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Calibration plots for multistate risk predictions models

Pate, Alexander; Sperrin, Matthew; Riley, Richard D.; Peek, Niels; Van Staa, Tjeerd; Sergeant, Jamie C.; Mamas, Mamas A.; Lip, Gregory Y. H.; O'Flaherty, Martin; Barrowman, Michael; Buchan, Iain; Martin, Glen P.


Alexander Pate

Matthew Sperrin

Richard D. Riley

Niels Peek

Tjeerd Van Staa

Jamie C. Sergeant

Gregory Y. H. Lip

Martin O'Flaherty

Michael Barrowman

Iain Buchan

Glen P. Martin


There is currently no guidance on how to assess the calibration of multistate models used for risk prediction. We introduce several techniques that can be used to produce calibration plots for the transition probabilities of a multistate model, before assessing their performance in the presence of random and independent censoring through a simulation.

We studied pseudo-values based on the Aalen-Johansen estimator, binary logistic regression with inverse probability of censoring weights (BLR-IPCW), and multinomial logistic regression with inverse probability of censoring weights (MLR-IPCW). The MLR-IPCW approach results in a calibration scatter plot, providing extra insight about the calibration. We simulated data with varying levels of censoring and evaluated the ability of each method to estimate the calibration curve for a set of predicted transition probabilities. We also developed evaluated the calibration of a model predicting the incidence of cardiovascular disease, type 2 diabetes and chronic kidney disease among a cohort of patients derived from linked primary and secondary healthcare records.

The pseudo-value, BLR-IPCW, and MLR-IPCW approaches give unbiased estimates of the calibration curves under random censoring. These methods remained predominately unbiased in the presence of independent censoring, even if the censoring mechanism was strongly associated with the outcome, with bias concentrated in low-density regions of predicted transition probability.

We recommend implementing either the pseudo-value or BLR-IPCW approaches to produce a calibration curve, combined with the MLR-IPCW approach to produce a calibration scatter plot. The methods have been incorporated into the “calibmsm” R package available on CRAN.


Pate, A., Sperrin, M., Riley, R. D., Peek, N., Van Staa, T., Sergeant, J. C., …Martin, G. P. (in press). Calibration plots for multistate risk predictions models. Statistics in Medicine,

Journal Article Type Article
Acceptance Date Apr 17, 2024
Online Publication Date May 8, 2024
Deposit Date May 13, 2024
Publicly Available Date May 13, 2024
Journal Statistics in Medicine
Print ISSN 0277-6715
Electronic ISSN 1097-0258
Publisher Wiley
Peer Reviewed Peer Reviewed
Keywords clinical prediction, calibration, model validation, multistate model, risk prediction
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