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In AIDS studies snch as HIV viral dynamics, statistical inference is often complicated because the viral load measurements may be subject to asymmetric (skewed) characteristics, left censoring due to detection limit and time-varying covariates such as CD4 cell counts may be measured with substantial errors.Norality of model random errors is a routine assumption for mixed-effects models in many longitudinal studies, but it may be unrealistically obscuring important features of subject variations.