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

European Journal of Preventive Cardiology, vol. 31

Abstract

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. Methods and Results 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. Model coefficients and individual predictions 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. An individual example is shown in Figure 1, for a 70-year old women with coronary artery disease. She has a predicted risk of 17.8%, and her individual 95%CrI was 15.1-21.0% based on the 2.5th and 97.5th quantile from the distribution of individual predicted risks. The figure also shows the possibilities of these methods to quantify the certainty of a patient having a risk higher than a certain treatment target. Figure 2 shows that 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 absolute risk reduction with uncertainty measures and the probability that a treatment option will result in a clinically relevant risk reduction. Interpretation 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 potential biases in risk prediction, physicians should be familiar with the interpretation before widespread clinical adaption. Figure 2

Authors 7

1. Steven H J Hageman

   University Medical Center Utrecht

   Affiliation as printed

   University Medical Center Utrecht , Utrecht , Netherlands (The)

2. F L F Visseren

   University Medical Center Utrecht

   Affiliation as printed

   University Medical Center Utrecht, Department of vascular medicine , Utrecht , Netherlands (The)

3. John William McEvoy

   Ollscoil na Gaillimhe – University of Galway

   Affiliation as printed

   National Institute of Preventive Cardiology , Galway , Ireland

4. J. Wouter Jukema Aachen

   Leiden University Medical Center

   Affiliation as printed

   Leiden University Medical Center , Leiden , Netherlands (The)

5. Yvo M. Smulders

   Amsterdam University Medical Centers

   Affiliation as printed

   Amsterdam UMC , Amsterdam , Netherlands (The)

6. Maarten van Smeden

   University Medical Center Utrecht

   Affiliation as printed

   University Medical Center Utrecht , Utrecht , Netherlands (The)

7. Jannick A N Dorresteijn

   University Medical Center Utrecht

   Affiliation as printed

   University Medical Center Utrecht , Utrecht , Netherlands (The)