Visualizing the Causal Effect of a Continuous Variable on a Time-To-Event Outcome

Visualization is a key aspect of communicating the results of any study aiming to estimate causal effects. In studies with time-to-event outcomes, the most popular visualization approach is depicting survival curves stratified by the variable of interest. However, this approach cannot be used when the variable of interest is continuous. Simple workarounds, such as categorizing the continuous covariates and plotting survival curves for each category, can result in misleading depictions of the main effects. Instead, we propose the use of g-computation based on a suitable time-to-event model to create a range of graphics. The proposed plots are able to depict the causal survival probability over time and as a function of a continuous covariate simultaneously. Due to their reliance on a regression model, they can be adjusted for confounding easily. We illustrate and compare them to simpler alternatives using data from a large German observational study investigating the effect of the Ankle Brachial Index on survival. To facilitate the usage of these plots, we additionally developed the contsurvplot R-package which includes all methods discussed in this paper.