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.
翻译:关于临床上最重要的最低差别的推断是医学上一个重要的实际问题。基本的想法是,在统计上意义重大的治疗可能不会导致病人福祉的改善。对诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性分析的临界值,如果诊断性措施超过这一临界值,那么病人就更有可能观察到改进。典型的配方使用一种未详细说明的模型,使真正的巴耶斯人解决方案无法达到。对于个人化的诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性诊断性