The Wally plot approach to assess the calibration of clinical prediction models

A prediction model is calibrated if, roughly, for any percentage x we can expect that x subjects out of 100 experience the event among all subjects that have a predicted risk of x%. Typically, the calibration assumption is assessed graphically but in practice it is often challenging to judge whether a "disappointing" calibration plot is the consequence of a departure from the calibration assumption, or alternatively just "bad luck" due to sampling variability. We propose a graphical approach which enables the visualization of how much a calibration plot agrees with the calibration assumption to address this issue. The approach is mainly based on the idea of generating new plots which mimic the available data under the calibration assumption. The method handles the common non-trivial situations in which the data contain censored observations and occurrences of competing events. This is done by building on ideas from constrained non-parametric maximum likelihood estimation methods. Two examples from large cohort data illustrate our proposal. The 'wally' R package is provided to make the methodology easily usable.