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The aim of this work is to estimate the effect of Imatinib, exosomes, and Imatinib-exosomes mixture in chronic myeloid leukemia (CML). For this purpose, mathematical models based on Gompertzian and logistic growth differential equations were proposed. The models contained parameters representing the effects of the three components on CML proliferation. Parameters estimation was performed under the Bayesian statistical approach. Experimental data reported in the literature were used, corresponding to four trials of a human leukemia xenograft in BALB/c female rats over a period of forty days. The models were fitted to the following growth dynamics: normal tumor growth, growth with exosomes, growth with Imatinib, and growth with exosomes-Imatinib mixture. For the proposed logistic growth model, it was determined that when using Imatinib treatment the growth rate is 0.93 (95% CrI: 84.33–99.64) slower and reduces the tumor volume to approximately 10% (95% CrI : 8.67–10.81). In the presence of exosome treatment, the growth rate is 0.83 (95% CrI: 1.52–16.59) faster and the tumor volume is expanded by 40% (95% CrI: 25.36–57.28). Finally, in the presence of Imatinib-exosomes mixture treatment, the growth rate is 0.82 (95% CrI: 76.87–88.51) slower and the tumor volume is reduced by 95% (95% CrI: 86.76–99.85). It is concluded that the presence of exosomes partially inactivates the effect of the Imatinib drug on tumor growth in a mouse xenograft model. [ABSTRACT FROM AUTHOR]

In this work, a simulation study is conducted to evaluate the performance of Bayesian estimators for the log–linear exponential regression model under different levels of censoring and degrees of collinearity for two covariates. The diffuse normal, independent Student-t and multivariate Student-t distributions are considered as prior distributions and to draw from the posterior distributions, the Metropolis algorithm is implemented. Also, the results are compared with the maximum likelihood estimators in terms of the mean squared error, coverages and length of the credibility and confidence intervals. [ABSTRACT FROM PUBLISHER]