Gibbs posterior inference on the minimum clinically important difference

TL;DR

This paper introduces a model-free Gibbs posterior approach for estimating the minimum clinically important difference (MCID), providing valid and efficient interval estimates even with small samples, addressing challenges of bias and inefficiency in traditional models.

Contribution

It develops a novel Gibbs posterior method for MCID inference that avoids parametric assumptions, balancing robustness and efficiency.

Findings

The Gibbs posterior converges at an optimal rate.

Interval estimates are valid and efficient for small samples.

The method outperforms traditional parametric and nonparametric approaches.

Abstract

IIt is known that a statistically significant treatment may not be clinically significant. A quantity that can be used to assess clinical significance is called the minimum clinically important difference (MCID), and inference on the MCID is an important and challenging problem. Modeling for the purpose of inference on the MCID is non-trivial, and concerns about bias from a misspecified parametric model or inefficiency from a nonparametric model motivate an alternative approach to balance robustness and efficiency. In particular, a recently proposed representation of the MCID as the minimizer of a suitable risk function makes it possible to construct a Gibbs posterior distribution for the MCID without specifying a model. We establish the posterior convergence rate and show, numerically, that an appropriately scaled version of this Gibbs posterior yields interval estimates for the MCID which are both valid and efficient even for relatively small sample sizes.