos, & Woike, 2008), and "zigzag" (Martignon et al., 2008) are no longer supported).

• max.levels: Changes the maximum number of levels allowed in the tree.

The following arguments apply to the “ifan” and “dfan” algorithms only:

• goal.chase: The goal.chase argument changes which statistic is maximized during tree construction (for the "ifan" and "dfan" algorithms). Possible arguments include "acc", "bacc", "wacc", "dprime", and "cost". The default is "wacc" with a sensitivity weight of 0.50 (which renders it identical to "bacc").

• goal: The goal argument changes which statistic is maximized when selecting trees after construction (for the "ifan" and "dfan" algorithms). Possible arguments include "acc", "bacc", "wacc", "dprime", and "cost".

• my.tree: We can define a tree verbally as a sentence using the my.tree argument. See the Defining an FFT verbally vignette for details.

### Step 3: Inspect and summarize FFTs

Now we can inspect and summarize the generated decision trees. We will start by printing the FFTrees object to return basic information to the console:

# Print an FFTrees object:
heart.fft
## Heart Disease
## FFTrees
## - Trees: 7 fast-and-frugal trees predicting diagnosis
## - Outcome costs: [hi = 0, mi = 1, fa = 1, cr = 0]
##
## FFT #1: Definition
## [1] If thal = {rd,fd}, decide High-Risk.
## [2] If cp != {a}, decide Low-Risk.
## [3] If ca > 0, decide High-Risk, otherwise, decide Low-Risk.
##
## FFT #1: Training Accuracy
## Training data: N = 150, Pos (+) = 66 (44%)
##
## |          | True + | True - | Totals:
## |----------|--------|--------|
## | Decide + | hi  54 | fa  18 |      72
## | Decide - | mi  12 | cr  66 |      78
## |----------|--------|--------|
##   Totals:        66       84   N = 150
##
## acc  = 80.0%   ppv  = 75.0%   npv  = 84.6%
## bacc = 80.2%   sens = 81.8%   spec = 78.6%
##
## FFT #1: Training Speed, Frugality, and Cost
## mcu = 1.74,  pci = 0.87,  E(cost) = 0.200

The output tells us several pieces of information:

• The tree with the highest weighted sensitivity wacc with a sensitivity weight of 0.5 is selected as the best tree.

• Here, the best tree, FFT #1 uses three cues: thal, cp, and ca.

• Several summary statistics for this tree in training and test data are summarized.

All statistics to evaluate each tree can be derived from a 2 x 2 confusion table:

For definitions of all accuracy statistics, see the accuracy statistics vignette.

### Step 4: Visualise the final FFT

Use plot() to visualize an FFT (an FFTrees object):

# Plot predictions of the best FFT when applied to test data:
plot(heart.fft,      # An FFTrees object
data = "test")  # data to use (i.e., either "train" or "test")?

#### Other arguments

• tree: Which tree in the object should beplotted? To plot a tree other than the best fitting tree (FFT #1), just specify another tree as an integer (e.g.; plot(heart.fft, tree = 2)).

• data: For which dataset should statistics be shown? Either data = "train" (showing fitting or “Training” performance by default), or data = "test" (showing prediction or “Testing” performance).

• stats: Should accuracy statistics be shown with the tree? To show only the tree, without any performance statistics, include the argument stats = FALSE.

# Plot only the tree, without accuracy statistics:
plot(heart.fft, what = "tree")

# plot(heart.fft, stats = FALSE)  #  The 'stats' argument has been deprecated.
• comp: Should statistics from competitive algorithms be shown in the ROC curve? To remove the performance statistics of competitive algorithms (e.g.; regression, random forests), include the argument comp = FALSE.

• what: To show individual cue accuracies (in ROC space), include the argument what = "cues":

# Plot cue accuracies (for training data) in ROC space:
plot(heart.fft, what = "cues")

See the Plotting FFTrees vignette for details on plotting FFTs.

#### Accessing outputs

An FFTrees object contains many different outputs, to see them all, run names()

# Show the names of all of the outputs in heart.fft:
names(heart.fft)
## [1] "criterion_name" "cue_names"      "formula"        "trees"
## [5] "data"           "params"         "competition"    "cues"

#### Predicting for new data

To predict classifications for a new dataset, use the standard predict() function. For example, here’s how to predict the classifications for data in the heartdisease object (which actually is just a combination of heart.train and heart.test):

# Predict classifications for a new dataset:
predict(heart.fft,
newdata = heartdisease)

#### Defining FFTs in words

To define a specific FFT and apply it to data, we can define a tree by providing its verbal description to the my.tree argument:

# Create an FFT manually (from description):
my.heart.fft <- FFTrees(formula = diagnosis ~.,
data = heart.train,
data.test = heart.test,
main = "Custom Heart FFT",
my.tree = "If chol > 350, predict True.
If cp != {a}, predict False.
If age <= 35, predict False, otherwise, predict True.")

Here is the resulting tree:

plot(my.heart.fft)

The resulting tree is actually not too bad, although its first node is pretty worthless (as it only classifies 3 cases, all as false alarms). Thus, omitting the first node will result in an even simpler FFT that cannot be worse. But see for yourself — and see the Defining an FFT verbally vignette for additional details on defining FFTs from verbal descriptions.

## Vignettes

Here is a complete list of the vignettes available in the FFTrees package:

Vignette Description
Main guide An overview of the FFTrees package
1 Tutorial: FFTs for heart disease An example of using FFTrees() to model heart disease diagnosis
2 Accuracy statistics Definitions of accuracy statistics used throughout the package
3 Creating FFTs with FFTrees() Details on the main function FFTrees()
4 Specifying FFTs directly How to directly create FFTs with my.tree without using the built-in algorithms
5 Visualizing FFTs with plot() Plotting FFTrees objects, from full trees to icon arrays
6 Examples of FFTs Examples of FFTs from different datasets contained in the package

## References

Martignon, L., Katsikopoulos, K. V., & Woike, J. K. (2008). Categorization with limited resources: A family of simple heuristics. Journal of Mathematical Psychology, 52(6), 352–361. https://doi.org/10.1016/j.jmp.2008.04.003

Phillips, N. D., Neth, H., Woike, J. K., & Gaissmaier, W. (2017). FFTrees: A toolbox to create, visualize, and evaluate fast-and-frugal decision trees. Judgment and Decision Making, 12(4), 344–368. Retrieved from https://journal.sjdm.org/17/17217/jdm17217.pdf