Cross product ratio under different sampling schemes and zero truncated negative binomial weighted Weibull distribution with applications

A successful clinical trial requires efficient strategies for enrolling and retaining the study participants. In fact, Global data research suggests that participant enrollment issues are one of the major problems for the clinical trial termination. This thesis aims to compute the point estimators for the cross-product ratio ρ from two independent Bernoulli samples and determine the best sampling scheme. The idea of using Bernoulli samples to conduct clinical trials has been very successful since it is cost effective. Bias and Mean Squared Errors are used as the principal criteria. According to the simulation results, the special case of Direct-Inverse Binomial sampling scheme works the best, where the number of successes in the Direct sampling scheme is used in the second sampling scheme of the Inverse Binomial scheme. Results of Bias and Mean Squared Errors are compiled in the tables for different levels of samples and probabilities. We focus on the idea of enrolling participants using the special case of the Direct- Inverse sampling scheme. Asymptotic confidence intervals for the cross-product ratio ρ are constructed. Closeness of the confidence coefficient to the nominal confidence level is our main evaluation criterion, and we use the Monte-Carlo method to investigate the key probability characteristics of intervals. We present estimations of the coverage probability and interval width in tables. As a real world practical application of the technique, CYP-GUIDES case study is discussed where the standard and genetically guided therapy are compared to determine whether one therapy is more effective than the other. We compute point estimators for the cross-product ratio under the different sample schemes and determine the confidence interval for the special case of Direct-Inverse sampling scheme. In this thesis, we propose two new discrete distributions, the negative binomialweighted Weibull and the zero truncated negative binomial-weighted Weibull distributions. Some statistical properties of the proposed distributions are presented. The parameter estimates for the proposed distributions have been derived by the maximum likelihood estimation. The applications to real data sets are presented in order to compare the performance with other distributions.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Doctoral -- first

Discipline thesis:degree_discipline

Statistics

Grantor dc:publisher

Faculty of Graduate Studies and Research, University of Regina

Year dc:date.issued

2022

Author dc:creator

• Nadeem, Hira

Advisors dc:contributor.advisor

• Volodin, Andrei
• Ahmed, Syed Ejaz

Committee members dc:contributor.committeemember

• Deng, Dianliang
• Sardali, Arzu

Language dc:language.iso

en

DOI

https://doi.org/10.82465/4381

OAI identifier oai:identifier

oai:uregina.scholaris.ca:10294/16033