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.
| Published in | International Journal of Data Science and Analysis (Volume 4, Issue 6) |
| DOI | 10.11648/j.ijdsa.20180406.11 |
| Page(s) | 106-111 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2019. Published by Science Publishing Group |
Survivorship Function, Cox-Proportional Hazard, Kernel Smoothing, Bandwidth Selection
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APA Style
Valerie Atieno Odhiambo, George Otieno Orwa, Romanus Odhiambo. (2019). Estimation of the Survivorship Function Using the Cox-Proportional Hazard Model with Relaxed Tsiatis Assumptions. International Journal of Data Science and Analysis, 4(6), 106-111. https://doi.org/10.11648/j.ijdsa.20180406.11
ACS Style
Valerie Atieno Odhiambo; George Otieno Orwa; Romanus Odhiambo. Estimation of the Survivorship Function Using the Cox-Proportional Hazard Model with Relaxed Tsiatis Assumptions. Int. J. Data Sci. Anal. 2019, 4(6), 106-111. doi: 10.11648/j.ijdsa.20180406.11
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Download@article{10.11648/j.ijdsa.20180406.11,
author = {Valerie Atieno Odhiambo and George Otieno Orwa and Romanus Odhiambo},
title = {Estimation of the Survivorship Function Using the Cox-Proportional Hazard Model with Relaxed Tsiatis Assumptions},
journal = {International Journal of Data Science and Analysis},
volume = {4},
number = {6},
pages = {106-111},
doi = {10.11648/j.ijdsa.20180406.11},
url = {https://doi.org/10.11648/j.ijdsa.20180406.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20180406.11},
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.},
year = {2019}
}
TY - JOUR T1 - Estimation of the Survivorship Function Using the Cox-Proportional Hazard Model with Relaxed Tsiatis Assumptions AU - Valerie Atieno Odhiambo AU - George Otieno Orwa AU - Romanus Odhiambo Y1 - 2019/01/25 PY - 2019 N1 - https://doi.org/10.11648/j.ijdsa.20180406.11 DO - 10.11648/j.ijdsa.20180406.11 T2 - International Journal of Data Science and Analysis JF - International Journal of Data Science and Analysis JO - International Journal of Data Science and Analysis SP - 106 EP - 111 PB - Science Publishing Group SN - 2575-1891 UR - https://doi.org/10.11648/j.ijdsa.20180406.11 AB - 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. VL - 4 IS - 6 ER -
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