Open AccessNadarajah-Haghighi Model for Survival Data With Long Term Survivors in the Presence of Right Censored Data
Author(s) -
Umar Usman,
Shamsuddeen Suleiman,
Bello Magaji Arkilla,
Yakubu Aliyu
Publication year - 2021
Publication title -
pakistan journal of statistics and operation research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.354
H-Index - 15
eISSN - 2220-5810
pISSN - 1816-2711
DOI - 10.18187/pjsor.v17i3.3511
Subject(s) - censoring (clinical trials) , mathematics , covariate , statistics , estimator , quantile , survival analysis , term (time) , bayesian probability , econometrics , quantum mechanics , physics
In this paper, a new long term survival model called Nadarajah-Haghighi model for survival data with long term survivors was proposed. The model is used in fitting data where the population of interest is a mixture of individuals that are susceptible to the event of interest and individuals that are not susceptible to the event of interest. The statistical properties of the proposed model including quantile function, moments, mean and variance were provided. Maximum likelihood estimation procedure was used to estimate the parameters of the model assuming right censoring. Furthermore, Bayesian method of estimation was also employed in estimating the parameters of the model assuming right censoring. Simulations study was performed in order to ascertain the performances of the MLE estimators. Random samples of different sample sizes were generated from the model with some arbitrary values for the parameters for 5%, 1:3% and 1:5% cure fraction values. Bias, standard error and mean square error were used as discrimination criteria. Additionally, we compared the performance of the proposed model with some competing models. The results of the applications indicates that the proposed model is more efficient than the models compared with. Finally, we fitted some models considering type of treatment as a covariate. It was observed that the covariate have effect on the shape parameter of the proposed model.