### A toolbox for rendering risk literacy more transparent

Risk-related information — like the prevalence of conditions and the sensitivity and specificity of diagnostic tests or treatment decisions — can be expressed in terms of probabilities or frequencies. By providing a toolbox of methods and metrics, riskyr computes, translates, and visualizes risk-related information in a variety of ways. Offering multiple complementary perspectives on the interplay between key parameters renders teaching and training of risk literacy more transparent.

## Motivation

Solving a problem simply means representing it
so as to make the solution transparent. (H.A. Simon)1

The goals of riskyr are less of a computational and more of a representational nature: We express risk-related information in multiple formats, facilitate the translation between them, and provide a variety of attractive visualizations that emphasize different aspects of risk-related scenarios. Whereas people find it difficult to understand and compute information expressed in terms of probabilities, the same information is easier to understand and compute when expressed in terms of frequencies (e.g., Gigerenzer, 2002, 2014; Gigerenzer & Hoffrage, 1995). But rather than just expressing probabilities in terms of frequencies, riskyr allows translating between formats and illustrates the relationships between different representations in a variety of ways. Switching between and interacting with different representations fosters transparency and boosts human understanding of risk-related information.2

The basic assumptions and aspirations driving the current development of riskyr include:

1. Effective training in risk literacy requires transparent representations, smart strategies, and simple tools.

2. We aim to provide a set of (computational and representational) functions that facilitate various calculations, translations between formats, and enable a range of alternative views on the interplay between probabilities and frequencies.

3. Just as no single tool fits all tasks, no single graph illustrates all aspects of a problem. A variety of visualizations that illustrate the interplay of parameters and metrics can facilitate active and explorative learning. It is particularly helpful to view relationships from alternative perspectives and to observe the change of one parameter as a function of others.

Based on these assumptions and goals, riskyr provides a range of computational and representational tools. Importantly, the objects and functions in the riskyr toolbox are not isolated, but complement, explain, and support each other. All functions and visualizations can be used separately or explored interactively, providing immediate feedback on the effect of changes in parameter values. By providing a variety of customization options, users can explore and design representations of risk-related information that fit to different tasks and meet their personal needs and goals.

## Getting riskyr

### Installation

install.packages('riskyr')  # install riskyr from CRAN client
library('riskyr')           # load to use the package
# install.packages('devtools')
devtools::install_github('hneth/riskyr')

## Quick start guide

### Defining a scenario

riskyr is designed to address problems like the following:3

Screening for hustosis

A screening device for detecting the clinical condition of hustosis is developed. The current device is very good, but not perfect. We have the following information:
1. About 4% of the people of the general population suffer from hustosis.
2. If someone suffers from hustosis, there is a chance of 80% that he or she will test positively for the condition.
3. If someone is free from hustosis, there is a chance of 5% that he or she will still test positively for the condition.

Mr. and Ms. Smith have both been screened with the device:
- Mr. Smith tested positively (i.e., received a diagnosis of hustosis).
- Ms. Smith tested negatively (i.e., was judged to be free of hustosis).

- What is the probability that Mr. Smith actually suffers from hustosis?
- What is the probability that Ms. Smith is actually free of hustosis?

#### Probabilities provided

The first challenge in solving such problems is in understanding the information that is being provided. The problem description provides three essential probabilities:

1. The condition’s prevalence (in the general population) is 4%: prev = .04.
2. The device’s or diagnostic decision’s sensitivity is 80%: sens = .80.
3. The device’s or diagnostic decision’s false alarm rate is 5%: fart = .05, implying a specificity of (100% $$-$$ 5%) = 95%: spec = .95.

The second challenge here lies in understanding the questions that are being asked — and in realizing that their answers are not simply the decision’s sensitivity or specificity values. Instead, we are asked to provide two conditional probabilities:

• The conditional probability of suffering from the condition given a positive test result,
aka. the positive predictive value (PPV).
• The conditional probability of being free of the condition given a negative test result,
aka. the negative predictive value (NPV).

#### Translating into frequencies

One of the best tricks in risk literacy education is to translate probabilistic information into frequencies.4 To do this, we imagine a representative sample of N = 1000 individuals. Rather than asking about the probabilities for Mr. and Ms. Smith, we could re-frame the questions as:

Assuming a representative sample of 1000 individuals:
- What proportion of individuals with a positive test result actually suffer from hustosis?
- What proportion of individuals with a negative test result are actually free of hustosis?

