Prior-Preconditioned Conjugate Gradient Method for Accelerated Gibbs Sampling in "Large n, Large p" Bayesian Sparse...

Area of Science:

• Computational Statistics
• Biostatistics
• Health Informatics

Background:

• Modern observational studies utilize large healthcare databases with millions of observations and tens of thousands of predictors.
• Estimating a large number of parameters in such high-dimensional data is computationally challenging for traditional methods.
• Sparse regression, particularly Bayesian methods with shrinkage priors, offers a solution but faces computational bottlenecks.

Purpose of the Study:

• To develop a novel algorithm to overcome the computational bottleneck in Bayesian inference for large-scale observational studies ('large n and large p' settings).
• To accelerate the repeated sampling from high-dimensional Gaussian distributions required for posterior computation.
• To enable efficient analysis of complex clinical datasets for risk assessment.

Main Methods:

• Introduced a new algorithm that avoids explicit computation and factorization of the high-dimensional precision matrix (Φ).
• Leveraged the generation of a random vector (z) and solved the linear system (Φx = z) using the conjugate gradient (CG) algorithm.
• Developed a theory of 'prior-preconditioning' to guarantee rapid convergence of the CG algorithm.

Main Results:

• The novel algorithm demonstrated an order of magnitude speed-up in posterior inference.
• Applied to a study of 72,489 patients and 22,175 covariates, computation time was reduced from two weeks to less than a day.
• Successfully enabled efficient risk assessment of adverse events for two anticoagulant therapies.

Conclusions:

• The proposed algorithm significantly enhances the feasibility and efficiency of Bayesian regression in large-scale observational health studies.
• Prior-preconditioning theory ensures computational efficiency for high-dimensional Gaussian sampling.
• This advancement facilitates more timely and comprehensive analysis of complex clinical data for improved healthcare insights.