# Cost-effectiveness acceptability curve plots

## Introduction

The intention of this vignette is to show how to plot different styles of cost-effectiveness acceptability curves using the BCEA package.

## Two interventions only

This is the simplest case, usually an alternative intervention (\(i=1\)) versus status-quo (\(i=0\)).

The plot show the probability that the alternative intervention is cost-effective for each willingness to pay, \(k\),

\[ p(NB_1 \geq NB_0 | k) \mbox{ where } NB_i = ke - c \]

Using the set of \(N\) posterior samples, this is approximated by

\[ \frac{1}{N} \sum_j^N \mathbb{I} (k \Delta e^j - \Delta c^j) \]

#### R code

To calculate these in BCEA we use the `bcea()`

function.

```
data("Vaccine")
he <- bcea(e, c)
#> No reference selected. Defaulting to first intervention.
# str(he)
ceac.plot(he)
```

The plot defaults to base R plotting. Type of plot can be set explicitly using the `graph`

argument.

`ceac.plot(he, graph = "base")`

`ceac.plot(he, graph = "ggplot2")`

`# ceac.plot(he, graph = "plotly")`

Other plotting arguments can be specified such as title, line colours and theme.

```
ceac.plot(he,
graph = "ggplot2",
title = "my title",
line = list(colors = "green"),
theme = theme_dark())
```

## Multiple interventions

This situation is when there are more than two interventions to consider. Incremental values can be obtained either always against a fixed reference intervention, such as status-quo, or for all pair-wise comparisons.

### Against a fixed reference intervention

Without loss of generality, if we assume that we are interested in intervention \(i=1\), then we wish to calculate

\[ p(NB_1 \geq NB_s | k) \;\; \exists \; s \in S \]

Using the set of \(N\) posterior samples, this is approximated by

\[ \frac{1}{N} \sum_j^N \mathbb{I} (k \Delta e_{1,s}^j - \Delta c_{1,s}^j) \]

#### R code

This is the default plot for `ceac.plot()`

so we simply follow the same steps as above with the new data set.

```
data("Smoking")
he <- bcea(e, c, ref = 4)
# str(he)
```

`ceac.plot(he)`

```
ceac.plot(he,
graph = "base",
title = "my title",
line = list(colors = "green"))
```

```
ceac.plot(he,
graph = "ggplot2",
title = "my title",
line = list(colors = "green"))
```

Reposition legend.

`ceac.plot(he, pos = FALSE) # bottom right`

`ceac.plot(he, pos = c(0, 0))`

`ceac.plot(he, pos = c(0, 1))`

`ceac.plot(he, pos = c(1, 0))`

`ceac.plot(he, pos = c(1, 1))`

`ceac.plot(he, graph = "ggplot2", pos = c(0, 0))`

`ceac.plot(he, graph = "ggplot2", pos = c(0, 1))`

`ceac.plot(he, graph = "ggplot2", pos = c(1, 0))`

`ceac.plot(he, graph = "ggplot2", pos = c(1, 1))`

Define colour palette.

```
mypalette <- RColorBrewer::brewer.pal(3, "Accent")
ceac.plot(he,
graph = "base",
title = "my title",
line = list(colors = mypalette),
pos = FALSE)
```

```
ceac.plot(he,
graph = "ggplot2",
title = "my title",
line = list(colors = mypalette),
pos = FALSE)
```

### Pair-wise comparisons

Again, without loss of generality, if we assume that we are interested in intervention \(i=1\), the we wish to calculate

\[ p(NB_1 = \max\{NB_i : i \in S\} | k) \]

This can be approximated by the following.

\[ \frac{1}{N} \sum_j^N \prod_{i \in S} \mathbb{I} (k \Delta e_{1,i}^j - \Delta c_{1,i}^j) \]

#### R code

In BCEA we first we must determine all combinations of paired interventions using the `multi.ce()`

function.

`he2 <- multi.ce(he)`

We can use the same plotting calls as before i.e. `ceac.plot()`

and BCEA will deal with the pairwise situation appropriately.
Note that in this case the probabilities at a given willingness to pay sum to 1.

`ceac.plot(he, graph = "base")`

```
ceac.plot(he,
graph = "base",
title = "my title",
line = list(colors = "green"),
pos = FALSE)
```

```
mypalette <- RColorBrewer::brewer.pal(4, "Dark2")
ceac.plot(he,
graph = "base",
title = "my title",
line = list(colors = mypalette),
pos = c(0,1))
```

```
ceac.plot(he,
graph = "ggplot2",
title = "my title",
line = list(colors = mypalette),
pos = c(0,1))
```