基于有序分类变量的部分线性可加模型的贝叶斯分位数回归及其应用

The Bayesian Quantile Regression for Ordinal Data for Partial Linear Additive Models with an Application to IVF Data

以云南省某医院生殖遗传中心所提供的试管婴儿数据为研究对象,考查了活胎分娩数目与相关影响指标即年龄、既往史、身体质量指数、优质胚胎率、基础性激素水平以及取卵数目之间的相关关系.具体的,建立起了贝叶斯分位数回归框架下的部分线性可加模型以反映指标与响应变量之间的线性关系和非线性趋势.值得注意的是,活胎分娩数目与相关影响因素之间的关系错综复杂,既可能是线性关系,也可能是非线性关系,甚至还能不显著.为此,本文将基函数的回归系数分解为两个部分,一部分为线性项,另一部分为非线性项,在此基础上,分别对这两部分考虑指标变量压缩先验并最终建立起完整的贝叶斯后验推断程序.这样一来,不仅能够在不同的分位数水平下(不同的风险水平下)度量活胎分娩数目与相关指标之间的关系,还能由数据驱动自动判断出相关关系的类型,这对于指导临床具有重要的价值和参考意义.本研究结果表明,为了获得理想结局,整个孕期都应严密关注身体质量指数这一指标,对于高危孕妇而言,尤其要注意年龄、取卵数目与优质胚胎率这三个指标,它们对妊娠的最终结局均有着较大的影响.

In this paper, we develop a partial linear additive model for ordinal data under Bayesian quantile regression framework. Inspired by the idea of data augmentation, the latent variable is augmented for the ordinal data and a location-scale mixing of hierarchical model for Bayesian quantile regression is established. Additionally, the regression coefficients of the B-spline base functions for the unknown smooth functions are decompose into two different parts, say,the linear part and the nonlinear part, respectively. Based on that, a ' spike and slab ' type prior is set for these coefficients and a full Bayesian posterior inference procedure is built for the propose model. The main advantage of our method is that it can automatically distinguish the correlation relationships, i.e., linear correlation, nonlinear correlation or even independent,between the response variable and the covariates. A real example from in vitro fertilization-embryo transfer(IVF-ET) is used for illustrating the usefulness and the effectiveness of the proposed methodology and the analysis results indicate that in order to get a good pregnancy result, the indicators of age, embryo rate and number of egg should be paid special attention.