Masters Degrees (Statistics)

Permanent URI for this collectionhttps://hdl.handle.net/10413/7127

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Application of survival analysis methods to study under-five child mortality in Uganda.
(2013) Nasejje, Justine.; Achia, Thomas Noel Ochieng.; Mwambi, Henry G.
Infant and child mortality rates are one of the health indicators in a given community or country. It is the fourth millennium development goal that by 2015, all the united nations member countries are expected to have reduced their infant and child mortality rates by two-thirds. Uganda is one of those countries in sub-Saharan Africa with high infant and child mortality rates and therefore has the need to find out the factors strongly associated to these high rates in order to provide alternative or maintain the existing interventions. The Uganda Demographic Health Survey (UDHS) funded by USAID, UNFPA, UNICEF, Irish Aid and the United kingdom government provides a data set which is rich in information. This information has attracted many researchers and some of it can be used to help Uganda monitor her infant and child mortality rates to achieve the fourth millennium goal. Survival analysis techniques and frailty modelling is a well developed statistical tool in analysing time to event data. These methods were adopted in this thesis to examine factors affecting under-five child mortality in Uganda using the UDHS data for 2011 using R and STATA software. Results obtained by fitting the Cox-proportional hazard model and frailty models and drawing inference using both the Frequentists and Bayesian approach showed that, Demographic factors (sex of the household head, sex of the child and number of births in the past one year) are strongly associated with high under-five child mortality rates. Heterogeneity or unobserved covariates were found to be signifcant at household but insignifcant at community level.
Garch modelling of volatility in the Johannesburg Stock Exchange index.
(2013) Mzamane, Tsepang Patrick.; Achia, Thomas Noel Ochieng.; Mwambi, Henry G.
Modelling and forecasting stock market volatility is a critical issue in various fields of finance and economics. Forecasting volatility in stock markets find extensive use in portfolio management, risk management and option pricing. The primary objective of this study was to describe the volatility in the Johannesburg Stock Exchange (JSE) index using univariate and multivariate GARCH models. We used daily log-returns of the JSE index over the period 6 June 1995 to 30 June 2012. In the univariate GARCH modelling, both asymmetric and symmetric GARCH models were employed. We investigated volatility in the market using the simple GARCH, GJR-GARCH, EGARCH and APARCH models assuming di erent distributional assumptions in the error terms. The study indicated that the volatility in the residuals and the leverage effect was present in the JSE index returns. Secondly, we explored the dynamics of the correlation between the JSE index, FTSE-100 and NASDAQ-100 index on the basis of weekly returns over the period 6 June 1995 to 30 June 2012. The DCC-GARCH (1,1) model was employed to study the correlation dynamics. These results suggested that the correlation between the JSE index and the other two indices varied over time.
Multilevel modelling of HIV in Swaziland using frequentist and Bayesian approaches.
(2012) Vilakati, Sifiso E.; Achia, Thomas Noel Ochieng.; Mwambi, Henry G.
Multilevel models account for different levels of aggregation that may be present in the data. Researchers are sometimes faced with the task of analysing data that are collected at different levels such that attributes about individual cases are provided as well as the attributes of groupings of these individual cases. Data with multilevel structure is common in the social sciences and other fields such as epidemiology. Ignoring hierarchies in data (where they exist) can have damaging consequences to subsequent statistical inference. This study applied multilevel models from frequentist and Bayesian perspectives to the Swaziland Demographic and Health Survey (SDHS) data. The first model fitted to the data was a Bayesian generalised linear mixed model (GLMM) using two estimation techniques: the Integrated Laplace Approximation (INLA) and Monte Carlo Markov Chain (MCMC) methods. The study aimed at identifying determinants of HIV in Swaziland and as well as comparing the different statistical models. The outcome variable of interest in this study is HIV status and it is binary, in all the models fitted the logit link was used. The results of the analysis showed that the INLA estimation approach is superior to the MCMC approach in Bayesian GLMMs in terms of computational speed. The INLA approach produced the results within seconds compared to the many minutes taken by the MCMC methods. There were minimal differences observed between the Bayesian multilevel model and the frequentist multilevel model. A notable difference observed between the Bayesian GLMMs and the the multilevel models is that of differing estimates for cluster effects. In the Bayesian GLMM, the estimates for the cluster effects are larger than the ones from the multilevel models. The inclusion of cluster level variables in the multilevel models reduced the unexplained group level variation. In an attempt to identify key drivers of HIV in Swaziland, this study found that age, age at first sex, marital status and the number of sexual partners one had in the last 12 months are associated with HIV serostatus. Weak between cluster variations were found in both men and women.
Multivariate analysis of the BRICS financial markets.
(2013) Ijumba, Claire.; Achia, Thomas Noel Ochieng.; Mwambi, Henry Godwell.
The co-movements and integration of financial markets has been a subject of great concern among many researchers and economists due to an interest in the impacts of stock market integration in terms of international portfolio diversification, asset allocation and asset pricing efficiency. Understanding the interdependence among financial markets is thus of immense importance especially to investors and stakeholders in making viable decisions, managing risks and monitoring portfolio performances. In this thesis, we investigated the levels of interdependence and dynamic linkages among the five emerging economies well known as the BRICS: Brazil, Russia, India, China and South Africa, using a Vector autoregressive (VAR), univariate GARCH(1,1) and multivariate GARCH models. Our data sample consisted of the BRICS weekly returns from the period of January 2000 to December 2012. We used a VAR model to examine the linear dependence among the BRICS markets. The results from the VAR model analysis provided some evidence of unidirectional linear dependencies of the Indian and Chinese markets on the Brazilian stock market. The univariate GARCH(1,1) and multivariate GARCH models were employed to explore the volatility and dynamic correlation in the BRICS stock returns respectively. The results of the univariate GARCH model suggested volatility persistence among all the BRICS stock returns where China appeared to be the most volatile followed by the Russian stock market while the South African market was found to be the least volatile. Results from the multivariate GARCH models revealed similar volatility persistence. Furthermore, we found that, the correlations among the five emerging markets varied with time. From this study, evidence of interdependence among the BRICS cannot be rejected. Moreover, it appears that there are other factors apart from the internal markets themselves that may affect the volatility and correlation among the BRICS.
