IntroductionHuman-Immunodeficiency Virus (HIV) is a virus that causes acquired-immunodeficiency syndrome (AIDS). It targets the immune system, specifically the CD4 cells or T cells of the infected individual weakening it and making an individual incapable of resisting attack from a wide range of infections (WHO, 2012). Currently, there is no cure or vaccination for HIV infected individuals but HIV Testing Services are being offered to people with HIV and AIDS to help in improving their quality of lives as well as controlling the spread. The general treatment of HIV positive people is with ARV and HAART drugs which can lower the viral load set point while prolonging the life of infected person (Ho, 1995). This treatment reduces the risk of HIV transmission. But before administering the ARV, an individual is first administered with prophylaxis for opportunistic, counseling and assessing the eligibility of ARV. Regardless of ART or HAART treatment, the infectiousness is not restored to susceptibility or reduced and hence an infected individual could still cause the infection. Research shows that there are millions approximately 34 million of individuals who have HIV and AIDS and died from the disease (UNAIDS, 2013; WHO, 2014). This is evident that further studies and researches on the disease are needed in order to reduce the number of infections. On the other hand, Pneumonia is an infectious disease that is caused by microbes including bacteria, virus, and fungi among people with severely weakened immune systems or example those infected with HIV. It is classified as an airborne disease more generally a lung infection involving alveoli (air sacs). The common causes of pneumonia are Streptococcus Pneumonae (bacterial), Pneumocystis Carinii Pneumonia (PCP) and histoplasma ( fungal ) and Haemophilus influenza type b and respiratory syncytial virus (RSV) (viral) (Gray and Zar, 2010; Greenwood ,2000). Currently, there is no specific effective prevention, treatment or vaccination of Pneumonia as its cause has several factors. Generally the disease can be vaccinated with pneumococcal conjugate vaccines or treated with antibiotics (cotrimoxazole prophylaxis, amoxillin, ampicillin and gentamycine dispersible tablets).The co-infection due to Pneumonia and HIV results once the immune system has been impaired with HIV in which CD4 or T-cells are less than 200 cells per millimetre cubed giving a chance to Pneumonia infection. Research shows that the lungs are the principal target of HIV associated complications and persons with HIV infections are at an increased risk for a wide spectrum of opportunistic cases of pneumonia, neoplasms and pulmonary condition (WHO, 2012; Sogaard, et al , 2008). It has become a burden to the society disrupting the social-economical systems as efforts have been directed to curb these instances.Several scholars have developed mathematical models which play a great role in proposing ways of controlling the transmission co-dynamics of HIV and pneumonia (
Pool testing for presence or absence of a trait is less expensive, less time consuming and therefore more cost effective. This study presents a multi-stage adaptive pool testing estimatorp en of prevalence of a trait in the absence of test errors. Pool testing is more efficient, less expensive and less time consuming. An increase in the number of stages improves the efficiency of the estimator, hence construction of a multi-stage model. The study made use of the Maximum Likelihood Estimate (MLE) method and Martingale method to obtain the adaptive estimator and Cramer-Rao lower bound method to determine the variance of the constructed estimator. Matlab and R, statistical softwares were used for Monte-carlo simulation and verification of the model, then analysis and discussion of properties of the constructed estimator in comparison with the non-adaptive estimator in the literature of pool testing done alongside provision of the confidence interval of the estimator. Results have shown that as the number of stages increases, the efficiency of the multi-stage adaptive estimator in the absence of test errors also increases in comparison with the non-adaptive estimator in the absence of test errors. This makes the multi-stage adaptive estimator better than the corresponding non-adaptive estimator in the literature of pool testing.
Background: Accuracy of pregnancy outcome predictions are essential for clinicians to be effective in handling pregnant women experiencing symptoms of miscarriage when presented in the Early Pregnancy Units (EPU). Therefore, the focus of this study is to improve accuracy in modeling risk of miscarriage during first trimester of subsequent intrauterine pregnancy. To achieve this, the study formulates and analyze a Bayesian two-level random intercept logistic model M2 that takes into consideration hierarchical structure in the subsequent pregnancy outcome. This research work is motivated by the recent epidemiological research works that indicated a two-level structure in the subsequent pregnancy outcome with respect to previous pregnancy outcome. Materials and Methods: The proposed Bayesian hierarchical logistic random intercept model M2 was formulated using the concept of multilevel and Bayesian modeling. Analysis of the proposed Bayesian hierarchical logistic random intercept modelM2 was implemented using the Markov Chain Monte Carlo simulation, in specific Gibbs sampling. Assessment and comparison of the proposed Bayesian hierarchical logistic random intercept model to other reviewed classical approaches using the DIC and AIC. Results: Assessment of model fitness using DIC and AIC indicates that the proposed Bayesian two-level random intercept logistic modelM2has the lowest value of DIC= 121.2 among both classical and Bayesian approaches M0, M1 and M2. This indicates that the proposed Bayesian model M2 is the most plausible approach in modeling risk of miscarriage during first trimester of subsequent intrauterine pregnancy. Assessment of the between cluster variation as a result of the two-level hierarchical structure in subsequent pregnancy outcome, and prior information which, according to this study, are revealed to be essential in modeling risk of miscarriage during first trimester of the subsequent intrauterine pregnancy in women. Relative biases for the model parameter estimates were all below maximum threshold of |0.2| thus indicating accurate model estimations. Conclusion: The proposed Bayesian two-level random intercept logistic model M2 is the most plausible approach in modeling risk of miscarriage during first trimester of subsequent pregnancy. Taking into account between previous pregnancy outcome cluster variations and updating observations with prior information is essential to improve accuracy in modeling the risk of miscarriage during first trimester of subsequent pregnancy.
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