After initiation of treatment, HIV viral load has multiphasic changes, which indicates that the viral decay rate is a time-varying process. Mixed-effects models with different time-varying decay rate functions have been proposed in literature. However, there are two unresolved critical issues: (i) it is not clear which model is more appropriate for practical use, and (ii) the model random errors are commonly assumed to follow a normal distribution, which may be unrealistic and can obscure important features of within- and among-subject variations. Because asymmetry of HIV viral load data is still noticeable even after transformation, it is important to use a more general distribution family that enables the unrealistic normal assumption to be relaxed. We developed skew-elliptical (SE) Bayesian mixed-effects models by considering the model random errors to have an SE distribution. We compared the performance among five SE models that have different time-varying decay rate functions. For each model, we also contrasted the performance under different model random error assumption such as normal, Student-t, skew-normal or skew-t distribution. Two AIDS clinical trial data sets were used to illustrate the proposed models and methods. The results indicate that the model with a time-varying viral decay rate that has two exponential components is preferred. Among the four distribution assumptions, the skew-t and skew-normal models provided better fitting to the data than normal or Student-t model, suggesting that it is important to assume a model with a skewed distribution in order to achieve reasonable results when the data exhibit skewness.

The Langevin equation and the Gaussian average of the stochastic quantization of Parisi and Wu are continued on the closed time-path, at the same time, the new non-Gaussian source is added into it. After assuming some properties of new source, the closed time-path Green functions are computed by using the adapted Langevin equations. While they are transformed into the physical representation, some important characters of closed time-path Green function, i.e. the normalization and causality, are obtained also.

The Green functions and the anomalous Green junctions of the systems with the unsymmetrical interactions are calculated by using the stochastic quantization. By the correct treatment, the Dyson equations including the Green functions and the anomalous Green junctions are obtained.

The finite temperature Green functions of the fermion systems was calculated by using the stochastic quantization method. By properly approzimation of the Langevin equations, Hartree-Fock, ring and ladder approzimations of Green functions was obtained.

By using the kernels consisting of the projectors and function δ(t), both the co-nvergence to equilibrium and to get the propagators in covariant gauge are solved to-gether under the vanishing initial condition. Thus, the SQ prescriptions of gauge and non-gauge fields are united in using only these same kernels. The Maxwell, Chern-Si-mon and the linear gravitational theories are considered respectively. Again, it is shown that the use of this kernel does not yield the influence on the equilibrium distri-bution.