"In this work, a saddlepoint-based method is developed for generating small sample confidence bands for the population survival function from the Kaplan-Meier (KM), the product limit (PL), and Abdushukurov-Cheng-Lin (ACL) survival function estimators, under the proportional hazards model. In the process the exact distribution of these estimators is derived and developed mid-population tolerance bands for said estimators. The proposed saddlepoint method depends upon the Mellin transform of the zero-truncated survival estimator which is derived for the KM, PL, and ACL estimators. These transforms are inverted via saddlepoint approximations to yield highly accurate approximations to the cumulative distribution functions of the respective cumulative hazard function estimators and these distribution functions are then inverted to produce saddlepoint confidence bands. The saddlepoint confidence bands for the KM, PL and ACL estimators is compared with those obtained from competing large sample methods as well as those obtained from the exact distribution. In the simulation studies it is found that the saddlepoint confidence bands are very close to the confidence bands derived from the exact distribution, while being much easier to compute, and outperform the competing large sample methods in terms of coverage probability"--Abstract, page iii.
Samranayake, V. A.
Wen, Xuerong Meggie
Olbricht, Gayla R.
Mathematics and Statistics
Ph. D. in Mathematics
Missouri University of Science and Technology
x, 77 pages
© 2016 Emad Mohamed Abdurasul, All rights reserved.
Dissertation - Open Access
Electronic OCLC #
Abdurasul, Emad Mohamed, "Small sample confidence bands for the survival functions under proportional hazards model" (2016). Doctoral Dissertations. 2640.