HIV RNA viral load measures are often subjected to some upper and lower detection limits depending on the quantification assays. Hence, the responses are either left or right censored. Linear/nonlinear mixed-effects models, with slight modifications to accommodate censoring, are routinely used to analyze this type of data. Usually, the inference procedures are based on normality (or elliptical distribution) assumptions for the random terms. However, those analyses might not provide robust inference when the distribution assumptions are questionable. In this paper, we discuss a fully Bayesian quantile regression inference using Markov Chain Monte Carlo (MCMC) methods for longitudinal data models with random effects and censored responses. Compared to the conventional mean regression approach, quantile regression can characterize the entire conditional distribution of the outcome variable, and is more robust to outliers and misspecification of the error distribution. Under the assumption that the error term follows an asymmetric Laplace distribution, we develop a hierarchical Bayesian model and obtain the posterior distribution of unknown parameters at the pth level, with the median regression (p = 0.5) as a special case. The proposed procedures are illustrated with two HIV AIDS studies on viral loads that were initially analyzed using the typical normal (censored) mean regression mixed-effects models, as well as a simulation study.

中文翻译：

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用于 HIV 研究的审查混合效应模型的分位数回归

根据定量分析，HIV RNA 病毒载量测量通常会受到一些检测上限和下限的影响。因此，响应被左删失或右删失。线性/非线性混合效应模型，稍加修改以适应审查，通常用于分析此类数据。通常，推理过程基于随机项的正态性（或椭圆分布）假设。然而，当分布假设有问题时，这些分析可能无法提供可靠的推断。在本文中，我们讨论了使用马尔可夫链蒙特卡罗 (MCMC) 方法对具有随机效应和审查响应的纵向数据模型进行完全贝叶斯分位数回归推理。与传统的均值回归方法相比，分位数回归可以表征结果变量的整个条件分布，并且对异常值和错误分布的错误指定更加稳健。在误差项遵循非对称拉普拉斯分布的假设下，我们开发了一个分层贝叶斯模型，并获得了第 p 层未知参数的后验分布，中值回归（p = 0.5）作为一个特例。提议的程序通过两项关于病毒载量的 HIV AIDS 研究进行说明，这些研究最初使用典型的正常（删失）平均回归混合效应模型以及模拟研究进行分析。我们开发了一个分层贝叶斯模型，并获得了第 p 层未知参数的后验分布，中值回归（p = 0.5）作为一个特例。提议的程序通过两项关于病毒载量的 HIV AIDS 研究进行说明，这些研究最初使用典型的正常（删失）平均回归混合效应模型以及模拟研究进行分析。我们开发了一个分层贝叶斯模型，并获得了第 p 层未知参数的后验分布，中值回归（p = 0.5）作为一个特例。提议的程序通过两项关于病毒载量的 HIV AIDS 研究进行说明，这些研究最初使用典型的正常（删失）平均回归混合效应模型以及模拟研究进行分析。