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A Bayesian Approach for Penalized Splines with Hierarchical Penalty

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Open Journal of Statistics 2022年第5期12卷 623-633页

作者： Anne Wanjira Ndung’u samuel musili mwalili Leo Odongo Pan African University Nairobi Kenya Department of Mathematics Statistics and Actuarial Sciences JKUAT University Nairobi Kenya Department of Mathematics and Actuarial Sciences Kenyatta University Nairobi Kenya

Penalized spline has largely been applied in many research studies not limited to disease modeling and epidemiology. However, due to spatial heterogeneity of the data because different smoothing parameter leads to different amount of smoothing in different regions the penalized spline has not been exclusively appropriate to fit the data. The study assessed the properties of penalized spline hierarchical model;the hierarchy penalty improves the fit as well as the accuracy of inference. The simulation demonstrates the potential benefits of using the hierarchical penalty, which is obtained by modelling the global smoothing parameter as another spline. The results showed that mixed model with penalized hierarchical penalty had a better fit than the mixed model without hierarchy this was demonstrated by the rapid convergence of the model posterior parameters and the smallest DIC value of the model. Therefore hierarchical model with fifteen sub-knots provides a better fit of the data.

关键词： Penalized Splines Mixed Model Hierarchical Penalty

A Simulation Study of Hierarchical Bayesian Fusion Spatial Small Area Model for Binary Outcome under Spatial Misalignment

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Open Journal of Statistics 2021年第6期11卷 993-1009页

作者： Kindie Fentahun Muchie Anthony Kibira Wanjoya samuel musili mwalili Institute for Basic Sciences Technology and Innovation Pan African University Nairobi Kenya Department of Epidemiology and Biostatistics School of Public Health College of Medicine and Health Sciences Bahir Dar University Bahir Dar Ethiopia Department of Statistics and Actuarial Sciences Jomo Kenyatta University of Agriculture and Technology Nairobi Kenya

Simulation (stochastic) methods are based on obtaining random samples θ5 from the desired distribution p(θ) and estimating the expectation of any function h(θ). Simulation methods can be used for high-dimensional distributions, and there are general algorithms which work for a wide variety of models. Markov chain Monte Carlo (MCMC) methods have been important in making Bayesian inference practical for generic hierarchical models in small area estimation. Small area estimation is a method for producing reliable estimates for small areas. Model based Bayesian small area estimation methods are becoming popular for their ability to combine information from sever

关键词： Simulation Small Area Estimation Hierarchical Bayesian Spatial Misalign-ment Fusion Process

Mixed-Effects Parametric Proportional Hazard Model with Generalized Log-Logistic Baseline Distribution

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Journal of Data Analysis and Information Processing 2023年第2期11卷 81-102页

作者： Maryrose Wausi Peter samuel musili mwalili Anthony Kibira Wanjoya Abdsalam Hassan Muse Pan African University Institute for Basic Sciences Technology and Innovation (PAUSTI) Nairobi Kenya Jomo kenyatta University of Agriculture and Technology (JKUAT) Nairobi Kenya

Clustered survival data are widely observed in a variety of setting. Most survival models incorporate clustering and grouping of data accounting for between-cluster variability that creates correlation in order to prevent underestimate of the standard errors of the parameter estimators but do not include random effects. In this study, we developed a mixed-effect parametric proportional hazard (MEPPH) model with a generalized log-logistic distribution baseline. The parameters of the model were estimated by the application of the maximum likelihood estimation technique with an iterative optimization procedure (quasi-Newton Raphson). The developed MEPPH model’s performance was evaluated using Monte Carlo simulation. The Leukemia dataset with right-censored data was used to demonstrate the model’s applicability. The results revealed that all covariates, except age in PH models, were significant in all considered distributions. Age and Townsend score were significant when the GLL distribution was used in MEPPH, while sex, age and Townsend score were significant in MEPPH model when other distributions were used. Based on information criteria values, the Generalized Log-Logistic Mixed-Effects Parametric Proportional Hazard model (GLL-MEPPH) outperformed other models.

