Huang Yangxin, Chen Jiaqing, Yan Chunning
University of South Florida, FL, USA.
Int J Biostat. 2012 Nov 26;8(1):/j/ijb.2012.8.issue-1/1557-4679.1426/1557-4679.1426.xml. doi: 10.1515/1557-4679.1426.
Longitudinal data arise frequently in medical studies and it is a common practice to analyze such complex data with nonlinear mixed-effects (NLME) models, which enable us to account for between-subject and within-subject variations. To partially explain the variations, time-dependent covariates are usually introduced to these models. Some covariates, however, may be often measured with substantial errors and missing observations. It is often the case that model random error is assumed to be distributed normally, but the normality assumption may not always give robust and reliable results, particularly if the data exhibit skewness. In the literature, there has been considerable interest in accommodating either skewed response or covariate measured with error and missing data in such models, but there has been relatively little study concerning all these features simultaneously. This article is to address simultaneous impact of skewness in response and measurement error and missing data in covariate by jointly modeling the response and covariate processes under a framework of Bayesian semiparametric nonlinear mixed-effects models. In particular, we aim at exploring how mixed-effects joint models based on one-compartment model with one phase time-varying decay rate and two-compartment model with two phase time-varying decay rates contribute to modeling results and inference. The method is illustrated by an AIDS data example to compare potential models with different distributional specifications and various scenarios. The findings from this study suggest that the one-compartment model with a skew-normal distribution may provide more reasonable results if the data exhibit skewness in response and/or have measurement error and missing observations in covariates.
纵向数据在医学研究中经常出现，使用非线性混合效应（NLME）模型分析此类复杂数据是一种常见做法，该模型使我们能够考虑个体间和个体内的变异。为了部分解释这些变异，通常会将随时间变化的协变量引入这些模型。然而，一些协变量可能经常存在大量测量误差和缺失观测值。通常假设模型随机误差呈正态分布，但正态性假设可能并不总是能给出稳健可靠的结果，特别是当数据呈现偏态时。在文献中，人们对在这类模型中处理偏态响应或带有误差和缺失数据的协变量有相当大的兴趣，但同时考虑所有这些特征的研究相对较少。本文旨在通过在贝叶斯半参数非线性混合效应模型框架下对响应和协变量过程进行联合建模，来解决响应中的偏态以及协变量中的测量误差和缺失数据的同时影响。特别是，我们旨在探索基于具有一个时变衰减率的一室模型和具有两个时变衰减率的二室模型的混合效应联合模型如何对建模结果和推断做出贡献。通过一个艾滋病数据示例来说明该方法，以比较具有不同分布规格和各种情景的潜在模型。这项研究的结果表明，如果数据在响应中呈现偏态和/或在协变量中存在测量误差和缺失观测值，具有偏态正态分布的一室模型可能会提供更合理的结果。
