Tools for checking calibration of a Cox model in external validation: Prediction of population-averaged survival curves based on risk groups
Patrick Royston
MRC Clinical Trials Unit at University College London
London, UK
[email protected]
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Abstract. Royston (2014, Stata Journal 14: 738–755) explained how a popular
application of the Cox proportional hazards model “is to develop a
multivariable prediction model, often a prognostic model to predict the future
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 one 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”. In this article, I suggest an
approach to assess calibration by comparing observed (Kaplan–Meier) and
predicted survival probabilities in several prognostic groups derived by
placing cutpoints on the prognostic index. I distinguish between full
validation, where all relevant quantities are estimated on the derivation
dataset and predicted on the validation dataset, and partial validation, where
the prognostic index and prognostic groups are derived from published
information and the baseline distribution function is estimated in the
validation dataset. Partial validation is more feasible in practice because it
is uncommon to have access to individual patient values in both datasets. I
exemplify the method by detailed analysis of two datasets in the disease
primary biliary cirrhosis; the datasets comprise a derivation and a validation
dataset. I describe a new ado-file, stcoxgrp, that performs the
necessary calculations. Results for stcoxgrp are 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:
stcoxgrp, Cox proportional hazards model, multivariable model, prognostic factors, prognostic groups, external validation, calibration, survival probabilities
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