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

Received: 18 May 2015/Accepted: 20 June 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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*Corresponding author; email: ebasar@gazi.edu.tr