Sains Malaysiana 46(3)(2017):
469–476
http://dx.doi.org/10.17576/jsm-2017-4603-15
Aalen's Additive, Cox Proportional Hazards and
The Cox-Aalen Model: Application to Kidney Transplant Data
(Aditif Aalen, Bahaya Berkadaran Cox dan Model
Cox-Aalen: Penggunaan ke atas Data Pemindahan Buah Pinggang)
EMEL BAŞAR*
Department of Statistics, Faculty of
Science, Gazi University 06500 Teknikokullar /Ankara /Turkey
Diserahkan: 18 Mei 2015/Diterima: 20 Jun
2016
ABSTRACT
The Cox proportional hazards model
is most widely used in survival analysis for modeling censored
survival data. In this model, the effect of the covariates is
assumed to act multiplicatively on the baseline hazard rate and
the ratio of the hazards is constant over survival time. This
is an important assumption and sometimes may not hold in some
survival studies. The Cox model can lead to biased results when
the proportionality assumption is not satisfied. In such a situation,
the additive hazards regression models have been an alternative
to proportional hazards models. The Aalen model allows for time-varying
covariate effects. In some situations, some covariate effects
may be constant but the others may not. In such cases, the Cox-Aalen
model is a better alternative since it allows to combine both kinds of covariates in the same model. In
this study the Cox proportional hazards model, Aalen's additive
hazards model and the Cox-Aalen model have been considered. These
models have been applied to kidney transplant data and the differences
in estimates of the unknown parameters obtained by the Aalen's
model, the Cox model and the Cox-Aalen model are investigated.
Keywords: Aalen's additive hazards
model; Cox-Aalen model; Cox proportional hazards model; kidney
transplant data; survival analysis
ABSTRAK
Model bahaya berkadaran Cox paling
meluas digunakan dalam analisis kemandirian untuk pemodelan data tertapis
kemandirian. Dalam model ini, kesan kovariat diandaikan bertindak secara
berdaya darab atas garis dasar kadar bahaya dan nisbah
bahaya adalah malar dari masa kemandirian. Ini adalah suatu
andaian yang penting dan kadang-kala tidak benar dalam beberapa kajian
kemandirian. Model Cox boleh membawa kepada keputusan yang pincang
apabila andaian perkadaran tidak dipenuhi. Dalam keadaan
sedemikian, model regresi bahaya aditif menjadi alternatif kepada model bahaya
berkadaran. Model Aalen membenarkan kesan kovariat masa yang berbeza.
Dalam sesetengah keadaan, beberapa kesan kovariat adalah malar tetapi yang lain
tidak. Dalam situasi tersebut, model Cox-Aalen adalah alternatif yang lebih
baik kerana ia membolehkan penggabungan kedua-dua
jenis kovariat dalam model yang sama. Dalam kajian ini, model bahaya berkadaran
Cox, model bahaya aditif Aalen dan model Cox-Aalen telah diambil kira.
Model-model ini telah digunakan untuk data pemindahan buah pinggang dan
perbezaan dalam anggaran parameter tidak diketahui yang diperoleh pada model
Aalen, model Cox dan model Cox-Aalen telah dikaji.
Kata kunci: Analisis penakatan; data pemindahan buah pinggang;
model bahaya berkadaran Cox; model bahaya aditif Aalen; model Cox-Aalen
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*Pengarang untuk
surat-menyurat; email: ebasar@gazi.edu.tr