关键词： Survival Analysis Generalized Log-Logistic Parametric Proportional Hazard Mixed-Effects Monte Carlo Maximum Likelihood Estimation

Forecasting the spread of the COVID-19 pandemic in Kenya using SEIR and ARIMA models

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Infectious Disease Modelling 2022年第2期7卷 179-188页

作者： Joyce Kiarie samuel mwalili Rachel Mbogo Institute of Mathematical Sciences Strathmore UniversityNairobiKenya School of Mathematical and Physical Sciences Jomo Kenyatta University of Agriculture and TechnologyNairobiKenya

COVID-19,a coronavirus disease 2019,is an ongoing pandemic caused by severe acute respiratory syndrome coronavirus 2(SARS-CoV-2).The first case in Kenya was identified on March 13,2020,with the pandemic increasing to about 237,000 confirmed cases and 4,746 deaths by August *** developed an SEIR model forecasting the COVID-19 pandemic in Kenya using an Autoregressive Integrated moving averages(ARIMA)*** average time difference between the peaks of wave 1 to wave 4 was observed to be about 130 *** 4th wave was observed to have had the least number of daily cases at the *** to the forecasts made for the next 60 days,the pandemic is expected to continue for a *** 4th wave peaked on August 26,2021(498th day).By October 26,2021(60th day),the average number of daily infections will be 454 new cases and 40 severe cases,which would require hospitalization,and 16 critically ill cases requiring intensive care unit *** findings of this study are key in developing informed mitigation strategies to ensure that the pandemic is contained and inform the preparedness of policymakers and health care workers.

关键词： ARIMA COVID-19 Infectious disease model Forecasting SEIR Kenya pandemic

Age-structured model for COVID-19: Effectiveness of social distancing and contact reduction in Kenya

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Infectious Disease Modelling 2021年第1期6卷 15-23页

作者： Mark Kimathi samuel mwalili Viona Ojiambo Duncan Kioi Gathungu Department of Mathematics and Statistics Machakos UniversityMachakosKenya Center for Health Analytics and Modeling Strathmore UniversityNairobiKenya School of Mathematical Sciences Jomo Kenyatta University of Agriculture and TechnologyNairobiKenya

Coronavirus disease 2019 is caused by severe acute respiratory syndrome coronavirus *** reported its first case on March 13,2020 and by March 16,2020 she instituted physical distancing strategies to reduce transmission and flatten the epidemic *** age-structured compartmental model was developed to assess the impact of the strategies on COVID-19 severity and *** between different ages are incorporated via contact *** results show that 45%reduction in contacts for 60-days period resulted to 11.5e13%reduction of infections severity and deaths,while for the 190-days period yielded 18.8e22.7%*** peak of infections in the 60-days mitigation was higher and happened about 2 months after the relaxation of mitigation as compared to that of the 190-days mitigation,which happened a month after mitigations were *** numbers of cases in children under 15 years was attributed to high number of asymptomatic *** numbers of cases are reported in the 15e29 years and 30e59 years age *** mitigation periods,considered in the study,resulted to reductions in severe and critical cases,attack rates,hospital and ICU bed demands,as well as deaths,with the 190-days period giving higher reductions.

关键词： Coronavirus Non-pharmaceutical intervention Age structured Contact matrix Mathematical model

Spatio-Temporal Variation of HIV Infection in Kenya

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Open Journal of Statistics 2018年第5期8卷 811-830页

作者： Benard Tonui samuel mwalili Anthony Wanjoya Department of Mathematics & Computer Science University of Kabianga Kericho Kenya Department of Statistics & Actuarial Science Jomo Kenyatta University of Agriculture & Technology Juja Kenya

Disease mapping is the study of the distribution of disease relative risks or rates in space and time, and normally uses generalized linear mixed models (GLMMs) which includes fixed effects and spatial, temporal, and spatio-temporal random effects. Model fitting and statistical inference are commonly accomplished through the empirical Bayes (EB) and fully Bayes (FB) approaches. The EB approach usually relies on the penalized quasi-likelihood (PQL), while the FB approach, which has increasingly become more popular in the recent past, usually uses Markov chain Monte Carlo (McMC) techniques. However, there are many challenges in conventional use of posterior sampling via McMC for inference. This includes the need to evaluate convergence of posterior samples, which often requires extensive simulation and can be very time consuming. Spatio-temporal models used in disease mapping are often very complex and McMC methods may lead to large Monte Carlo errors if the dimension of the data at hand is large. To address these challenges, a new strategy based on integrated nested Laplace approximations (INLA) has recently been recently developed as a promising alternative to the McMC. This technique is now becoming more popular in disease mapping because of its ability to fit fairly complex space-time models much more quickly than the McMC. In this paper, we show how to fit different spatio-temporal models for disease mapping with INLA using the Leroux CAR prior for the spatial component, and we compare it with McMC using Kenya HIV incidence data during the period 2013-2016.

