Abstracts

 

Msc thesis is here:  https://staff.ksu.edu.sa/sites/default/files/Alhazzani's%20thesis%20u.pdf 

It introduces the discrete gamma distribution and the generalised discrete Lindley distribution.

Abstract of the discrete gamma distribution

A new discrete counterpart of gamma distribution for modelling discrete life data is defined based on similar mathematical form and properties of the continuous version. The main statistical and reliability properties of this distribution are derived and it is shown that this model can deal with both over and under-dispersed data. Geometric variables and finite sum of geometric variables i.e. negative binomial are shown to be special cases of the proposed discrete gamma. Also, the size-biased discrete gamma distribution is derived and discussed. Moreover, different estimation methods of the underlying parameters of this distribution are utilized and comparisons of their performance have been made. Finally, an application in real-life data is to elucidate the earlier results of the paper. 

 

Abstract of case-base-control analysis (Part of my PhD)

Most genetic association studies use controls who have been randomly selected from the population (hereafter bases) rather than controls who have been screened to ensure unaffectedness. This approach is successful when the trait of interest is very rare. However, if the prevalence is high then using the bases as a set of controls will lead to unreliable results as the power is compromised in this case.

In this work, the case-base-control design which allows the three sample types to be used in a single analysis is introduced. The multinomial logistic regression model that predicts genotype conditioning on trait status (case or control) is used. For the bases category, a mixture of cases and controls is formed with mixture weights K (prevalence) and 1-K. Under this design, the score test of association between genotype and phenotype taking into account the bases is derived. Maximum likelihood method for estimation of the underlying parameters using expectation-maximization algorithm is utilized. Following estimation, the Wald's and the likelihood ratio tests are performed. A comparison between the three tests on the basis of their empirical sizes and powers is conducted. Moreover, a comparison between the CBC, case-control and case-base designs has been made. Specifically, the range for which the CBC design would provide more power compared to the CC and CB is identified. Finally, optimal designs in the case of having a very large set of bases are investigated.