Clinical prediction models to predict the risk of multiple binary outcomes: a comparison of approaches

Glen P Martin*, Matthew Sperrin, Kym I E Snell, Iain Buchan, Richard D Riley

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Abstract

Clinical prediction models (CPMs) can predict clinically relevant outcomes or events. Typically, prognostic CPMs are derived to predict the risk of a single future outcome. However, there are many medical applications where two or more outcomes are of interest, meaning this should be more widely reflected in CPMs so they can accurately estimate the joint risk of multiple outcomes simultaneously. A potentially naïve approach to multi-outcome risk prediction is to derive a CPM for each outcome separately, then multiply the predicted risks. This approach is only valid if the outcomes are conditionally independent given the covariates, and it fails to exploit the potential relationships between the outcomes. This paper outlines several approaches that could be used to develop CPMs for multiple binary outcomes. We consider four methods, ranging in complexity and conditional independence assumptions: namely, probabilistic classifier chain, multinomial logistic regression, multivariate logistic regression, and a Bayesian probit model. These are compared with methods that rely on conditional independence: separate univariate CPMs and stacked regression. Employing a simulation study and real-world example, we illustrate that CPMs for joint risk prediction of multiple outcomes should only be derived using methods that model the residual correlation between outcomes. In such a situation, our results suggest that probabilistic classification chains, multinomial logistic regression or the Bayesian probit model are all appropriate choices. We call into question the development of CPMs for each outcome in isolation when multiple correlated or structurally related outcomes are of interest and recommend more multivariate approaches to risk prediction.

Original languageEnglish
Pages (from-to)498-517
Number of pages20
JournalStatistics in Medicine
Volume40
Issue number2
Early online date26 Oct 2020
DOIs
Publication statusPublished - 30 Jan 2021

Bibliographical note

© 2020 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Keywords

  • Bayes Theorem
  • Computer Simulation
  • Humans
  • Logistic Models
  • Models, Statistical
  • Prognosis

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