#### Using riskyr

Here is how riskyr allows you to view and solve such problems:

library(riskyr)  # loads the package

#### Creating a scenario from probabilities

We define a new riskyr scenario (called hustosis) by using the riskyr() function and entering the information provided by our problem as its arguments:

hustosis <- riskyr(scen_lbl = "Example",
cond_lbl = "Hustosis",
dec_lbl = "Screening test",
popu_lbl = "Sample",
N = 1000,  # population size
prev = .04, sens = .80, spec = (1 - .05)  # 3 probabilities
)

By providing the argument N = 1000 we define the scenario for a target population of 1000 people. If we leave this parameter unspecified (or NA), the riskyr() function will automatically pick a suitable value of N.

#### Summary

To obtain a quick overview of key parameter values, we ask for the summary of hustosis:

summary(hustosis)  # summarizes key parameter values: 

The summary distinguishes between probabilities, frequencies, and accuracy information. In Probabilities we find the answer to both of our questions that take into account all the information provided above:

• The conditional probability that Mr. Smith actually suffers from hustosis given his positive test result is 40% (as PPV = 0.400).

• The conditional probability that Ms. Smith is actually free of hustosis given her negative test result is 99.1% (as NPV = 0.991).

If find these answers surprising, you are an ideal candidate for additional insights into the realm of risk literacy. A key component of riskyr is to analyze and view a scenario from a variety of different perspectives. To get you started immediately, we only illustrate some introductory commands here and focus on different types of visualizations. (Call riskyr.guide() for various vignettes that provide more detailed information.)

#### Creating a scenario from frequencies

Rather than defining our hustosis scenario by providing 3 essential probabilities (prev, sens, and spec), we could define the same scenario by providing 4 essential frequencies (hi, mi, fa, and cr) as follows:

hustosis_2 <- riskyr(scen_lbl = "Example",
cond_lbl = "Hustosis",
dec_lbl = "Screening test",
popu_lbl = "Sample",
hi = 32, mi = 8, fa = 48, cr = 912  # 4 key frequencies
)

As we took the values of these frequencies from the summary of hustosis, the hustosis_2 scenario should contain exactly the same information as hustosis:

all.equal(hustosis, hustosis_2)  # do both contain the same information?
#> [1] TRUE

### Visualizations

Various visualizations of riskyr scenarios can be created by a range of plotting functions.

#### Prism plot

The default type of plot used in riskyr is a prism plot (or network diagram) that shows key frequencies of a scenario as nodes and key probabilities as edges linking the nodes:

plot(hustosis)  # default plot

# => internally calls plot_prism(...) with many additional arguments:
# plot(hustosis, type = "prism", by = "cddc", area = "no", f_lbl = "num", p_lbl = "mix")

#### Tree diagram

A tree diagram is the upper half of a prism plot, which can be obtained by plotting a scenario with 1 of 3 perspectives:

1. by condition (by = "cd"), to split the population into TRUE vs. FALSE (cond_true vs. cond_false) cases;
2. by decision (by = "dc"), to split the population into negative vs. positive (dec_neg vs. dec_pos) decisions;
3. by accuracy (by = "ac"), to split the population into correct vs. incorrect (dec_cor vs. dec_err) decisions.

For instance, the following command plots a frequency tree by decisions:

plot(hustosis, by = "dc")  # plot a tree diagram (by decision)

This particular tree splits the population of N = 1000 individuals into two subgroups by decision (by = "dc") and contains the answer to the second (frequency) version of our questions:

• The proportion of individuals with a positive test result who actually suffer from hustosis is the frequency of “true positive” cases (shown in darker green) divided by “decision positive” cases (shown in purple): 32/80 = .400 (corresponding to our value of PPV above).
• The proportion of individuals with a negative test result who are actually free from hustosis is the frequency of “true negative” cases (shown in lighter green) divided by “decision negative” cases (shown in blue): 912/920 = .991 (corresponding to our value of NPV above, except for minimal differences due to rounding).

