Sains Malaysiana 42(5)(2013): 673 –683
A Non-parametric Survival Estimate After Elimination
of a Cause of Failure
(Penganggaran Kemandirian Tak-Berparameter Selepas Penghapusan
Punca Risiko)
Fang Yen Yen* & Suraiya Kassim
School
of Mathematical Sciences, Universiti Sains Malaysia
11800
USM, Penang, Malaysia
Diserahkan:
9 Mei 2012/Diterima: 17 September 2012
ABSTRACT
In competing risks analysis, the primary interest of researchers
is the estimation of the net survival probability (NSP) if a cause of
failure could be eliminated from a population. The Kaplan-Meier product-limit
estimator under the assumption that the eliminated risk is non-informative to
the other remaining risks, has been widely used in the estimation of the NSP.
The assumption implies that the hazard of the remaining risks before and after
the elimination are equal and it could be biased. This paper addressed this
possible bias by proposing a non-parametric multistate approach that accounts
for an informative eliminated risk in the estimation procedure, whereby the
hazard probabilities of the remaining risks before and after the elimination of
a risk are not assumed to be equal. When a non-informative eliminated risk was
assumed, it was shown that the proposed multistate estimator reduces to the
Kaplan-Meier estimator. For illustration purposes, the proposed procedure was
implemented on a published dataset and the change in hazard after elimination
of a cause is investigated. Comparing the results to those obtained from using
the Kaplan-Meier method, it was found that in the presence of (both constant
and non-constant) informative eliminated risk, the proposed multistate approach
was more sensitive and flexible.
Keywords: Competing risks; Kaplan-Meier estimator; latent-failure-time
approach; multistate approach; net survival probability
ABSTRAK
Dalam analisis risiko bersaing, minat utama penyelidik ialah
penganggaran kebarangkalian kemandirian bersih (NSP) sekiranya punca
risiko boleh dihapuskan daripada satu populasi. Penganggar had-hasil darab
Kaplan-Meier, dengan andaian bahawa punca risiko yang dihapuskan adalah tidak
bermaklumat kepada punca risiko yang lain, telah digunakan secara meluas dalam
penganggaran NSP.
Andaian ini membawa implikasi bahawa kadaran bahaya baki risiko sebelum dan
selepas penghapusan adalah sama dan ia mungkin tak saksama. Kertas ini
menangani kemungkinan ketaksamaan ini dengan mencadangkan suatu pendekatan
multi-keadaan tak-berparameter yang mengambil kira risiko dihapus yang
bermaklumat dalam prosedur penganggaran, dengan kebarangkalian bahaya bagi
risiko lain sebelum dan selepas penghapusan suatu risiko tidak diandaikan sama.
Apabila risiko dihapus diandaikan tak bermaklumat, ditunjukkan bahawa
penganggar multi-keadaan yang dicadangkan menurun kepada penganggar
Kaplan-Meier. Bagi tujuan illustrasi, prosedur yang dicadangkan dilaksanakan
pada satu set data yang telah diterbitkan dan perubahan kadar bahaya selepas
penghapusan suatu risiko disiasat. Membandingkan keputusan yang diperoleh
dengan keputusan daripada kaedah Kaplan-Meier, didapati bahawa dengan kehadiran
risiko dihapus yang bermaklumat (malar dan bukan malar), pendekatan
multi-keadaan yang dicadangkan adalah lebih peka dan lebih lentur.
Kata kunci: Kebarangkalian kemandirian bersih; pendekatan
masa-risiko-terpendam; pendekatan multi-keadaan; penganggar Kaplan-Meier;
risiko bersaing
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*Pengarang
untuk surat-menyurat; email: fangyenyen@hotmail.com