knitr::opts_chunk$set( collapse = TRUE, comment = "#>" ) # URLs: url_riskyr_org <- "https://riskyr.org/" # Load pkg: library("riskyr")
The greatest value of a picture is when it forces us to notice what we never expected to see.
(John W. Tukey)^[Tukey, J.W. (1977), Exploratory data analysis. Reading, MA: Addison-Wesley. (p. vi).]
The key riskyr data structure essentially describes a network of dependencies.
This is best illustrated by the network diagram (see examples of plot_fnet()
in the user guide and data formats).
However, sometimes it is instructive to view all possible values of a parameter as a function of some other variable.
A functional perspective illustrates how the value of some variable (or its values) changes as a function of another (and their values).
The basic format of a function is $y = f(x)$, which illustrates how values of\ $y$ depend on values of\ $x$ given some function\ $f$. riskyr provides two functions for viewing parameters as a function of other parameters (and their values).
The plot_curve()
function draws the curves (or lines) of selected parameters as a function of the prevalence (with prev
ranging from\ 0 to\ 1)
for a given decision process or diagnostic test (i.e., given values of\ sens
and\ spec
):
$$y \ = \ f(\texttt{prev} \textrm{, from 0 to 1}) \textrm{ with } y \in {\texttt{PPV}, \texttt{NPV}, \texttt{ppod}, \texttt{acc}} \ \ \ \ \ \ (1)$$
As an example, reconsider our original scenario (on mammography screening, see user guide). Earlier, we computed a positive predictive value (PPV) of\ 7.8%.
But rather than just computing a single value, we could ask: How do values of PPV develop as a function of prevalence? The plot_curve()
function illustrates this relationship:
plot_curve(prev = .01, sens = .80, spec = (1 - .096), what = c("prev", "PPV", "NPV"), title_lbl = "Mammography screening", cex.lbl = .8)
The curves illustrate that values of PPV
and NPV
crucially depend on the prevalence value\ prev
in the current population. In fact, they actually vary across their entire range (i.e., from\ 0 to\ 1), rendering any communication of their value utterly meaningless without specifying the current population's prevalence value.
The dependency of\ PPV
and\ NPV
on\ prev
can be illustrated by assuming a higher prevalence rate. For instance, if we knew that some woman was genetically tested and known to exhibit the notorious BRCA1 mutation, the prevalence value of her corresponding population (given a positive mammography result in a routine screening) is increased to about 60% (graph not shown here to save space, but try running the following code for yourself):
high.prev <- .60 # assume increased prevalence due to BRCA1 mutation plot_curve(prev = high.prev, sens = .80, spec = (1 - .096), what = c("prev", "PPV", "NPV"), title_lbl = "Mammography screening (BRCA1 mutation)", cex.lbl = .80)
This shows that ---\ given an increased prevalence value prev
of 60%\ --- the positive predictive value\ PPV
of a positive test result increases from\ 7.8% (in the standard population) to around\ 93% (given the BRCA1 mutation).
In addition, the actual values of population and test parameters are often unclear. The plot_curve()
function reflects this by providing an uncertainty parameter\ uc
that is expressed as a percentage of the specified value. For instance, the following assumes that our parameter values may deviate up to\ 5% from the specified values and marks the corresponding ranges of uncertainty as shaded areas around the curves that assume exact parameter values.
Both the notions of expressing probabilities as a function of prevalence and of uncertainty ranges for imprecise parameter estimates can be extended to other probabilities. The following curves show the full set of curves currently drawn by\ plot_curve()
. In addition to the predictive values\ PPV
and\ NPV
, we see that the bias or proportion of positive decisions\ ppod
and the overall accuracy\ acc
also vary as a function of the prevalence\ prev
:
high.prev <- .60 # assume increased prevalence due to BRCA1 mutation plot_curve(prev = high.prev, sens = .80, spec = (1 - .096), what = c("prev", "PPV", "NPV", "ppod", "acc"), title_lbl = "Mammography screening (BRCA1 mutation)", uc = .05, cex.lbl = .80)
The plot_plane()
function draws a plane for a selected parameter as a function of sensitivity and specificity values (with\ sens
and\ spec
both ranging from\ 0 to\ 1) for a given prevalence\ prev
:
$$y \ = \ f(\texttt{sens} \times\ \texttt{spec} \textrm{, both from 0 to 1, for given value of } \texttt{prev}) \textrm{ with } y \in {\texttt{PPV}, \texttt{NPV}, \texttt{ppod}, \texttt{acc}} \ \ \ \ \ \ \ (2)$$
Some examples (not shown here, but please try evaluating the following function calls):
plot_plane(prev = high.prev, sens = .80, spec = (1 - .096), what = "PPV", title_lbl = "A. Mammography (BRCA1)", cex.lbl = .8)
Related plots (showing different probabilities) include:
plot_plane(prev = high.prev, sens = .80, spec = (1 - .096), what = "NPV", title_lbl = "B. Mammography (BRCA1)", cex.lbl = .8) plot_plane(prev = high.prev, sens = .80, spec = (1 - .096), what = "ppod", what_col = "firebrick", title_lbl = "C. Mammography (BRCA1)", phi = 45, cex.lbl = .8) plot_plane(prev = high.prev, sens = .80, spec = (1 - .096), what = "acc", what_col = "forestgreen", title_lbl = "D. Mammography (BRCA1)", cex.lbl = .8)
Overall, viewing conditional probabilities (like\ PPV
or NPV
, but also\ ppod
or\ acc
) as a function of other probabilities (e.g., prev
, sens
, spec
or fart
) often reveals unexpected relationships and can enable new insights.
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 | https://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/ |
We appreciate your feedback, comments, or questions.
Please report any riskyr-related issues at https://github.com/hneth/riskyr/issues/.
Contact us at contact.riskyr@gmail.com with any comments, questions, or suggestions.
| Nr. | Vignette | Content |
| ---: |:---------|:-----------|
| A. | User guide | Motivation and general instructions |
| B. | Data formats | Data formats: Frequencies and probabilities |
| C. | Confusion matrix | Confusion matrix and accuracy metrics |
| D. | Functional perspectives | Adopting functional perspectives |
| E. | Quick start primer | Quick start primer |
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