Approximate Methods for Maximum Likelihood Estimation of Multivariate Nonlinear Mixed-Effects Models

Multivariate longitudinal data analysis with censored and intermittent missing responses

The multivariate linear mixed model (MLMM) has emerged as an important analytical tool for longitudinal data with multiple outcomes. However, the analysis of multivariate longitudinal data could be complicated by the presence of censored measurements because of a detection limit of the assay in combination with unavoidable missing values arising when subjects miss some of their scheduled visits intermittently. This paper presents a generalization of the MLMM approach, called the MLMM-CM, for a joint analysis of the multivariate longitudinal data with censored and intermittent missing responses. A computationally feasible expectation maximization-based procedure is developed to carry out maximum likelihood estimation within the MLMM-CM framework. Moreover, the asymptotic standard errors of fixed effects are explicitly obtained via the information-based method. We illustrate our methodology by using simulated data and a case study from an AIDS clinical trial. Experimental results reveal that the proposed method is able to provide more satisfactory performance as compared with the traditional MLMM approach.

Bayesian semiparametric modeling for HIV longitudinal data with censoring and skewness

In biomedical studies, the analysis of longitudinal data based on Gaussian assumptions is common practice. Nevertheless, more often than not, the observed responses are naturally skewed, rendering the use of symmetric mixed effects models inadequate. In addition, it is also common in clinical assays that the patient's responses are subject to some upper and/or lower quantification limit, depending on the diagnostic assays used for their detection. Furthermore, responses may also often present a nonlinear relation with some covariates, such as time. To address the aforementioned three issues, we consider a Bayesian semiparametric longitudinal censored model based on a combination of splines, wavelets, and the skew-normal distribution. Specifically, we focus on the use of splines to approximate the general mean, wavelets for modeling the individual subject trajectories, and on the skew-normal distribution for modeling the random effects. The newly developed method is illustrated through simulated data and real data concerning AIDS/HIV viral loads.