# Calibration of cause-specific absolute risk for external validation using each cause-specific hazards model in the presence of competing events

## TL;DR

This paper introduces a method to better calibrate risk predictions in the presence of competing events by evaluating each cause-specific model separately during external validation.

## Contribution

The paper proposes a novel approach to assess and improve calibration of cause-specific absolute risks using cause-specific hazards models in external validation.

## Key findings

- Miscalibration in one cause-specific model can affect predictions for all-cause and other cause-specific risks.
- Using components from each cause-specific model improves identification of mis-specified models in external validation.
- Calibration plots and statistics for each cause-specific model help reveal sources of miscalibration.

## Abstract

When developing/validating prognostic models, it is typical to assess calibration between predicted and observed risks — either in the development dataset or in an external sample. For competing risks data, correct specification of more than one model may be required to ensure well-calibrated predicted risks for the event of interest. Furthermore, interest may be in the predicted risks of the event of interest, competing events and all-causes. Therefore, calibration must be assessed simultaneously using various measures.

We focus on the calibration of prediction models for external validation using a cause-specific hazards approach. We propose that miscalibration for cause-specific hazard models be assessed using components specific to each model through the complement of the cause-specific survival alongside the assessment of the calibration of the cause-specific absolute risks. We simulated a range of scenarios to illustrate how to identify which model(s) are mis-specified in an external validation setting. Calibration plots and calibration statistics (calibration slope, calibration-in-the-large) are presented alongside performance measures such as the Brier score and Index of Prediction Accuracy. We use pseudo-observations to calculate observed risks and generate a smooth calibration curve with restricted cubic splines. We fitted flexible parametric survival models to the simulated data to flexibly estimate baseline cause-specific hazards for the prediction of individual cause-specific absolute risks.

Our simulations illustrate that miscalibration due to changes in the baseline cause-specific hazards in external validation data is better identified using components from each cause-specific model. A mis-calibrated model on one cause could lead to poor calibration of the predicted absolute risks for each cause of interest, including the all-cause absolute risk. This is because prediction of a single cause-specific absolute risk is impacted by effects of variables on the cause of interest and competing events.

If accurate predictions for both all-cause and each cause-specific absolute risks are of interest, this is best achieved by developing and validating models via the cause-specific hazards approach. For each cause-specific model, researchers should evaluate calibration plots separately using the complement of the cause-specific survival function to reveal the cause of any miscalibration. However, this also requires careful consideration of dependent censoring which must be sufficiently accounted for.

The online version contains supplementary material available at 10.1186/s41512-025-00197-5.