The estimation of transmitted drug resistance mutation strains probability in the treatment of HIV using the Beta-Binomial model

Background 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 is among the highest in the sub-Saharan Africa. With no HIV vaccine and cure for HIV/AIDS, the antiretroviral (ARV) therapy that slows the spread of the virus remains the only option. The administration of ARV has challenges of Transmitted Drug Resistance Mutation strains (TDRMs) in the treatment of HIV naïve patients. To address these challenges, we propose use of transition probabilities when prescribing a switch from first-line to second-line or to third-line regimen on ARV drugs combination. Methods We formulate a statistical technique for determining an optimal ARV drugs combination. Using data from the Zambia National Health Research Authority, we compute transition probability matrix chart on ARV therapy combination of the first and second baseline regimens using a Beta-Binomial Hierarchical model. We check parameter convergence using history and density plots, and check model adequacy using the deviation information criteria. Results The estimates converge to the fitted model as demonstrated by the history and density plots. The transition probability matrices corresponding to, 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 the probabilities. We observe a higher probability of remaining in the same regimen state than that of moving to another state. The computed transition probability matrix chart aid in deciding on the most effective combination to prescribe to a patient, in the presence of TDRM test results. Based on transition probabilities TDF+ETC+NVP, TDF+FTC+EFV, AZT+3TC+EFV and D4T+3TC+EFV cannot be prescribed to the patients who test K101 E and 115Y F strains. The available option to the patients’ remains either AZT + 3TC + NVP or D4T + 3TC + NVP. Combination AZT + 3TC + NVP with success probability of 0.97027 should be prescribed to the patient. Conclusion The transmission probabilities play a major role in aiding the physicians make an informed decision when prescribing an optimal drug combination. All newly diagnosed HIV individuals should have a TDRM test before any prescription on ARV therapy combination is made.