##### Applications of Genetic Distances on Blood-group Gene Frequencies and their Statistical Genetic Similarities

Onu, Obineke Henry, Inamete, Emem Ndah Happiness, Onyekwuluje, Makuachukwu James-Patrick

Asian Journal of Probability and Statistics, Page 1-7
DOI: 10.9734/ajpas/2022/v20i130478

This paper studied the applications of genetic distances on Blood-group gene frequencies and their Statistical genetic similarities characterizing four populations, for data from Eakimo, Bantu, English and Korea. The study compared the following distances: Euclidean, squared Euclidean, Minkowski, Chebychev and City Block on the above mentioned data for the outlined countries. Correlation analysis was applied to evaluate the relationships between these countries on their blood group gene frequencies. Similarity check was also conducted to know the countries that have similar blood-group gene frequency. It was observed that Euclidean distance and Minkowski distance had equal distances. This means that the two distances are more similar in this particular data set than the other studied distances. The study revealed that Chebychev distance had the smallest neighbor distance as compared to other distances studied while City Block had the highest distance. It has been stated in literature that Chebychev and Minkowski distances are concentric circle shape, this suggests the reason behind their equality of distance. It is therefore proposed that the data may be a concentric circle data.

##### Estimation of Quality Adjusted Life Years (QALYs) for HIV Patients on Art in Kenya Using Proxy Utility Function

Winnie Chacha, Jane Akinyi, Samuel Mwalili

Asian Journal of Probability and Statistics, Page 8-15
DOI: 10.9734/ajpas/2022/v20i130479

Aims: This study seeks to estimate QALYs for HIV/AIDS patients on ART in Kenya to quantitatively evaluate the health impact of ART treatment on patients. QALYs values are important as they form a                 basis for evidence based decision making and policy formulation in the country with regards to HIV/               AIDS.

Study Design: The study involved secondary data obtained from a retrospective follow up study on hospital records of HIV/AIDS patients enrolled for ART from 2005 to 2017.

Place and Duration of Study: Jomo Kenyatta University of Agriculture and Technology, between January 2019-April 2022.

Methodology: The study involved a retrospective study of 3000 patients on ART in Kenya from the period of 2005-2017. All the patient records are identified using random patient id ensuring the privacy and anonymity of patients. The inclusion criteria is patients who had complete information on the covariates used in the model during follow up. The joint modelling of the longitudinal and survival data of each patient was applied and the results applied to proxy utility function to estimate the QALYs for patients on ART. To get the average QALYs gained by all patients, we aggregate the total QALYs from each patient. R. Software version 4.0.2 was used in the analysis.

Results: Sex, age, Marital Status and weight are significant predictors of survival of HIV Patients on ART in Kenya. Being on ART therapy resulted in a gain of 9.688313 QALYs for HIV/AIDS patients. The association parameter estimate is-0.0345 implying that increase in the values of CD4 count results in a decrease in the hazard of death for HIV patients on ART therapy.

Conclusion: The proxy utility function methodology is appropriate for the calculation of QALYs values for HIV patients on ART. It has the advantage of allowing utilities of each patient to vary and are calculated at every time point. Since ART results in the improvement in QALYs of patients, efforts should be directed towards ensuring patients who are enrolled for the therapy continue with it for sustained health and non health benefits.

##### Chris-Jerry Distribution and Its Applications

Chrisogonus K. Onyekwere, Okechukwu J. Obulezi

Asian Journal of Probability and Statistics, Page 16-30
DOI: 10.9734/ajpas/2022/v20i130480

In this paper, a new one-parameter distribution named Chris-Jerry is suggested from two component mixture of Exponential ($$\theta$$) distribution and Gamma(3; $$\theta$$) distribution with mixing proportion $$p=\frac{\theta}{\theta + 2}$$ having a flexibility advantage in modeling lifetime data. The statistical properties are discussed and the maximum likelihood estimation procedure is used to obtain the parameter estimate. The Convolution of the product of Pareto random variable with the proposed Chris-Jerry distributed random variable is explored with its marginal density derived. To illustrate the usefulness, three sets of lifetime data are employed and LL, AIC, BIC and K-S statistics are obtained for Exponential, Ishita, Akash, Rama, Pranav, Rani, Lindley, Sujatha, Aradhana, Shanker and XGamma and the Chris-Jerry distributions.

##### The Utility of Health and Wealth for HIV Patients on Antiretroviral Therapy in Kenya

Winnie Chacha, Jane Akinyi, Samuel Mwalili

Asian Journal of Probability and Statistics, Page 31-38
DOI: 10.9734/ajpas/2022/v20i130481

Aims/ Objectives: To determine the appropriate utility function that models the trade o between health and wealth for HIV/AIDS patients on Antiretroviral Therapy in Kenya.

Study Design: Retrospective study.

Place and Duration of Study: Jomo Kenyatta University of Agriculture and Technology, between January 2019-April 2022.

Methodology: The study involved a retrospective study of 2800 patients on Antiretroviral Therapy in Kenya from the period of 2005-2017. All the records are in terms of random patient id and in no way is the privacy and anonymity of patients is compromised. The inclusion criteria is patients who had complete information on the covariates used in the model over the follow up period. The logarithmic utility function, the negative exponential utility function and the power utility function are compared using the Akaike Information Criterion to determine which one best fits the empirical data to model the health and wealth trade off of patients on Antiretroviral Therapy in Kenya.

Results: Women constituted 66% of the sample. Only patients over the age of 18 years were included in the study. The mean age was 40.3. The health related quality of life values were calculated for each patient on Antiretroviral Therapy using the proxy utility function approach. The costs associated with receiving Antiretroviral Therapy treatment were obtained from simulating from a gamma distribution with ranges from existing published literature. The logarithmic utility function had the least AKaike Information Criterion.

Conclusion: The marginal utility of health increases with wealth for People living with HIV and the logarithmic utility function is suitable for modelling the shape of preferences for the trade off between health and wealth for HIV patients on Antiretroviral Therapy.