Cuddy, Rich
(2019)
Restricted confidence intervals for ordered binary and survival data.
Master's Thesis, University of Pittsburgh.
(Unpublished)
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Abstract
This paper considers restricted confidence intervals for binary and survival data with simple ordering. An example in a cancer clinical trial is that we expect patients with a lower stage of cancer to have higher progression free or overall survival rates at all times than those with a higher stage. This type of information is often neglected by Public Health investigators, while appropriately incorporating this information may significantly improve the efficiency in the estimators of interest. When data are normally distributed, a method has been proposed to construct restricted confidence intervals. The process is done by first identifying intermediate variables between two observations, optimizing based on the new parameter space, and then modifying the confidence interval upper and lower bounds using confidence interval limits for the intermediate random variables. In this paper, we explore and extend this method to binary data and survival data. Simulation study shows that the proposed restricted confidence intervals preserve the coverage rate well by closing to the nominal level, even when the sample size is small. The reduction of confidence interval lengths is significant when the underlying true parameters are close to each other, particularly for those with smaller sample sizes.
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Details
| Item Type: |
University of Pittsburgh ETD
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| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
| Title | Member | Email Address | Pitt Username | ORCID |
|---|
| Committee Chair | Park, Yongseok | | | | | Committee Member | Kang, Chaeryon | | | | | Committee Member | T.A. Marques Jr, Ernesto | | | |
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| Date: |
26 September 2019 |
| Date Type: |
Publication |
| Defense Date: |
29 July 2019 |
| Approval Date: |
26 September 2019 |
| Submission Date: |
23 July 2019 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
21 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
School of Public Health > Biostatistics |
| Degree: |
MS - Master of Science |
| Thesis Type: |
Master's Thesis |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Binomial distribution, Kaplan-Meier Estimator, Ordered Statistics, Restricted Confidence Interval |
| Date Deposited: |
26 Sep 2019 16:53 |
| Last Modified: |
27 Sep 2019 18:11 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/37363 |
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