Sains
Malaysiana 41(4)(2012): 471-480
Interval Estimations for Parameters of
Gompertz Model with Time-Dependent
Covariate and Right Censored Data
(Anggaran
Selang Keyakinan bagi
Parameter Model Gompertz dengan Kovariat yang
Berubah
Mengikut Masa dan Data Tertapis Kanan)
Kaveh
Kiani*
Laboratory
of Computational Statistics and Operations Research
Institute
for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor
D.E.
Malaysia
Jayanthi
Arasan & Habshah Midi
Department
of Mathematics, Faculty of Science, Universiti Putra Malaysia
43400
Serdang, Selangor D.E. Malaysia
Diserahkan:
4 Mac 2010 / Diterima: 7 Oktober 2011
ABSTRACT
There
are numerous parametric models for analyzing survival data such as exponential,
Weibull, log normal and gamma. One of such models is the Gompertz model which
is widely used in biology and demography. Most of these models are extended to
new forms for accommodating different types of censoring mechanisms and different
types of covariates. In this paper the performance of the Gompertz model with
time-dependent covariate in the presence of right censored data was studied.
Moreover, the performance of the model was compared at different censoring
proportions (CP) and sample sizes. Also, the model was compared with fixed
covariate model. In addition, the effect of fitting a fixed covariate model wrongly
to a data with time-dependent covariate was studied. Finally, two confidence
interval estimation techniques, Wald and jackknife, were applied to the parameters
of this model and the performance of the methods was compared.
Keywords:
Gompertz model; jackknife; right censored; time-dependent covariate
ABSTRAK
Terdapat
banyak model parametrik untuk menganalisis data mandirian seperti, eksponen,
Weibull, log-normal dan gamma. Salah satu model tersebut adalah
model Gompertz yang digunakan secara meluas dalam biologi dan
demografik. Sebahagian besar daripada model ini dikembangkan kepada bentuk bentuk
baru untuk menampung pelbagai jenis data tertapis dan kovariat. Dalam makalah
ini kebolehan model Gompertz dengan kovariat yang berubah dengan masa dengan
data tertapis dikaji. Selain itu, prestasi model ini pada kadaran data tertapis
dan saiz sampel yang berbeza dibandingkan. Juga, model ini dibandingkan dengan
model kovariat tetap. Di samping itu, kesan menggunakan model kovariat tetap
untuk data dengan kovariat yang berubah dengan masa dikaji. Akhirnya, dua
kaedah selang keyakinan, Wald dan jackknife diaplikasikan pada parameter model
ini dan prestasinya dibandingkan.
Kata
kunci: Data tertapis kanan; jackknife;
kovariat bergantung masa; model Gompertz
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*Pengarang untuk surat-menyurat; email: kaveh@inspem.upm.edu.my
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