Of course, the frequencies of these ratios were already contained in the hustosis summary above. But the representation in the form of a tree diagram makes it easier to understand the decomposition of the population into subgroups and to see which frequencies are required to answer a particular question.

#### Icon array

An icon array shows the classification result for each of N = 1000 individuals in our population:

plot(hustosis, type = "icons")   # plot an icon array 

While this particular icon array is highly regular (as both the icons and classification types are ordered), riskyr provides many different versions of this type of graph. This allows viewing the probability of diagnostic outcomes as either frequency, area, or density (see ?plot_icons for details and examples).

#### Area plot

An area plot (or mosaic plot) offers a way of expressing classification results as the relationship between areas. Here, the entire population is represented as a square and the probability of its subgroups as the size of rectangles (see ?plot_area for details and examples):

plot(hustosis, type = "area")  # plot an area/mosaic plot (by = "cddc")

#### Table plot

When not scaling the size of rectangles by their relative frequencies or probabilities, we can plot basic scenario information as a 2-by-2 confusion (or contingency) table (see ?plot_tab for details and examples):

plot(hustosis, type = "tab")  # plot 2x2 confusion table (by = "cddc") 

#### Bar plot

A bar plot allows comparing relative frequencies as the heights of bars (see ?plot_bar for details and examples):

plot(hustosis, type = "bar", f_lbl = "abb")  # plot bar chart (by "all" perspectives): 

#### Curves

By adopting a functional perspective, we can ask how the values of some probabilities (e.g., the predictive values PPV and NPV) change as a function of another (e.g., the condition’s prevalence prev, see ?plot_curve for details and examples):

plot(hustosis, type = "curve", uc = .05)   # plot probability curves (by prevalence):

#### Planes

When parameter values systematically depend on two other parameters, we can plot this as a plane in a 3D cube. The following graph plots the PPV as a function of the sensitivity (sens) and specificity (spec) of our test for a given prevalence (prev, see ?plot_plane for details and examples):

plot(hustosis, type = "plane")  # plot probability plane (by sens x spec):

The L-shape of this plane reveals a real problem with our current test: Given a prevalence of 4% for hustosis in our target population, the PPV remains very low for the majority of the possible range of sensitivity and specificity values. To achieve a high PPV, the key requirement for our test is an extremely high specificity. Although our current specificity value of 95% (spec = .95) may sound pretty good, it is still not high enough to yield a PPV beyond 40%.

### Using existing scenarios

As defining your own scenarios can be cumbersome and the literature is full of risk-related problems (often referred to as “Bayesian reasoning”), riskyr provides a set of — currently 24 — pre-defined scenarios (stored in a list scenarios). Here, we provide an example that shows how you can select and explore them.

#### Selecting a scenario

Let us assume you want to learn more about the controversy surrounding screening procedures of prostate-cancer (known as PSA screening). Scenario 10 in our collection of scenarios is from an article on this topic (Arkes & Gaissmaier, 2012). To select a particular scenario, simply assign it to an R object. For instance, we can assign Scenario 10 to s10:

s10 <- scenarios$n10 # assign pre-defined Scenario 10 to s10 #### Scenario summary Our selected scenario object s10 is a list with 30 elements, which describe it in both text and numeric variables. The following commands provide an overview of s10 in text form: s10$scen_lbl   # a descriptive label
#> [1] "PSA test (patients)"
s10$cond_lbl # the current condition #> [1] "Prostate cancer" s10$dec_lbl    # the current decision
#> [1] "PSA-Test"
s10$popu_lbl # the current population #> [1] "Male patients with symptoms" s10$scen_apa   # scenario source (APA)
#> [1] "Arkes, H. R., & Gaissmaier, W. (2012). Psychological research and the prostate-cancer screening controversy. Psychological Science, 23(6), 547--553."

# summary(s10) # summarises a scenario

Generating some riskyr plots allows a quick visual exploration of the scenario. We only illustrate some selected plots and options here, and trust that you will play with and explore the rest for yourself.

