## Statistical Methods For Biomarker Threshold Models in Clinical Trials

 dc.contributor.author Gavanji, Parisa en dc.contributor.department Mathematics and Statistics en dc.contributor.supervisor Jiang, Wenyu en dc.date.accessioned 2017-01-30T17:51:46Z dc.date.available 2017-01-30T17:51:46Z dc.degree.grantor Queen's University at Kingston en dc.description.abstract In clinical trials, the main objective is to investigate the treatment effects on patients. However, many molecularly targeted drugs or treatments tend to benefit a subset of patients more, identified by a certain biomarker. The cut-point value defining patient subsets is often unknown. For this situation, the ordinary likelihood ratio test cannot be applied for testing treatment-biomarker interaction because of the model irregularities. We develop a residual bootstrap method to approximate the distribution of a proposed test statistic to test for treatment-biomarker interaction in survival data. Simulation studies show that the residual bootstrap test works well. The proposed method is applied to BIG 1-98 randomized clinical trial of breast cancer with Ki-67 as biomarker to consider the treatment effects on patients in two subsets. We also extend the residual bootstrap method to clustered survival data with an application to data from the I-SPY 1 clinical trial with the estrogen receptor total score as a biomarker. Another research topic of the thesis is deriving the asymptotic distribution of a penalized likelihood ratio test statistic for testing biomarker effect and treatment-biomarker interaction in binary data. The model can be viewed as a mixture of logistic regression models with unknown cut-point for which the regularity conditions of ordinary likelihood methods are not satisfied. We first approximate the indicator function defining biomarker subgroups by a smooth continuous function. To overcome irregularities, we develop a penalized likelihood method, introducing a new idea of using random penalty term. Proposing a new set of regularity conditions helps us to study the properties and limiting distributions of the maximum penalized likelihood estimates of the parameters. We further prove that the penalized likelihood ratio test statistic has an asymptotic $\chi^{2}_{3}$ distribution under the null hypothesis. Extensive simulation studies show that the proposed test procedure works well for hypothesis testing. The proposed method is applied to a clinical trial of prostate cancer with the serum pro-static acid phosphatase (AP) as a biomarker. en dc.description.degree PhD en dc.identifier.uri http://hdl.handle.net/1974/15345 dc.language.iso eng en dc.relation.ispartofseries Canadian theses en dc.rights Queen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada en dc.rights ProQuest PhD and Master's Theses International Dissemination Agreement en dc.rights Intellectual Property Guidelines at Queen's University en dc.rights Copying and Preserving Your Thesis en dc.rights This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner. en dc.subject Biomarker en dc.subject Statistical methods en dc.subject Threshold en dc.subject clinical trials en dc.title Statistical Methods For Biomarker Threshold Models in Clinical Trials en dc.type thesis en
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