Visualising survival data regression models using pseudo-observations

Methods for visualising data are an essential part of model fitting procedures and are commonly used within all fields of statistics. Various graphical checks can be performed, either using scatter plots of the data itself or some kind of informative residuals. However, in survival data, with the existence of censored observations as one of its defining properties, these elementary plots are not meaningful as the censored observations cannot be sensibly plotted. In this paper, we review a recently introduced [6] general solution of this problem that is based on pseudo-observations. These are defined for each individual at any point of the follow-up time and therefore offer a way around the censoring problems. Using pseudo-observations, we can apply methods analogous to those in regression with binary outcomes and plot various kinds of scatter plots or residuals that give an important insight into the quality of the data fit. An important property of this approach is that it applies to any hazard regression model, with the Cox and the additive model being the focus of this paper. We describe methods for single as well as multiple covariate cases and illustrate them using simulated data sets.