In this short vignette, we will introduce the `plot`

method for `absoluteRisk`

objects. This method allows you to plot cumulative incidence (CI) or survival curves as a function of time and a given covariate profile. More specifically, the cumulative incidence is given by:

\[ CI(x, t) = 1 - exp\left[ - \int_0^t h(x, u) \textrm{d}u \right] \] where \( h(x, t) \) is the hazard function, \( t \) denotes the numerical value (number of units) of a point in prognostic/prospective time and \( x \) is the realization of the vector \( X \) of variates based on the patientâ€™s profile and intervention (if any). And the survival function is given by \[ S(x, t) = 1 - CI(x,t) = exp\left[ - \int_0^t h(x, u) \textrm{d}u \right] \]

`brcancer`

datasetTo illustrate hazard function plots, we will use the breast cancer dataset which contains the observations of 686 women taken from the `TH.data`

package. This dataset is also available from the `casebase`

package. In the following, we will show the CI curve for several covariate profiles.

```
library(casebase)
library(survival)
library(ggplot2)
data("brcancer")
mod_cb_glm <- fitSmoothHazard(cens ~ estrec*log(time) +
horTh +
age +
menostat +
tsize +
tgrade +
pnodes +
progrec,
data = brcancer,
time = "time", ratio = 10)
summary(mod_cb_glm)
```

We can use the `plot`

method for objects of class `absRiskCB`

, which is returned by the `absoluteRisk`

function, to plot cumulative incidence curves. For example, suppose we want to compare the cumulative incidence curves of the 1st and 50th individuals in the `brcancer`

dataset. We first call the `absoluteRisk`

function and specify the `newdata`

argument. Note that since time is missing, the risk estimate is calculated at the observed failure times.

```
smooth_risk_brcancer <- absoluteRisk(object = mod_cb_glm,
newdata = brcancer[c(1,50),])
class(smooth_risk_brcancer)
plot(smooth_risk_brcancer)
```

These curves can be further customized. For example, suppose we want to change the legend title and legend keys:

```
plot(smooth_risk_brcancer,
id.names = c("Covariate Profile 1","Covariate Profile 50"),
legend.title = "Type",
xlab = "time (days)",
ylab = "Cumulative Incidence (%)")
```

The call to `plot`

on a `absRiskCB`

object returns a `ggplot2`

object, and therefore can be used downstream with other `ggplot2`

functions. For example, suppose we want to change the theme:

`graphics::matplot`

By default, the `plot`

method uses `ggplot2`

to produce the curves. Alternatively, you can use `graphics::matplot`

by specifying `gg = FALSE`

. This option is particularly useful if you want to add the cumulative incidence curve to an existing plot, e.g., adding the adjusted smooth curve to a Kaplan-Meier curve. In this example, we calculate the cumulative incidence for a *typical* individual in the dataset:

```
cols <- c("#8E063B","#023FA5")
smooth_risk_typical <- absoluteRisk(object = mod_cb_glm, newdata = "typical")
y <- with(brcancer, survival::Surv(time, cens))
plot(y, fun = "event", conf.int = F, col = cols[1], lwd = 2)
plot(smooth_risk_typical, add = TRUE, col = cols[2], lwd = 2, gg = FALSE)
legend("bottomright",
legend = c("Kaplan-Meier", "casebase"),
col = cols,
lty = 1,
lwd = 2,
bg = "gray90")
```

We can also easily calculate and plot survival curves by specifying `type = 'survival'`

in the call to `absoluteRisk`

. The corresponding call to `plot`

is the same as with cumulative incidence curves:

`glmnet`

We can also plot cumulative incidence curves for other families. For example, using the `family = "glmnet"`

, we can plot the cumulative incidence curves for the first 10 individuals in the `brcancer`

dataset, using the tuning parameter which minimizes the 10-fold cross-validation error (\(\lambda_{min}\)):

```
mod_cb_glmnet <- fitSmoothHazard(cens ~ estrec*time +
horTh +
age +
menostat +
tsize +
tgrade +
pnodes +
progrec,
data = brcancer,
time = "time",
ratio = 1,
family = "glmnet")
smooth_risk_glmnet <- absoluteRisk(object = mod_cb_glmnet,
newdata = brcancer[1:10,],
s = "lambda.min")
plot(smooth_risk_glmnet)
```

`gam`

Here we produce the same plot but for `family = "gam"`

for generalised additive models.