The `riskyr`

data structures essentially describe networks 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 some parameter as a function of others. A functional perspective illustrates how the value of some parameter (or its values) changes as a function of other parameters (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 2 functions for viewing parameters as a function of other parameters (and their values).

The function `plot_curve`

draws the curves (or lines) of selected parameters as a function of the prevalene (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 value of prevalence `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 `prev`

.

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%:

```
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 = .8)
```

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).

Other curves (or rather lines) drawn by `plot_curve`

include the proportion of positive decisions `ppod`

and overall accuracy `acc`

, each as a function of 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)", cex.lbl = .8)
```

The function `plot_plane`

draws a plane for a selected parameter as a function of sensitivity and specificity (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:

`plot_plane(prev = high.prev, sens = .80, spec = (1 - .096), what = "PPV", title.lbl = "A. Mammography (BRCA1)", cex.lbl = .8)`

`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", title.lbl = "C. Mammography (BRCA1)", phi = 45, cex.lbl = .8)`

`plot_plane(prev = high.prev, sens = .80, spec = (1 - .096), what = "acc", title.lbl = "D. Mammography (BRCA1)", cex.lbl = .8)`

`riskyr`

VignettesNr. | 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 |