Bayesian Cox regression for large-scale inference with applications to electronic health records

The Cox model is an indispensable tool for time-to-event analysis, particularly in biomedical research. However, medicine undergoing a profound transformation, generating data at unprecedented scale, which opens new frontiers to study and understand diseases. With the wealth of collected, challenges statistical inference arise, as datasets are often high dimensional, exhibit increasing number measurements irregularly spaced time points, simply too large fit memory. Many current implementations analysis ill-suited these problems, computationally demanding requires access full once. Here, we propose Bayesian version counting process representation Cox’s partial likelihood efficient on large-scale with millions points thousands time-dependent covariates. Through combination stochastic variational reweighting log-likelihood, obtain approximation posterior distribution that factorizes over subsamples data, enabling big settings. Crucially, method produces viable uncertainty estimates high-dimensional datasets. We show utility our through simulation application myocardial infarction UK Biobank, where characterize multivariate effects risk factors replicate results from individual studies. Our framework extends sources, like biobanks EHR, can provide insights into understanding