Clinical prediction models provide predictions for individuals, typically expressed as point estimates derived from a deterministic function, such as a logistic regression equation. Such 'plug-in' predictions hide inherent uncertainty. In contrast, Bayesian methods offer a coherent mechanism for uncertainty propagation, and allow the computation of the posterior mean as the measure of centrality of choice for clinical decision-making. However, Bayesian methods are not widely utilised in predictive analytics for healthcare. We investigated the feasibility and performance of a Bayesian adaptation of the commonly used frequentist framework for risk prediction modelling. We assessed (i) the use of shrinkage priors with complementary features (simplicity, user input, and automatic shrinkage) that enable Laplace/normal approximation of the posterior, and (ii) exact and approximate methods for efficient computation of the posterior mean. Using examples and simulations, we demonstrate that this Bayesian approach is feasible and improves predictive performance, while enabling uncertainty quantification with suitable coverage. In small-to-medium sample sizes, the gain in clinical utility by using the posterior mean over plug-in predictions was equivalent to the gain from using a noticeably larger sample size. Adapting the widely used parametric regression methods to an approximate Bayesian framework for prediction modelling is both pragmatic and clinically advantageous.

翻译：临床预测模型为个体提供预测结果，通常以确定性函数（如逻辑回归方程）导出的点估计形式呈现。此类"点估计"预测隐藏了固有的不确定性。相比之下，贝叶斯方法为不确定性传播提供了连贯机制，并支持将后验均值作为临床决策中集中趋势的度量指标。然而，贝叶斯方法在医疗预测分析中尚未得到广泛应用。本研究探讨了常用频率学派风险预测建模框架的贝叶斯化改造的可行性及性能。我们评估了：(i) 具有互补特征（简洁性、用户输入、自动收缩）的收缩先验用于实现后验的拉普拉斯/正态逼近；(ii) 高效计算后验均值的精确与近似方法。通过实例与模拟研究，我们证明了该贝叶斯方法的可行性及其对预测性能的提升作用，同时能以适当的覆盖率实现不确定性量化。在中低样本量条件下，使用后验均值相比点估计预测所获得的临床效用增益，相当于使用显著更大样本量所能获得的增益。将广泛应用的参数回归方法改造为近似贝叶斯框架用于预测建模，既具有实用价值，又具备临床优势。