#### Prism plots

A tree diagram is a prism plot that views the population from only one perspective, but provides a quick overview. In the following plot, the boxes are depicted as squares with area sizes that are scaled by relative frequencies (using the area = "sq" argument):

plot(s10, type = "tree", by = "cd", area = "sq",  # tree/prism plot with scaled squares
f_lbl = "def", f_lbl_sep = ":\n")            # custom frequency labels 

The prism plot (or network diagram) combines 2 tree diagrams to simultaneously provide two perspectives on a population (see Wassner et al., 2004). riskyr provides several variants of prism plots. To avoid redundancy to the previous tree diagram, the following version splits the population by accuracy and by decision (see the by = "acdc" argument). In addition, the frequencies are represented as horizontal rectangles (area = "hr") so that their relative width reflect the number of people in the corresponding subgroup:

plot(s10, type = "prism", by = "acdc", area = "hr",  # prism plot with horizontal rectangles
p_lbl = "num")                                  # numeric probability labels

#### Icon array

plot(s10, type = "icons", arr_type = "shuffled")   # plot a shuffled icon array 

#### Area plot

plot(s10, type = "area", p_split = "v", p_lbl = "def")  # plot an area/mosaic plot (with probabilities) 

#### Table plot

plot(s10, type = "tab", p_split = "h", p_lbl = "def")  # plot a 2x2 table (with probabilities)

#### Curves

The following curves show the values of several conditional probabilities as a function of prevalence:

plot(s10, type = "curve", what = "all", uc = .05)  # plot all curves (by prev):

Adding the argument what = "all" also shows the proportion of positive decisions (ppod) and the decision’s overall accuracy (accu) as a function of the prevalence (prev). Would you have predicted their shape without seeing this graph?

#### Planes

The following surface shows the negative predictive value (NPV) as a function of sensitivity and specificity (for a given prevalence):

plot(s10, type = "plane", what = "NPV")  # plot plane (as a function of sens x spec):

Hopefully, this brief overview managed to whet your appetite for visual exploration. If so, call riskyr.guide() for viewing the package vignettes and obtaining additional information.

riskyr originated out of a series of lectures and workshops on risk literacy.
The current version (0.2.0, as of Dec. 20, 2018) is under active development. Its primary designers are Hansjörg Neth, Felix Gaisbauer, Nico Gradwohl, and Wolfgang Gaissmaier, who are researchers at the department of Social Psychology and Decision Sciences at the University of Konstanz, Germany.

The riskyr package is open source software written in R and released under the GPL 2 | GPL 3 licenses.

### Resources

The following resources and versions are currently available:

Type: Version: URL:
A. riskyr (R package): Release version https://CRAN.R-project.org/package=riskyr
Development version https://github.com/hneth/riskyr
B. riskyrApp (R Shiny code): Online version http://riskyr.org
Development version https://github.com/hneth/riskyrApp
C. Online documentation: Release version https://hneth.github.io/riskyr
Development version https://hneth.github.io/riskyr/dev

### Reference

To cite riskyr in derivations and publications please use:

• Neth, H., Gaisbauer, F., Gradwohl, N., & Gaissmaier, W. (2018).
riskyr: A toolbox for rendering risk literacy more transparent.
Social Psychology and Decision Sciences, University of Konstanz, Germany.
Computer software (R package version 0.2.0, Dec. 20, 2018).

A BibTeX entry for LaTeX users is:

@Manual{riskyr,
title = {riskyr: A toolbox for rendering risk literacy more transparent},
author = {Hansjörg Neth and Felix Gaisbauer and Nico Gradwohl and Wolfgang Gaissmaier},
year = {2018},
organization = {Social Psychology and Decision Sciences, University of Konstanz},
note = {R package (version 0.2.0, Dec. 20, 2018)},
url = {https://CRAN.R-project.org/package=riskyr},
}    

Calling citation("riskyr") in the package also displays this information.

### References

• Arkes, H. R., & Gaissmaier, W. (2012). Psychological research and the prostate-cancer screening controversy. Psychological Science, 23, 547–553.

• Garcia-Retamero, R., & Cokely, E. T. (2017). Designing visual aids that promote risk literacy: A systematic review of health research and evidence-based design heuristics. Human Factors, 59, 582–627.

• Gigerenzer, G. (2002). Reckoning with risk: Learning to live with uncertainty. London, UK: Penguin.

• Gigerenzer, G. (2014). Risk savvy: How to make good decisions. New York, NY: Penguin.

