Sains Malaysiana 46(12)(2017): 2529–2539

http://dx.doi.org/10.17576/jsm-2017-4612-31

 

Bootstrap Intervals in the Presence of Left-Truncation, Censoring and Covariates with a Parametric Distribution

(Selang Butstrap dalam Kehadiran Pemangkasan Kiri, Penapisan dan Kovariat dengan Taburan Parametrik)

 

THIRUNANTHINI MANOHARAN*, JAYANTHI ARASAN, HABSHAH MIDI & MOHD BAKRI ADAM

 

Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor Darul Ehsan, Malaysia

 

Laboratory of Computational Statistics and Operations Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor Darul Ehsan, Malaysia

 

Diserahkan: 29 Mac 2016/Diterima: 18 April 2017

 

ABSTRACT

Left-truncated and censored survival data are commonly encountered in medical studies. However, traditional inferential methods that heavily rely on normality assumptions often fail when lifetimes of observations in a study are both truncated and censored. Thus, it is important to develop alternative inferential procedures that ease the assumptions of normality and unconventionally relies on the distribution of data in hand. In this research, a three parameter log-normal parametric survival model was extended to incorporate left-truncated and right censored medical data with covariates. Following that, bootstrap inferential procedures using non-parametric and parametric bootstrap samples were applied to the parameters of this model. The performance of the parameter estimates was assessed at various combinations of truncation and censoring levels via a simulation study. The recommended bootstrap intervals were applied to a lung cancer survival data.

 

Keywords: Bootstrap method; covariate; left-truncation; random censoring

 

ABSTRAK

Data terpangkas kiri dan tertapis wujud dalam bidang perubatan dan kaedah inferensi tradisi yang sangat bergantung kepada andaian normal sering kali gagal apabila data tidak lengkap akibat mekanisme terpangkas dan tertapis data. Oleh itu, adalah menjadi keperluan untuk mengkaji kaedah selang keyakinan alternatif yang kurang bergantung dengan andaian lazim semata-mata, sebaliknya bergantung kepada taburan data yang sedia ada. Dalam kajian ini, model mandiran log-lazim dengan kehadiran kovariat dipertimbangkan untuk data perubatan yang terpangkas kiri dan tertapis. Seterusnya, kesesuaian selang keyakinan butstrap yang berasaskan persampelan parametrik dan bukan parametrik diuji untuk setiap parameter yang wujud dalam model mandirian log-lazim menerusi kajian kebarangkalian liputan. Simulasi data jangka hayat dijalankan pada pelbagai kombinasi peratusan data terpangkas dan tertapis. Berikutan hasil kajian tersebut, kaedah selang keyakinan yang dicadangkan telah diuji dengan data pesakit kanser paru-paru.

 

Kata kunci: Kaedah butstrap; kovariat; terpangkas kiri; tertapis rawak

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*Pengarang untuk surat-menyurat; email: mthirunanthini@gmail.com