Department of Epidemiology and Biostatistics, University of South Florida, Tampa, FL 33612, USA.
Stat Med. 2010 Oct 15;29(23):2384-98. doi: 10.1002/sim.3996.
Studies of HIV dynamics in AIDS research are very important in understanding the pathogenesis of HIV-1 infection and also in assessing the effectiveness of antiviral therapies. Nonlinear mixed-effects (NLME) models have been used for modeling between-subject and within-subject variations in viral load measurements. Mostly, normality of both within-subject random error and random-effects is a routine assumption for NLME models, but it may be unrealistic, obscuring important features of between-subject and within-subject variations, particularly, if the data exhibit skewness. In this paper, we develop a Bayesian approach to NLME models and relax the normality assumption by considering both model random errors and random-effects to have a multivariate skew-normal distribution. The proposed model provides flexibility in capturing a broad range of non-normal behavior and includes normality as a special case. We use a real data set from an AIDS study to illustrate the proposed approach by comparing various candidate models. We find that the model with skew-normality provides better fit to the observed data and the corresponding estimates of parameters are significantly different from those based on the model with normality when skewness is present in the data. These findings suggest that it is very important to assume a model with skew-normal distribution in order to achieve robust and reliable results, in particular, when the data exhibit skewness.
在艾滋病研究中，研究 HIV 动力学对于理解 HIV-1 感染的发病机制以及评估抗病毒治疗的效果非常重要。非线性混合效应（NLME）模型已被用于对病毒载量测量中的个体间和个体内变异进行建模。通常，NLME 模型的个体内随机误差和随机效应的正态性是一个常规假设，但如果数据存在偏态，则该假设可能不切实际，掩盖了个体间和个体内变异的重要特征。在本文中，我们通过考虑模型随机误差和随机效应具有多元偏态正态分布，为 NLME 模型开发了一种贝叶斯方法，并放宽了正态性假设。所提出的模型在捕捉广泛的非正态行为方面具有灵活性，并包括正态性作为特例。我们使用来自艾滋病研究的真实数据集通过比较各种候选模型来说明所提出的方法。我们发现，当数据存在偏态时，具有偏态正态性的模型对观察数据的拟合更好，并且相应的参数估计与基于正态性模型的参数估计有显著差异。这些发现表明，为了获得稳健可靠的结果，特别是当数据存在偏态时，假设具有偏态正态分布的模型非常重要。
