Flexible Bayesian quantile regression for counts via generative modeling.

Area of Science:

• Biostatistics
• Statistical modeling
• Bayesian inference

Background:

• Count data, common in biomedical fields (e.g., hospital stay length), presents challenges for modeling conditional quantiles due to its discrete nature.
• Accurate modeling of conditional quantiles is vital for understanding outcome variability and heterogeneous effects.

Purpose of the Study:

• To propose a novel general Bayesian framework for quantile regression specifically designed for count data.
• To address the practical difficulties in modeling discrete count responses and their conditional quantiles.

Main Methods:

• Developed a Bayesian nonparametric kernel mixture model for the joint distribution of count responses and covariates.
• Estimated regression parameters by minimizing expected loss concerning the conditional quantile distribution of an underlying latent continuous variable.
• Utilized a simple optimization process to obtain the posterior distribution of the regression parameter.

Main Results:

• The proposed Bayesian framework demonstrated improved bias and estimation accuracy compared to existing count quantile regression methods.
• Numerical simulations confirmed the enhanced performance of the novel approach.
• Application to hospital stay length data for acute myocardial infarction yielded more interpretable and flexible results than traditional methods.

Conclusions:

• The novel Bayesian quantile regression framework effectively handles count data, offering superior performance over existing methods.
• The method provides a more flexible and interpretable approach for analyzing biomedical count data, particularly in healthcare outcome studies.
• This framework advances the statistical toolkit for analyzing discrete outcomes in biostatistics and related fields.