A Computational Framework for the Mixing Times in the QBD Processes with Infinitely-Many Levels

In this paper, we develop some matrix Poisson's equations satisfied by the mean and variance of the mixing time in an irreducible positive-recurrent discrete-time Markov chain with infinitely-many levels, and provide a computational framework for the solution to the matrix Poisson's equations by means of the UL-type of $RG$-factorization as well as the generalized inverses. In an important special case: the level-dependent QBD processes, we provide a detailed computation for the mean and variance of the mixing time. Based on this, we give new highlight on computation of the mixing time in the block-structured Markov chains with infinitely-many levels through the matrix-analytic method

Client Acceptability for Integrating Antiretroviral Therapy in Methadone Maintenance Therapy Clinics in Sichuan, China.

BackgroundUsing methadone maintenance therapy (MMT) clinics to deliver antiretroviral therapy (ART) has proven to be effective for promoting treatment initiation and adherence in drug users living with HIV.ObjectivesThe objective of this study was to investigate the HIV-positive client acceptability of integrated ART services and to identify the reasons for and factors associated with service acceptability.MethodsA total of 86 HIV-positive MMT clients were recruited from 12 MMT clinics in Sichuan Province, China. They participated in a cross-sectional survey that queried their willingness to receive seven different types of MMT-based ART services. The reasons for their willingness/unwillingness to accept these services were documented. The association between service acceptability and background characteristics was examined.ResultsThe most accepted integrated services were ART-related counseling (75.6%) and referral (73.2%). Concerns regarding the provider's lack of ART expertise and confidentiality issues were common barriers for the acceptance of MMT-based ART services. A trust relationship with MMT providers was a reason for service acceptance. Service acceptability was associated with a poorer perceived health status. Conclusions/Importance: ART-related services, based on the client perspective, can be delivered at MMT clinics. However, service provider training and the protection of confidentiality must be strengthened for the effective implementation of integrated service delivery