Estimating uncertainty when providing individual cardiovascular risk predictions: a Bayesian survival analysis

Journal of Clinical Epidemiology, vol. 173, pp. 111464

Abstract

BACKGROUND: Cardiovascular disease (CVD) risk scores provide point estimates of individual risk without uncertainty quantification. The objective of the current study was to demonstrate the feasibility and clinical utility of calculating uncertainty surrounding individual CVD-risk predictions using Bayesian methods. STUDY DESIGN AND SETTING: Individuals with established atherosclerotic CVD were included from the Utrecht Cardiovascular Cohort-Secondary Manifestations of ARTerial disease (UCC-SMART). In 8,355 individuals, followed for median of 8.2 years (IQR 4.2-12.5), a Bayesian Weibull model was derived to predict the 10-year risk of recurrent CVD events. RESULTS: Model coefficients and individual predictions from the Bayesian model were very similar to that of a traditional ('frequentist') model but the Bayesian model also predicted 95% credible intervals (CIs) surrounding individual risk estimates. The median width of the individual 95%CrI was 5.3% (IQR 3.6-6.5) and 17% of the population had a 95%CrI width of 10% or greater. The uncertainty decreased with increasing sample size used for derivation of the model. Combining the Bayesian Weibull model with sampled hazard ratios based on trial reports may be used to estimate individual estimates of absolute risk reduction with uncertainty measures and the probability that a treatment option will result in a clinically relevant risk reduction. CONCLUSION: Estimating uncertainty surrounding individual CVD risk predictions using Bayesian methods is feasible. The uncertainty regarding individual risk predictions could have several applications in clinical practice, like the comparison of different treatment options or by calculating the probability of the individual risk being below a certain treatment threshold. However, as the individual uncertainty measures only reflect sampling error and no biases in risk prediction, physicians should be familiar with the interpretation before widespread clinical adaption.

Authors 7

1. Steven H J Hageman corresponding

   University Medical Center Utrecht

   Affiliation as printed

   Department of Vascular Medicine, University Medical Center Utrecht, Utrecht, The Netherlands. Electronic address: S.H.J.Hageman-4@umcutrecht.nl

   Department of Vascular Medicine, University Medical Center Utrecht, Utrecht, The Netherlands

2. Frank L.J. Visseren

   University Medical Center Utrecht

   Affiliation as printed

   Department of Vascular Medicine, University Medical Center Utrecht, Utrecht, The Netherlands

3. John William McEvoy

   Ollscoil na Gaillimhe – University of Galway

   Affiliation as printed

   University of Galway and National Institute for Prevention and Cardiovascular Health, Galway, Ireland

4. J. Wouter Jukema Aachen Department of Cardiology, Leiden University Medical Center

   Leiden University Medical Center · Netherlands Heart Institute

   Affiliation as printed

   Department of Cardiology, Leiden University Medical Center, Leiden, The Netherlands; Netherlands Heart Institute, Utrecht, The Netherlands

   Department of Cardiology, Leiden University Medical Center, Leiden, The Netherlands

   Netherlands Heart Institute, Utrecht, The Netherlands

5. Yvo M. Smulders

   Amsterdam University Medical Centers

   Affiliation as printed

   Internal Medicine, Amsterdam UMC, Amsterdam, The Netherlands

6. Maarten van Smeden

   Utrecht University · University Medical Center Utrecht

   Affiliation as printed

   Julius Center for Health Science and Primary Care, University Medical Center Utrecht, University of Utrecht, Utrecht, the Netherlands

7. Jannick A N Dorresteijn

   University Medical Center Utrecht

   Affiliation as printed

   Department of Vascular Medicine, University Medical Center Utrecht, Utrecht, The Netherlands