关键词： HIV INLA McMC Leroux CAR Prior Disease Mapping Spatio-Temporal Models

Predicting the Underlying Structure for Phylogenetic Trees Using Neural Networks and Logistic Regression

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Open Journal of Statistics 2020年第2期10卷 239-251页

作者： Hassan W. Kayondo samuel mwalili Pan African University Institute of Basic Sciences Technology and Innovation Nairobi Kenya Department of Statistics and Actuarial Sciences Jomo Kenyatta University of Agriculture and Technology Nairobi Kenya

Understanding an underlying structure for phylogenetic trees is very important as it informs on the methods that should be employed during phylogenetic inference. The methods used under a structured population differ from those needed when a population is not structured. In this paper, we compared two supervised machine learning techniques, that is artificial neural network (ANN) and logistic regression models for prediction of an underlying structure for phylogenetic trees. We carried out parameter tuning for the models to identify optimal models. We then performed 10-fold cross-validation on the optimal models for both logistic regression?and ANN. We also performed a non-supervised technique called clustering to identify the number of clusters that could be identified from simulated phylogenetic trees. The trees were from?both structured?and non-structured populations. Clustering and prediction using classification techniques were?done using tree statistics such as Colless, Sackin and cophenetic indices, among others. Results from 10-fold cross-validation revealed that both logistic regression and ANN models had comparable results, with both models having average accuracy rates of over 0.75. Most of the clustering indices used resulted in 2 or 3 as the optimal number of clusters.

关键词： Artificial Neural Networks Logistic Regression Phylogenetic Tree Tree Statistics Classification Clustering

Stability Analysis of a Deterministic Epidemic Model in Metapopulation Setting

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Advances in Pure Mathematics 2018年第3期8卷 219-231页

作者： Petros Kelkile Desalegn samuel mwalili John Mango Department of Mathematics Pan Africa University Institute of Basic Sciences Technology and Innovation Nairobi Kenya

We present in this article an epidemic model with saturated in metapopulation setting. We develop the mathematical modelling of HIV transmission among adults in Metapopulation setting. We discussed the positivity of the system. We calculated the reproduction number, If ?for , then each infectious individual in Sub-Population j infects on average less than one other person and the disease is likely to die out. Otherwise, if ?for , then each infectious individual in Sub-Population j infects on average more than one other person;the infection could therefore establish itself in the population and become endemic. An epidemic model, where the presence or absence of an epidemic wave is characterized by the value of ?both ideas of the inner equilibrium point of stability properties are discussed.

关键词： Basic Reproduction Ratio Lyapunov Function Meta-Population Disease-Free and the Endemic Equilibrium

Inferring Multi-Type Birth-Death Parameters for a Structured Host Population with Application to HIV Epidemic in Africa

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Computational Molecular Bioscience 2019年第4期9卷 108-131页

作者： Hassan W. Kayondo samuel mwalili John M. Mango Pan African University Institute of Basic Sciences Technology and Innovation Nairobi Kenya Department of Statistics and Actuarial Sciences Jomo Kenyatta University of Agriculture and Technology Nairobi Kenya Department of Mathematics Makerere University Kampala Uganda

Human Immunodeficiency Virus (HIV) dynamics in Africa are purely characterised by sparse sampling of DNA sequences for individuals who are infected. There are some sub-groups that are more at risk than the general population. These sub-groups have higher infectivity rates. We came up with a likelihood inference model of multi-type birth-death process that can be used to make inference for HIV epidemic in an African setting. We employ a likelihood inference that incorporates a probability of removal from infectious pool in the model. We have simulated trees and made parameter inference on the simulated trees as well as investigating whether the model distinguishes between heterogeneous and homogeneous dynamics. The model makes fairly good parameter inference. It distinguishes between heterogeneous and homogeneous dynamics well. Parameter estimation was also performed under sparse sampling scenario. We investigated whether trees obtained from a structured population are more balanced than those from a non-structured host population using tree statistics that measure tree balance and imbalance. Trees from non-structured population were more balanced basing on Colless and Sackin indices.

关键词： HIV Likelihood Inference Multi-Type Birth-Death Process Probability of Removal Structured Population