• Gigerenzer, G., & Gaissmaier, W. (2011). Heuristic decision making. Annual Review of Psychology, 62, 451–482. [Available online]

• Gigerenzer, G., Gaissmaier, W., Kurz-Milcke, E., Schwartz, L., & Woloshin, S. (2007). Helping doctors and patients make sense of health statistics. Psychological Science in the Public Interest, 8, 53–96. [Available online]

• Gigerenzer, G., & Hoffrage, U. (1995). How to improve Bayesian reasoning without instruction: Frequency formats. Psychological Review, 102, 684–704.

• Hoffrage, U., Gigerenzer, G., Krauss, S., & Martignon, L. (2002). Representation facilitates reasoning: What natural frequencies are and what they are not. Cognition, 84, 343–352.

• Hoffrage, U., Krauss, S., Martignon, L., & Gigerenzer, G. (2015). Natural frequencies improve Bayesian reasoning in simple and complex inference tasks. Frontiers in Psychology, 6, 1473. [Available online]

• Hoffrage, U., Lindsey, S., Hertwig, R., & Gigerenzer, G. (2000). Communicating statistical information. Science, 290, 2261–2262.

• Khan, A., Breslav, S., Glueck, M., & Hornbæk, K. (2015). Benefits of visualization in the mammography problem. International Journal of Human-Computer Studies, 83, 94–113.

• Kurzenhäuser, S., & Hoffrage, U. (2002). Teaching Bayesian reasoning: An evaluation of a classroom tutorial for medical students. Medical Teacher, 24, 516–521.

• Kurz-Milcke, E., Gigerenzer, G., & Martignon, L. (2008). Transparency in risk communication. Annals of the New York Academy of Sciences, 1128, 18–28.

• Micallef, L., Dragicevic, P., & Fekete, J.-D. (2012). Assessing the effect of visualizations on Bayesian reasoning through crowd-sourcing. IEEE Transactions on Visualization and Computer Graphics, 18, 2536–2545.

• Neth, H., & Gigerenzer, G. (2015). Heuristics: Tools for an uncertain world. In R. Scott & S. Kosslyn (Eds.), Emerging trends in the social and behavioral sciences. New York, NY: Wiley Online Library. [Available online]

• Sedlmeier, P., & Gigerenzer, G. (2001). Teaching Bayesian reasoning in less than two hours. Journal of Experimental Psychology: General, 130, 380–400.

• Wassner, C., Martignon, L., & Biehler, R. (2004). Bayesianisches Denken in der Schule. Unterrichtswissenschaft, 32, 58–96.

[Updated 2019-05-24 by hn.]

1. Simon, H.A. (1996). The Sciences of the Artificial (3rd ed.). The MIT Press, Cambridge, MA. (p. 132).

2. To clarify our notion of “risk” in this context, we need to distinguish it from its everyday usage as anything implying a chance of danger or harm.
In basic research on judgment and decision making and the more applied fields of risk perception and risk communication, the term risk typically refers to decisions or events for which the options and their consequences are known and probabilities for all possible outcomes can be provided.
For our present purposes, the notion of risk-related information refers to any scenario in which some events of interest are determined by probabilities. While it is important that quantitative (estimates of) probabilities are provided, their origin, reliability and validity is not questioned here. Thus, the probabilities provided can be based on clinical intuition, on recordings of extensive experience, or on statistical simulation models (e.g., repeatedly casting dice and counting the frequencies of outcomes).
This notion of risk is typically contrasted with the much wider notion of uncertainty in which options or probabilities are unknown or cannot be quantified. (See Gigerenzer and Gaissmaier, 2011, or Neth and Gigerenzer, 2015, on this conceptual distinction and corresponding decision strategies.)

3. See Gigerenzer (2002, 2014), Gigerenzer and Hoffrage, U. (1995), Gigerenzer et al. (2007), and Hoffrage et al. (2015) for scientific background information and similar problems. See Sedlmeier and Gigerenzer (2001) and Kurzenhäuser and Hoffrage (2002) for related training programs (with remarkable results), and Micallef et al. (2012) and Khan et al. (2015) for (rather sceptical and somewhat sobering) studies on the potential benefits of static representations for solving Bayesian problems.

4. See Gigerenzer and Hoffrage (1995) and Hoffrage et al. (2000, 2002) on the concept of natural frequencies.