### Journals Information

Mathematics and Statistics Vol. 10(3), pp. 588 - 602
DOI: 10.13189/ms.2022.100315
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## Weibull Distribution as the Choice Model for State-Specific Failure Rates in HIV/AIDS Progression

Nahashon Mwirigi 1,*, Stanley Sewe 1, Mary Wainaina 1, Richard Simwa 2
1 Department of Mathematics and Actuarial Sciences, Catholic University of Eastern Africa (CUEA), Kenya
2 Department of Mathematics, University of Nairobi (UoN), University Way, Kenya

ABSTRACT

This study considered the problem of selecting the best single model for modeling state-specific failure rates in HIV/AIDS progression for patients on antiretroviral therapy with age and gender as risk factors using exponential, twoparameter, and three-parameter Weibull distributions. CD4 count changes in any two consecutive visits, the mean waiting time (μ), and transitional rates (λ) for remaining in the same state or transiting to a better or a worse state were analyzed. Various model selection criteria, namely, Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC), and Log-Likelihood (LL), were used in each specific disease state. The Maximum Likelihood Estimation (MLE) method was applied to obtain the parameters of the distributions used. Plots of State-specific transition rates (λ) depicted constant, increasing, decreasing, and unimodal trends. Three-parameter Weibull distribution was the best for male patients and patients aged (40-69) years transiting in the states 1-2, 3-4, and 4-5, and 1-2, 3-4, and 5-6, respectively, and for male, female patients, and patients aged (40-69), remaining in the same state. Two-parameter Weibull distribution was the best for female patients and patients aged (20-39) years transiting in the states 1-2, 2-3, 4-5, and 1-2, 2-3, 3-4, respectively. Exponential distribution proved inferior to the other two distributions used.

KEYWORDS
Markov Chain, Markov Process, Semi Markov Process, Stochastic Process

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Nahashon Mwirigi , Stanley Sewe , Mary Wainaina , Richard Simwa , "Weibull Distribution as the Choice Model for State-Specific Failure Rates in HIV/AIDS Progression," Mathematics and Statistics, Vol. 10, No. 3, pp. 588 - 602, 2022. DOI: 10.13189/ms.2022.100315.

(b). APA Format:
Nahashon Mwirigi , Stanley Sewe , Mary Wainaina , Richard Simwa (2022). Weibull Distribution as the Choice Model for State-Specific Failure Rates in HIV/AIDS Progression. Mathematics and Statistics, 10(3), 588 - 602. DOI: 10.13189/ms.2022.100315.