3. Electronic Theses and Dissertations (ETDs) - All submissions

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    On some likelihood lnference for the destructive COM-Poison cure rate model with generalised gamma lifetime
    (2018) Majakwara, Jacob
    In this thesis, based on a competing causes scenario, the destructive Conway-Maxwell Poisson (COM-Poisson) cure rate model is studied. The model assumes the occurrence of the event under study to undergo a destructive process of the initial competing causes and only the undamaged portion relating to the initial number of competing causes is recorded. This provides a real and practical way of interpreting the occurrence of the event under study in a biological system. This research assumes the distribution of competing causes to be COM-Poisson which includes some of the commonly used discrete distributions as its particular cases. Furthermore, we propose to model the lifetime by the generalised gamma distribution, which includes some of the commonly used lifetime distributions as its particular cases. The main contribution of this thesis is to develop the expectation maximisation (EM) algorithm to determine the maximum likelihood estimates (MLEs) of the model parameters and to carry out the likelihood inference assuming the data to be right censored. Model discrimination within the COM-Poisson and generalised gamma families are carried out to select a parsimonious distribution for the competing cause and the lifetime that jointly provides an adequate fit to the data. We develop the estimation procedure using both profile likelihood and complete likelihood approaches and make a comparison between the two techniques through the EM algorithm. The performance of the proposed method of inference is demonstrated by carrying out a comprehensive Monte Carlo simulation study. The flexibilities of the COM-Poisson and generalised gamma families are utilised to carry out a two-way model discrimination using the likelihood-and information-based methods. The proposed estimation technique is then applied to a real melanoma data for illustrative purpose. The results show that both the COM-Poisson and generalised gamma distributions provide additional flexibility in modelling survival data with surviving fraction. We have also shown how covariates can influence the cure rate. Most importantly, the model fits the data better when the destructive mechanism is taken into account.
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    Closed left ideal decompositions of G*1
    (2017) Botha, Garith John
    Let G be a countably in nite discrete group and let G be the Stone- Cech compacti cation of G. The group operation of G extends to G making it a compact right shift continuous semigroup. The semigroup G has import applications to Ramsey theory and to topological dynamics. It has long been known that remainder G = GnG can be decomposed into 2c left ideals of G (E. van Dowen 1980-s, D. Davenport and N. Hindman 1991). In 2005 I. Protasov strengthened this theorem by proving that G can be decomposed into 2c closed left ideals of G such that the corresponding quotient space is Hausdor . Let I denote the nest decomposition of G into closed left ideals of G with the property that the corresponding quotient space of G is Hausdor and let I0 denote the nest decomposition of G into closed left ideals of G. If p 2 G is a P-point then ( G)p 2 I. We show that it is consistent with ZFC, the system of usual axioms of set theory, that if G can be algebraically embedded into a compact group, then every I 2 I contains 2c maximal principal left ideals of G, in particular, neither member of I is a principal left ideal of G. We also show that there is a dense subset of points p 2 G such that ( G) p 2 I0 n I, in particular, I0 is ner than I
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    Extensions of the first Borel-Cantelli Lemma in Riesz spaces
    (2018) Mushambi, Nyasha Takunda
    The classical First and Second Borel-Cantelli theorems as well as the Kolmogorov Zero-One Laws have been extended to the abstract setting of Riesz spaces by Wen-Chi Kuo, Coenraad C. A. Labuschagne and Bruce A. Watson. This dissertation aims to extend upon the work of these authors. In particular, an extension of the Barndorff-Nielsen Zero-One Law to the Riesz space setting.
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    Modelling graft survival after kidney transplantation using semi-parametric and parametric survival models
    (2017) Achilonu, Okechinyere Juliet
    This study presents survival modelling and evaluation of risk factors of graft survival in the context of kidney transplant data generated in South Africa. Beyond the Kaplan-Meier estimator, the Cox proportional hazard (PH) model is the standard method used in identifying risk factors of graft survival after kidney transplant. The Cox PH model depends on the proportional hazard assumption, which is rarely met. Assessing and accounting for this assumption is necessary before using this model. When the PH assumption is not valid, modi cation of the Cox PH model could o er more insight into parameter estimates and the e ect of time-varying predictors at di erent time points. This study aims to identify the survival model that will e ectively describe the study data by employing the Cox PH and parametric accelerated failure time (AFT) models. To identify the risk factors that mediate graft survival after kidney transplant, secondary data involving 751 adults that received a single kidney transplant in Charlotte Maxeke Johannesburg Academic Hospital between 1984 and 2004 was analysed. The graft survival of these patients was analysed in three phases (overall, short-term and long-term) based on the follow-up times. The Cox PH and AFT models were employed to determine the signi cant risk factors. The purposeful method of variable selection based on the Cox PH model was used for model building. The performance of each model was assessed using the Cox-Snell residuals and the Akaike Information Criterion. The t of the appropriate model was evaluated using deviance residuals and the delta-beta statistics. In order to further assess how appropriately the best model t the study data for each time period, we simulated a right-censored survival data based on the model parameter-estimates. Overall, the PH assumption was violated in this study. By extending the standard Cox PH model, the resulting models out-performed the standard Cox PH model. The evaluation methods suggest that the Weibull model is the most appropriate in describing the overall graft survival, while the log-normal model is more reasonable in describing short-and long-term graft survival. Generally, the AFT models out-performed the standard Cox regression model in all the analyses. The simulation study resulted in parameter estimates comparable with the estimates from the real data. Factors that signi cantly in uenced graft survival are recipient age, donor type, diabetes, delayed graft function, ethnicity, no surgical complications, and interaction between recipient age and diabetes. Statistical inferences made from the appropriate survival model could impact on clinical practices with regards to kidney transplant in South Africa. Finally, limitations of the study are discussed in the context of further studies.
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    Country risk analysis: an application of logistic regression and neural networks
    (2017) Ncube, Gugulethu
    Country risk evaluation is a crucial exercise when determining the ability of countries to repay their debts. The global environment is volatile and is filled with macro-economic, financial and political factors that may affect a country’s commercial environment, resulting in its inability to service its debt. This re search report compares the ability of conventional neural network models and traditional panel logistic regression models in assessing country risk. The mod els are developed using a set of economic, financial and political risk factors obtained from the World Bank for the years 1996 to 2013 for 214 economies. These variables are used to assess the debt servicing capacity of the economies as this has a direct impact on the return on investments for financial institu tions, investors, policy makers as well as researchers. The models developed may act as early warning systems to reduce exposure to country risk. Keywords: Country risk, Debt rescheduling, Panel logit model, Neural net work models
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