The role of immune-genetic factors in modelling longitudinally measured HIV bio-markers including the handling of missing data.
(2013) Odhiambo, Nancy.; Achia, Thomas Noel Ochieng.; Mwambi, Henry G.
Since the discovery of AIDS among the gay men in 1981 in the United States of America, it has become a major world pandemic with over 40 million individuals infected world wide. According to the Joint United Nations Programme against HIV/AIDS epidermic updates in 2012, 28.3 million individuals are living with HIV world wide, 23.5 million among them coming from sub-saharan Africa and 4.8 million individuals residing in Asia. The report showed that approximately 1.7 million individuals have died from AIDS related deaths, 34 million ± 50% know their HIV status, a total of 2:5 million individuals are newly infected, 14:8 million individuals are eligible for HIV treatment and only 8 million are on HIV treatment (Joint United Nations Programme on HIV/AIDS and health sector progress towards universal access: progress report, 2011). Numerous studies have been carried out to understand the pathogenesis and the dynamics of this deadly disease (AIDS) but, still its pathogenesis is poorly understood. More understanding of the disease is still needed so as to reduce the rate of its acquisition. Researchers have come up with statistical and mathematical models which help in understanding and predicting the progression of the disease better so as to find ways in which its acquisition can be prevented and controlled. Previous studies on HIV/AIDS have shown that, inter-individual variability plays an important role in susceptibility to HIV-1 infection, its transmission, progression and even response to antiviral therapy. Certain immuno-genetic factors (human leukocyte antigen (HLA), Interleukin-10 (IL-10) and single nucleotide polymorphisms (SNPs)) have been associated with the variability among individuals. In this dissertation we are going to reaffirm previous studies through statistical modelling and analysis that have shown that, immuno-genetic factors could play a role in susceptibility, transmission, progression and even response to antiviral therapy. This will be done using the Sinikithemba study data from the HIV Pathogenesis Programme (HPP) at Nelson Mandela Medical school, University of Kwazulu-Natal consisting of 451 HIV positive and treatment naive individuals to model how the HIV Bio-markers (viral load and CD4 count) are associated with the immuno-genetic factors using linear mixed models. We finalize the dissertation by dealing with drop-out which is a pervasive problem in longitudinal studies, regardless of how well they are designed and executed. We demonstrate the application and performance of multiple imputation (MI) in handling drop-out using a longitudinal count data from the Sinikithemba study with log viral load as the response. Our aim is to investigate the influence of drop-out on the evolution of HIV Bio-markers in a model including selected genetic factors as covariates, assuming the missing mechanism is missing at random (MAR). We later compare the results obtained from the MI method to those obtained from the incomplete dataset. From the results, we can clearly see that there is much difference in the findings obtained from the two analysis. Therefore, there is need to account for drop-out since it can lead to biased results if not accounted for.
Statistical modelling of the relationship between intimate partner violence and HIV infection among women in Zimbabwe.
(2014) Chimatira, Isobella.; Achia, Thomas Noel Ochieng.; Mwambi, Henry Godwell.
Zimbabwean women between the ages of 15-49 years are among the women most affected by HIV and Intimate Partner Violence in the world. The high rates of HIV infection among women have raised an alarm and stimulated research on the problem of violence against women. Intimate Partner Violence (IPV) is a well-known violation of human rights and is a problem in public health. It usually overlaps with the HIV/AIDS epidemic and has been reported to be a determinant of women's risk for HIV. The present study explored relevant statistical methods in modelling the relationship between Intimate Partner Violence (IPV) and HIV in Zimbabwe. The data used in the current research is from a Demographic and Health Survey (DHS) conducted in Zimbabwe for year 2005 - 06. The study aimed at analysing the relationship between IPV and HIV using the following explanatory variables: age; marital status; religion; education; wealth index; region; decision making; media exposure; STI; physical and sexual violence. Principal Component Analysis was used to create indices of IPV, media exposure and decision making among women in the age group 15 - 49. Survey Logistic Regression models accounting for multi-stage survey design was also used to adjust for socio-demographic and socio-economic factors. In order to explore the relationship between IPV and HIV prevalence among women, a generalised linear mixed model was adapted, controlling for socio-demographic variables and treating DHS survey clusters as random effects. Since IPV takes up more than two categories, Multinomial Logit Modelling was used to analyse the relationship of IPV with socio demographic and socio-economic variables. The results from the survey logistic regression modelling were as follows: unadjusted odds ratios (OR) for sexual or physical IPV ranged from 0:91 - 1:09 and 95% confidence intervals (CI) were (0:72; 1:14) for sexual and (0:92; 1:28) for physical violence. The adjusted odds ratios for sexual violence 0:82 [95%CI : 0:63; 1:06] and physical violence 1:12 [95%CI : 0:97; 1:36]. Both survey logistic regression models and generalised linear mixed models found no association between HIV and IPV among women in Zimbabwe. This study provides further evidence that IPV and HIV are not associated. In addition, the analysis revealed that the covariates which were associated with HIV and IPV were age, education, marital status, STI, religion and wealth index. As a result the study recommends that more research is required to find the situations or circumstances under which IPV is associated with HIV prevalence.

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Browsing Masters Degrees (Statistics) by Author "Achia, Thomas Noel Ochieng."