Plot a Discretized Heatmap of the Effect of a Continuous Covariate on a Time-To-Event Outcome

Using a previously fit time-to-event model, this function plots a discretized heatmap with the continuous covariate on the y-axis and the time-to-event on the x-axis. This is essentially a discretized version of the plot_surv_heatmap plot, which makes it look very similar to a correlation matrix.

Usage

plot_surv_matrix(time, status, variable, group=NULL, data, model,
                 cif=FALSE, na.action=options()$na.action,
                 horizon=NULL, fixed_t=NULL, max_t=Inf,
                 n_col=10, n_row=10,
                 start_color="red", end_color="blue",
                 alpha=1, xlab="Time", ylab=variable,
                 title=NULL, subtitle=NULL,
                 legend.title="S(t)", legend.position="none",
                 gg_theme=ggplot2::theme_bw(),
                 facet_args=list(),
                 panel_border=FALSE, axis_dist=0,
                 border_color="white", border_size=0.5,
                 numbers=TRUE, number_color="white",
                 number_size=3, number_family="sans",
                 number_fontface="plain", number_digits=2,
                 ...)

Arguments

time: A single character string specifying the time-to-event variable. Needs to be a valid column name of a numeric variable in data.
status: A single character string specifying the status variable, indicating if a person has experienced an event or not. Needs to be a valid column name of a numeric or logical variable in data.
variable: A single character string specifying the continuous variable of interest, for which the survival curves should be estimated. This variable has to be contained in the data.frame that is supplied to the data argument.
group: An optional single character string specifying a factor variable in data. When used, the plot is created conditional on this factor variable, meaning that a facetted plot is produced with one facet for each level of the factor variable. See curve_cont for a detailed description of the estimation strategy. Set to NULL (default) to use no grouping variable.
data: A data.frame containing all required variables.
model: A model describing the time-to-event process (such as an coxph model). Needs to include variable as an independent variable. It also has to have an associated predictRisk method. See ?predictRisk for more details.
cif: Whether to plot the cumulative incidence (CIF) instead of the survival probability. If multiple failure types are present, the survival probability cannot be estimated in an unbiased way. This function will always return CIF estimates in that case.
na.action: How missing values should be handled. Can be one of: na.fail, na.omit, na.pass, na.exclude or a user-defined custom function. Also accepts strings of the function names. See ?na.action for more details. By default it uses the na.action which is set in the global options by the respective user.
horizon: A numeric vector containing a range of values of variable for which the survival curves should be calculated or NULL (default). If NULL, the horizon is constructed as a sequence from the lowest to the highest value observed in variable with 100 equally spaced steps. In this function, this needs to be a equally spaced vector.
fixed_t: A numeric vector containing points in time at which the survival probabilities should be calculated or NULL (default). If NULL, the survival probability is estimated at 100 equally spaced steps from 0 to the maximum observed event time. In this function, this needs to be a equally spaced vector.
max_t: A number indicating the latest survival time which is to be plotted.
n_col: The number of columns to use in the matrix style heatmap. This parameter only controls how many tiles are shown, not how many are estimated. The amount of estimated probabilities is controlled using the fixed_t and horizon arguments. See details.
n_row: The number of rows to use in the matrix style heatmap. See n_col.
start_color: The color used for the lowest value in horizon. This and the end_color argument can be used to specify custom continuous color scales used in the plot. For example, if a black and white plot is desired, the user can set start_color="white" and end_color="black". See ?scale_color_gradient for more information. Defaults to "red", set to NULL to use the default ggplot2 palette.
end_color: The color used for the highest value in horizon. Defaults to "blue". See argument start_color.
alpha: The transparency level of the plot.
xlab: A character string used as the x-axis label of the plot.
ylab: A character string used as the y-axis label of the plot.
title: A character string used as the title of the plot.
subtitle: A character string used as the subtitle of the plot.
legend.title: A character string used as the legend title of the plot.
legend.position: Where to put the legend. See ?theme for more details.
gg_theme: A ggplot2 theme which is applied to the plot.
facet_args: A named list of arguments that are passed to the facet_wrap function call when creating a plot separated by groups. Ignored if group=NULL. Any argument except the facets argument of the facet_wrap function can be used. For example, if the user wants to allow free y-scales, this argument could be set to list(scales="free_y").
panel_border: Whether to draw a border around the heatmap or not. Is set to FALSE by default to mimic standard heatmaps.
axis_dist: The distance of the axis ticks to the colored heatmap. Is set to 0 by default to mimic standard heatmaps.
border_color: The color of the individual rectangles borders. Defaults to "white".
border_size: The size of the individual rectangles borders. Defaults to 0.5.
numbers: Whether to put the numbers of the average estimated probabilities into the rectangles or not. Defaults to TRUE.
number_color: The color of the numbers inside the rectangles. Ignored if numbers=FALSE.
number_size: The size of the numbers inside the rectangles. Ignored if numbers=FALSE.
number_family: The font family of the numbers inside the rectangles. Ignored if numbers=FALSE.
number_fontface: The fontface of the numbers inside the rectangles. Ignored if numbers=FALSE.
number_digits: The amount of digits the numbers inside the rectangles should be rounded to. Ignored if numbers=FALSE.
...: Further arguments passed to curve_cont.

Details

Heatmaps are a great tool to visualize a three dimensional surface in a two-dimensional plot. Continuously changing colors over a single area can, however, be difficult to interpret correctly if the color does not change a lot. This version makes the heatmap easier to understand by discretizing the space into equally spaced rectangles. The survival or failure probability is still estimated at a very fine grid of points in time (controlled using the fixed_t and horizon arguments), but is then aggregated into average probabilities afterwards. The number inside each rectangle then shows the *average* probability inside the region defined by the rectangle. This makes the plot look a lot like a correlation matrix.

The dimensions of the plot can be controlled using the n_col and n_row arguments. Using high numbers in these parameters makes the plot look more similar to a standard plot_surv_heatmap plot. It is recommended to create the plot_surv_heatmap plot first to pick appropriate dimensions for the discretized version here.

Value

Returns a ggplot2 object.

Author

Robin Denz

References

Robin Denz, Nina Timmesfeld (2023). "Visualizing the (Causal) Effect of a Continuous Variable on a Time-To-Event Outcome". In: Epidemiology 34.5

Examples

library(contsurvplot)
library(riskRegression)
library(survival)
library(ggplot2)
library(splines)

# using data from the survival package
data(nafld, package="survival")

# take a random sample to keep example fast
set.seed(42)
nafld1 <- nafld1[sample(nrow(nafld1), 150), ]

# fit cox-model with age
model <- coxph(Surv(futime, status) ~ age, data=nafld1, x=TRUE)

# plot effect of age on survival using defaults
plot_surv_matrix(time="futime",
                 status="status",
                 variable="age",
                 data=nafld1,
                 model=model)


# plot it only for 60 to 80 year old people
plot_surv_matrix(time="futime",
                 status="status",
                 variable="age",
                 data=nafld1,
                 model=model,
                 horizon=seq(60, 80, 0.5))


## showing non-linear effects

# fit cox-model with bmi modelled using B-Splines,
# adjusting for age and sex
model2 <- coxph(Surv(futime, status) ~ age + male + bs(bmi, df=3),
                data=nafld1, x=TRUE)

# plot effect of bmi on survival using defaults
plot_surv_matrix(time="futime",
                 status="status",
                 variable="bmi",
                 data=nafld1,
                 model=model2)