The mechanism of resistance of tumor cells to chemotherapeutic agents is explored using probabilistic methods where it is assumed that resistant cells arise spontaneously with a defined frequency. The resistance process is embedded in a discrete time Markov branching process which models the growth of the tumor and contains three seperate cell types: stem, transitional and end cells. Using the asymptotic properties of such models it is shown that the proportion of each type of cell converge to constants almost surely. It is shown that the parameters relating to stem cell behaviour determine the asymptotic behaviour of the system. It is argued that for biologically likely parameter values, cure of the tumor will occur if, and only if, all stem cells are eliminated. A model is developed for the acquisition of resistance by stem cells to a single drug. Probability generating functions are derived which describe the behaviour of the process after an arbitrary sequence of drug treatments. The probability of cure, defined as the probability of ultimate extinction of the stem cell compartment, is characterised as the central quantity reflecting the success of therapeutic intervention. Expressions for this function are derived for a number of experimental situations. The effects of variation in the parameter values are examined. The model is extended to the case where two anticancer drugs are available and formulae for the probability of cure are developed. The problem of therapeutic scheduling is examined and under situations where drugs are of "equal" effectiveness, but may not be given together, it is shown that the mean number of tumor cells is minimised by sequential alternation of the drugs. The models are applied to data collected on the L1210 leukemia treated by the drugs Cyclophosphamide and Arabinosylcytosine. In both cases the analysis of the data provide evidence that resistant cells arise spontaneously with a frequency of approximately 10⁻⁷ per division. When applied to human breast cancer, the model indicates that neoadjuvant therapy is unlikely to greatly influence the likelihood that the patient will die from the growth of drug-resistant cells. / Science, Faculty of / Statistics, Department of / Graduate

A research report submitted to the Faculty of Science, in partial fulfilment of the requirements for the degree of Master of Science, University of the Witwatersrand, Johannesburg, 2016. / The study explores the application of statistical methods to determine factors influencing learners to commit offences at school. Focus is on the time taken to commit a second offence and the number of repeat offences committed by learners after the first offence. The survival time from the first offence to a second offence is analysed by using Kaplan-Meier estimate of the survival function, the tests for equality of survivor functions, the Cox proportional hazards model, and the parametric hazards models. The number of repeat offences is analysed by fitting the Poisson regression model and Negative Binomial regression model. As many learners are expected not to offend again, the Zero Inflated Poisson (ZIP) model is also fitted to determine which factors influence learners not to commit a repeat offence. Factors that are related to the school environment were used in the study of learner offence. The categorical variables are learner grade (class), gender, home location, parental involvement, repeating a grade, suspected substance abuse, and hostel residence. The learner performance in the three selected subjects were used as continuous variables. The results of the analysis should also assist the schools in assessing the effectiveness of other forms of punishment since corporal punishment was abolished. / TG2017

No description available.

No description available.

published_or_final_version / Psychiatry / Doctoral / Doctor of Philosophy

Sit, Tony. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 49-51). / Abstracts in English and Chinese. / Acknowledgement --- p.v / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Background --- p.4 / Chapter 2.1 --- Approaches to Risk Measurement --- p.4 / Chapter 2.2 --- Is VaR a “Good´ح Risk Measure? --- p.9 / Chapter 2.3 --- "Efficient Capital Market, Random Walk and Unit Root" --- p.11 / Chapter 3 --- Historical VaR and Limitations --- p.17 / Chapter 3.1 --- Regression Analysis --- p.18 / Chapter 3.2 --- A Possible Artifact --- p.19 / Chapter 4 --- "Parametric VaR with GARCH(1,1)" --- p.27 / Chapter 4.1 --- "GARCH(1,1), a Conditional Heteroscedastic Model" --- p.27 / Chapter 4.2 --- RiskMctrics VaR --- p.29 / Chapter 5 --- VaR with Regression Quantiles --- p.34 / Chapter 5.1 --- Quantilc Regression --- p.35 / Chapter 5.1.1 --- "Quantiles, Ranks and Optimisation" --- p.35 / Chapter 5.2 --- CAViaR --- p.39 / Chapter 5.2.1 --- The model --- p.39 / Chapter 5.2.2 --- Empirical Studies --- p.42 / Chapter 6 --- Conclusion and Future Research --- p.46 / Bibliography --- p.48

published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

Not available / text

published_or_final_version / Statistics / Doctoral / Doctor of Philosophy

This dissertation presents an exploration of the use of nonparametric statistical methods based on ranks for use in financial market research. Applications to event study methodology and the estimation of security systematic risk are analyzed using a simulation methodology with actual daily security return data. The results indicate that procedures based on ranks are more efficient than normal theory procedures currently in common use.