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

Received: 9 May 2012/Accepted: 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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*Corresponding author; email: fangyenyen@hotmail.com