Tools for checking calibration of a Cox model in external validation: Approach based on individual event probabilities
Patrick Royston
MRC Clinical Trials Unit at University College London
London, UK
[email protected]
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Abstract. The Cox proportional hazards model has been used extensively in
medicine over the last 40 years. A popular application is to develop a multivariable
prediction model, often a prognostic model to predict the clinical outcome
of patients with a particular disorder from “baseline” factors measured at some
initial time point. For such a model to be useful in practice, it must be “validated”;
that is, it must perform satisfactorily in an external sample of patients
independent of the sample on which the model was originally developed. One key
aspect of performance is calibration, which is the accuracy of prediction, particularly
of survival (or equivalently, failure or event) probabilities at any time after
the time origin. We believe systematic evaluation of the calibration of a Cox model
has been largely ignored in the literature. In this article, we suggest an approach
to assessing calibration using individual event probabilities estimated at different
time points. We exemplify the method by detailed analysis of two datasets in the
disease primary biliary cirrhosis; the datasets comprise a derivation and a validation
dataset. We describe a new command, stcoxcal, that performs the necessary
calculations. Results for stcoxcal can be displayed graphically, which makes it
easier for users to picture calibration (or lack thereof) according to follow-up time.
View all articles by this author:
Patrick Royston
View all articles with these keywords:
stcoxcal, Cox proportional hazards model, multivariable model, prognostic factors, external validation, calibration, survival probabilities
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