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

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.

Keywords: Bayesian; CI; Cardiovascular; Credible interval; Risk prediction; Uncertainty.