Generalized Bayes inference on a linear personalized minimum clinically important difference

TL;DR

This paper develops a novel generalized Bayesian inference method for personalized minimum clinically important difference (MCID), addressing model misspecification and enabling reliable, efficient estimation in medical decision-making.

Contribution

It introduces a generalized posterior framework based on binary quantile regression for personalized MCID, with bias control and a calibration method for reliable inference.

Findings

The method achieves controlled bias under model misspecification.

Efficient Gibbs sampling is enabled by latent variable representation.

Calibration improves frequentist coverage of Bayesian inferences.

Abstract

Inference on the minimum clinically important difference, or MCID, is an important practical problem in medicine. The basic idea is that a treatment being statistically significant may not lead to an improvement in the patients' well-being. The MCID is defined as a threshold such that, if a diagnostic measure exceeds this threshold, then the patients are more likely to notice an improvement. Typical formulations use an underspecified model, which makes a genuine Bayesian solution out of reach. Here, for a challenging personalized MCID problem, where the practically-significant threshold depends on patients' profiles, we develop a novel generalized posterior distribution, based on a working binary quantile regression model, that can be used for estimation and inference. The advantage of this formulation is two-fold: we can theoretically control the bias of the misspecified model and it has a latent variable representation which we can leverage for efficient Gibbs sampling. To ensure that the generalized Bayes inferences achieve a level of frequentist reliability, we propose a variation on the so-called generalized posterior calibration algorithm to suitably tune the spread of our proposed posterior.