Browsing by Author "Ndlovu, Bonginkosi Duncan."

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Analysis of discrete time competing risks data with missing failure causes and cured subjects.
(2023) Ndlovu, Bonginkosi Duncan.; Zewotir, Temesgen Tenaw.; Melesse, Sileshi Fanta.
This thesis is motivated by the limitations of the existing discrete time competing risks models vis-a-vis the treatment of data that comes with missing failure causes or a sizableproportions of cured subjects. The discrete time models that have been suggested to date (Davis and Lawrance, 1989; Tutz and Schmid, 2016; Ambrogi et al., 2009; Lee et al., 2018) are cause-specific-hazard denominated. Clearly, this fact summarily disqualifies these models from consideration if data comes with missing failure causes. It is also a well documented fact that naive application of the cause-specific-hazards to data that has a sizable proportion of cured subjects may produce downward biased estimates for these quantities. The existing models can be considered within the multiple imputation framework (Rubin, 1987) for handling missing failure causes, but the prospects of scaling them up for handling cured subjects are minimal, if not nil. In this thesis we address these issues concerning the treatment of missing failure causes and cured subjects in discrete time settings. Towards that end, we focus on the mixture model (Larson and Dinse, 1985) and the vertical model (Nicolaie et al., 2010) because these models possess certain properties which dovetail with the objectives of this thesis. The mixture model has been upgraded into a model that can handle cured subjects. Nicolaie et al. (2015) have demonstrated that the vertical model can also handle missing failure causes as is. Nicolaie et al. (2018) have also extended the vertical model to deal with cured subjects. Our strategy in this thesis is to exploit both the mixture model and the vertical model as a launching pad to advance discrete time models for handling data that comes with missing failure causes or cured subjects.
Modelling time to graduation of Durban University of Technology students using event history analysis.
(2015) Ndlovu, Bonginkosi Duncan.; Zewotir, Temesgen Tenaw.
Tertiary institutions experienced a steady growth of students from other races after the repeal of the apartheid laws. This growth picked up pace after the promulgation of the Education White Paper of 1997 whose main thrust was to make the previously exclusive institutions accessible to the wider populace. Disturbingly, however, and contrary to the goals and the spirit of the White Paper, these institutions also experienced higher failure and lower retention rates amongst the previously disadvantaged students. This study seeks to model time to graduation using survival analysis methods. We begin the analysis by assessing the relevance of the available variables to the exercise of modelling time to graduation using descriptive statistics and non-parametric techniques. We compared the Cox regression to its extensions in discrete time, the Discrete Time to Event Approach, with the view to find the best model to explain time to graduation given the available variables. In light of limited availability of relevant data, we evaluated unobserved heterogeneity in both models. We closed the analysis by considering the cure models and mixture competing risks in discrete time. Notwithstanding arguments against suitability of the Cox regression in continuous time for modelling inherently discrete data such as found in our study, we found that Cox's regression over all, provided a reasonably good fit given the available data. We also found that in relation to the Cox proportional hazard model, there was a lesser degree of exibility as certain variable effects were sacrificed to satisfy the proportionality assumption by stratifying on those variables. The advantage of the Discrete Time to Event Approach is that we could assess the effects of all variables in the model and also obtain the estimates of risks to graduation which are true probabilities of graduation with fewer assumptions or conditions to satisfy. We found that the data limitations did not compromise either the box Cox regression model or the Discrete Time to Event Approach. The data also suggested existence of a sizable proportion of subjects that will eventually not graduate based on cure models. We also fractionated subjects censored due to closure of the observation period into those that will eventually graduate and those that will eventually dropout, using discrete mixture competing risks. We found that the mixture competing risks model explained graduation better than the cure model.