Mixed-Effects Joint Models with Skew-Normal Distribution for HIV Dynamic Response with Missing and Mismeasured Time-Varying Covariate

Abstract

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 skewnormal distribution may provide more reasonable results if the data exhibit skewness in response and/or have measurement error and missing observations in covariates.

Retracted: Bayesian inference on mixed‐effects location scale models with skew‐t distribution and mismeasured covariates for longitudinal data

“…Huang and Dagne developed a skew‐normal nonlinear mixed‐effects (NLME) joint model for longitudinal data with skewness and mismeasured covariates. A semiparametric NLME joint model has also been studied to deal with longitudinal data with skewness, missing responses, and measurement errors in covariates . Lu and Huang proposed a mixed‐effects varying coefficient joint model to study the multiple data features in longitudinal data.…”

Bayesian Approach to Nonlinear Mixed-Effects Quantile Regression Models for Longitudinal Data with Non-normality and Left-censoring

“…In contrast, the mean regression-based NLME models [9,10,16,11,7,39] only quantify the viral dynamics and treatment effects at the average of the viral load observations, and thus cannot detect such quantile differences.…”

“…It is generally assumed that λ 1 > λ 2 , which assures that the model is identifiable and is appropriate for empirical studies [3]. It was noted that equation (8) can be only applied to the early segment or longer term of the viral load response with decreasing trajectory patterns [3,39]. However, we noted in Figure 1(c) that for some patients viral loads increase at the later period, indicating that the second-phase viral decay rate λ 2 may vary over time and negative values of the second-phase decay rate may correspond to viral increase and lead to viral rebound [3]; it suggests that variation in the dynamic parameters, particularly λ 2 , may be partially associated with time-varying covariates such as repeated CD4 cell counts.…”

Bayesian analysis of nonlinear mixed-effects mixture models for longitudinal data with heterogeneity and skewness

“…It is generally assumed that 1 > 2 in (13), which assures that the model is identifiable and is appropriate for empirical studies [2]. Models (12) and (13) offer almost equal performance to capture the early fast-decaying segment of viral load trajectory [34], but model (13) performs better for a long term of viral load trajectory [35]. It was noted that both models can be only applied to the early segment or longer term of the viral load response with decreasing trajectory patterns as discussed in Section 1 and shown in Figure 1(a)(two solid and two dashed lines).…”