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- ItemA copula-based approach to differential gene expression analysisChaba, Linda Akoth; Odhiambo, John W.; Omolo, BernardMelanoma is a major public health concern in the developed world. Melanoma research has been enhanced by the introduction of microarray technology, whose main aim is to identify genes that are associated with outcomes of interest in melanoma biology and disease progression. Many statistical methods have been proposed for gene selection but so far none of them is regarded as the standard method. In addition, none of the proposed methods have applied copulas to identify genes that are associated with quantitative traits. In this study, we developed a copula-based approach to identify genes that are associated with quantitative traits in the systems biology of melanoma. To assess the statistical properties of model , we evaluated the power, the false-rejection rate and the true-rejection rate using simulated gene expression data . The model was then applied to a melanoma dataset for validation. Comparison of the copula approach with the Bayesian and other parametric approaches was performed, based on the false discovery rate (FOR) , the value of R-square and prognostic properties. It turned out that the copula model was more robust and better than the others in the selection of genes that were biologically and clinically significant.
- ItemA smooth test of goodness-of-fit for the baseline hazard function in recurrent event modelsOdhiambo, John W.; Odhiambo, Collins; Omolo, BernardIn this paper, we formulate a smooth test of goodness-of-fit for a simple hypothesis about the baseline hazard function in recurrent-event models. The formulation is an extension of Neyman' s goodness-of-fit approach, whose score tests are obtained by embedding the null hypothesis in a larger class of hazard rate functions. Since the application is in recurrent event models , the data is dynamic.A useful feature about this test is the parametric approach that makes inference about the hazard function more efficient. To examine the finite-sample properties of this test, we used simulated data . For validation, we applied the test to a real-life recurrent event data. Results show that the test possesses better power over wide range of alternatives, when compared with similar tests of the chi-square type in the literature.
- ItemModel-Assisted Estimation of Finite Population Mean in Two-stage Cluster SamplingBii, Nelson Kiprono; Onyango, Christopher OumaEstimation of finite population parameters has been an area of concern to statisticians for decades. This paper presents an estimation of the population mean under a model-assisted approach.Dorfman (1992), Breidt and Opsomer (2000) and Ouma et al(2010) carried out theestimation of finite population total on the assumption that the sample size is large and the sampling distribution is approximately normal. Unlike their researches, this paper considered a case when the sample size is small under a model-assisted approach. A model-assisted regression model was considered in a case where the cluster sizes are known only for the sampled clusters in order to predict the unobserved part of the population mean. Under mild assumptions, the proposed estimator is asymptotically unbiased and its conditional error variance tends to zero. Simulation studies show that model assisted estimation performs better than model based estimation of a finite population mean in a case where the sample size is small.
- ItemSemi-Markov model for evaluating the HIV patient treatment costMbogo, Rachel Waema; Luboobi, Livingstone S.; Odhiambo, John W.The aim of this study is to model the progression of HIV/AIDS disease and evaluate the cost of the anti-retroviral therapy for an HIV infected patient under ART follow-up using Non homogeneous semi-Markov processes. States of the Markov process are defined by the seriousness of the sickness based on the clinical scores. The five states considered are: Asymptomatic (CD$^{+}_{4}$ count > 500 cells/microliter); Symptomatic 1 (350 < CD$^{+}_{4}$ count ≤ 500 cells/microliter); Symptomatic 2 (200 < CD$^{+}_{4}$ count ≤ 350 cells/microliter); AIDS (CD$^{+}_{4}$ count ≤ 200 cells/microliter) and Death (Absorbing state). The first four states are named as good or alive states. The models formulated can be used to gain insights on the transition dynamics of the HIV patient given the follow-up time. The transition probability Model, when fitted with data will give insights on the conditional probability of a patient moving from one disease state to another, given the current state and the follow-up time. This model will also give the probability of survival for the HIV patient under treatment given the current state and follow-up time. The total Lifetime Treatment Cost model obtained, when applied to real data will give the cost of managing an HIV patient given the starting state, the treatment combination which incurs minimum cost and which treatment combination is most effective at each state. The treatment reward model also when applied to real data will give the state, which a patient should be maintained so that they remain healthy, noninfectious and productive to the society. Also the model will show the optimal/effective time to initiate treatment, which can be used to give advice on how to handle the HIV infecteds given their states.
- ItemStochastic Model for Langerhans cells and HIV Dynamics in VivoMbogo, Rachel Waema; Luboobi, Livingstone S.; Odhiambo, John W.Many aspects of the complex interaction between HIV and the human immune system remain elusive. Our objective is to study these inter-actions, focusing on the speci c roles of langerhans cells (LCs) in HIV infection. In patients infected with HIV, a large amount of virus is as-sociated with LCs in lymphoid tissue. To assess the influence of LCs on HIV viral dynamics during anti-retroviral therapy, we present and analyse a stochastic model describing the dynamics of HIV, CD4+ T-cells, and LCs interactions under therapeutic intervention in vivo. We per-form sensitivity analyses on the model to determine which parameters and/or which interaction mechanisms strongly affect infection dynamics.