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When modeling longitudinal data, the true values of time-varying covariates may be unknown because of detection-limit censoring or measurement error. A common approach in the literature is to empirically model the covariate process based on observed data and then predict the censored values or mismeasured values based on this empirical model. Such an empirical model can be misleading, especially for censored values since the (unobserved) censored values may behave very differently than observed values due to the underlying data-generation mechanisms or disease status. In this paper, we propose a mechanistic nonlinear covariate model based on the underlying data-generation mechanisms to address censored values and mismeasured values. Such a mechanistic model is based on solid scientific or biological arguments, so the predicted censored or mismeasured values are more reasonable. We use a Monte Carlo EM algorithm for likelihood inference and apply the methods to an AIDS dataset, where viral load is censored by a lower detection limit. Simulation results confirm that the proposed models and methods offer substantial advantages over existing empirical covariate models for censored and mismeasured covariates. [ABSTRACT FROM AUTHOR]

Traditional Chinese medicine (TCM) is a very complex mixture containing many different ingredients. Thus, statistical analysis of traditional Chinese medicine data becomes challenging, as one needs to handle the association among the observed data across different time points and across different ingredients of the multivariate response. This paper builds a 3-stage Bayesian hierarchical model for analyzing multivariate response pharmacokinetic data. Usually, the dimensionality of the parameter space is very huge, which leads to the parameter-estimation difficulty. So we take the hybrid Markov chain Monte Carlo algorithms to obtain the posterior Bayesian estimation of corresponding parameters in our model. Both simulation study and real-data analysis show that our theoretical model and Markov chain Monte Carlo algorithms perform well, and especially the correlation among different ingredients can be calculated very accurately. [ABSTRACT FROM AUTHOR]

Longitudinal measurement of biomarkers is important in determining risk factors for binary endpoints such as infection or disease. However, biomarkers are subject to measurement error, and some are also subject to left-censoring due to a lower limit of detection. Statistical methods to address these issues are few. We herein propose a generalized linear mixed model and estimate the model parameters using the Monte Carlo Newton-Raphson (MCNR) method. Inferences regarding the parameters are made by applying Louis's method and the delta method. Simulation studies were conducted to compare the proposed MCNR method with existing methods including the maximum likelihood (ML) method and the ad hoc approach of replacing the left-censored values with half of the detection limit (HDL). The results showed that the performance of the MCNR method is superior to ML and HDL with respect to the empirical standard error, as well as the coverage probability for the 95% confidence interval. The HDL method uses an incorrect imputation method, and the computation is constrained by the number of quadrature points; while the ML method also suffers from the constrain for the number of quadrature points, the MCNR method does not have this limitation and approximates the likelihood function better than the other methods. The improvement of the MCNR method is further illustrated with real-world data from a longitudinal study of local cervicovaginal HIV viral load and its effects on oncogenic HPV detection in HIV-positive women. [ABSTRACT FROM AUTHOR]