Volume 4, Issue 6, December 2018, Page: 106-111
Estimation of the Survivorship Function Using the Cox-Proportional Hazard Model with Relaxed Tsiatis Assumptions
Valerie Atieno Odhiambo, Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
George Otieno Orwa, Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Romanus Odhiambo, Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Received: Oct. 10, 2018;       Accepted: Oct. 22, 2018;       Published: Jan. 25, 2019
DOI: 10.11648/j.ijdsa.20180406.11      View  104      Downloads  20
Abstract
Survival analysis is the primary statistical method of analysing time to event data. The most popular method for estimating the survivor function is the Cox-Proportional Hazard model. It assumes that the effect on the hazard function of a particular factor of interest remains unchanged throughout the observation. This is known as Proportional Hazards. Tsiatis assumed that the underlying hazard function is constant over distinct intervals. In the current study, no shape assumption is imposed other than that the hazard function is a smooth function with an arbitrary choice of a smoother. Such an approach involves the implementation of kernel-smoothing of the initial hazard estimate which have proved in studies to provide a trade-off between bias and variance. The cross-validation and plug-in bandwidth selectors are considered to determine the optimal bandwidth, h to be used as a smoothing parameter. Consequently, the survivorship function is estimated using the Cox-Proportional Hazards model. Proper application of the smoothing procedure is seen to improve the statistical performance of the resulting hazard rate estimator. No constraints are implored on the form of the underlying hazard proving to be less bias than Tsiatis’ method. This implies that the kernel smoothed survivorship function is more appropriate than the common standard techniques in survival analysis as it provides piecewise smooth estimates. Coverage probabilities of the estimate are then obtained which are found to be more accurate and closer to the nominal level compared to those estimated by Tsiatis.
Keywords
Survivorship Function, Cox-Proportional Hazard, Kernel Smoothing, Bandwidth Selection
To cite this article
Valerie Atieno Odhiambo, George Otieno Orwa, Romanus Odhiambo, Estimation of the Survivorship Function Using the Cox-Proportional Hazard Model with Relaxed Tsiatis Assumptions, International Journal of Data Science and Analysis. Vol. 4, No. 6, 2018, pp. 106-111. doi: 10.11648/j.ijdsa.20180406.11
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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