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The human immunodeficiency virus (HIV) is a viral infection that destroys the human immune system resulting in acquired immunodeficiency syndrome (AIDS). The Zambia HIV prevalence rate (11.3%) remains among the highest in the sub-Saharan Africa. In the treatment of HIV-naive patients, a problem that relates to the transmitted drug resistance mutation strains (TDRMs) occurs in the administration of antiretroviral (ARV) drugs. To address this problem, we propose the use of transition probabilities when prescribing a switch from the first-line to the second-line or to the third-line regimen on the ARV drugs combination. We formulate a statistical technique to determine an optimal ARV drugs combination. To compute a transition probability matrix chart on ARV drugs combinations of the first-line and second-line regimens, we apply a beta-binomial hierarchical model on HIV data. The transition probability matrices corresponding to the ARV drugs combinations TDF+ETC+NVP, TDF+FTC+EFV, AZT+3TC+NVP, AZT+3TC+EFV, D4T+3TC+NVP, and D4T+3TC+EFV provide an upper triangular matrix of probabilities. We observe a higher probability of remaining in the same regimen state than moving to another state. A transition probability chart provides information on the most effective combination to prescribe to a patient in the presence of transmitted drug resistance mutation (TDRM) test results. The transmission probabilities play a major role in aiding the physicians make an informed decision to prescribe an optimal ARV drugs combination. We suggest a TDRM test to be carried out to all newly diagnosed HIV individuals before prescribing any of the ARV drugs combination.

The Estimation of Transmitted Drug Resistance Mutation Strains Probability in the Treatment of HIV Using the Beta-Binomial Model