Mathematics Ph.D. Dissertations

Title

Simultaneous Inference on Survival Data

Date of Award

2019

Document Type

Dissertation

Degree Name

Doctor of Philosophy (Ph.D.)

Department

Mathematics/Mathematical Statistics

First Advisor

John Chen (Advisor)

Second Advisor

Hanfeng Chen (Committee Member)

Third Advisor

Wei Ning (Committee Member)

Fourth Advisor

Arthur Yeh (Other)

Abstract

Simultaneous inference is a traditional topic in analyzing data. In survival analysis, simultaneous inferences are usually required for comparisons on various treatment levels, on different time periods, and moreover, on both. To solve the aforementioned research goals, this dissertation proposes a methodology of drawing simultaneous conclusion of treatment effects over a time period when confidence band for the treatment effects is available.

This dissertation starts with deriving the specific expressions of confidence bands for the treatment effects on exponential and Weibull populations respectively. After obtaining the confidence bands, a main theorem is provided that simultaneous inference on several treatment levels over a time period can be derived by a stepwise confidence procedure. Additionally, to study the treatment regimes and system reliability, an issue of substitutable confidence intervals is raised. The idea of the proposed methodology can be applied on this issue, and a stepwise confidence procedure is provided as well.

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