Abstract
This research focuses on assessing the goodness of fit for the Gompertz model in the presence of right and interval censored data with covariate. The performance of the maximum likelihood estimates was evaluated via a simulation study at various censoring proportions and sample sizes. The conclusions were drawn based on the results of bias, standard error and root mean square error at different settings. Following that, another simulation study was carried out to compare the performance of the proposed modifications to the Cox-Snell residuals for both censored and uncensored observations at different combinations of sample sizes and censoring levels. The results show that standard error and root mean square error values of the parameter estimates increase with the increase in censoring proportions and decrease in the number of sample size. This indicates that the estimates perform better when sample sizes are larger and censoring proportions are lower. The performance of the proposed modifications of the Cox-Snell residuals showed that they perform slightly better than existing method.
Highlights
Survival analysis consists of statistical procedures used for analysis of data where the outcome variable is time until an event occurs and is often referred to as time to event data
Standard error and root mean square error, we can conclude that poorer performance for the parameter estimates at higher censoring proportions and smaller sample sizes
This indicates that the estimates perform better when sample sizes are larger and censoring proportions are lower
Summary
Survival analysis consists of statistical procedures used for analysis of data where the outcome variable is time until an event occurs and is often referred to as time to event data. We have considered the Gompertz distribution with covariate in the presence of right and interval censored data to study extensively on the performance of this model. Kiani, Arasan, and Midi (2012) deliberated on performance of the Gompertz model with time-dependent covariate in the presence of right censored data and applied two confidence interval estimation techniques known as Wald and Jackknife. Kiani and Arasan (2013) was extended the Gompertz model to incorporate time-dependent covariate in the presence of interval-, right-, left-censored and uncensored data. Abu-Zinadah (2014) implemented the maximum likelihood method of estimation for estimating the parameters and performed the goodness-of-fit tests for testing the three-parameters exponentiated Gompertz distribution based on complete and type II censored sampling. Results from Leung, Elashoff, and Afifi (1997) summarised that various methods used to deal with censored data which includes complete data analysis, the imputation techniques, analysis based on dichotomized data and the likelihood-based approach. Farrington (2000) had applied several diagnostic tools such as CoxSnell, Lagakos (or martingale), deviance, and Schoenfeld residuals for use with proportional hazards models for interval-censored survival data. Sparling, Younes, Lachin, and Bautista (2006) were presented a parametric family of regression models for interval-censored eventtime (survival) data that accommodates both fixed and time-dependent covariates. Prinja, Gupta, and Verma (2010) devised that problem of interval censoring arises when time to event may be known only up to a time interval which the situation occurs in a case where the assessment of monitoring is done at a periodical frequency. Kiani and Arasan (2018) discussed on the survival model with doubly interval censored data and time dependent covariate where the life-time is the elapsed time between two related events which means that the first event and the second event are interval censored. Sakurai and Hattori (2018) developed a modelchecking procedure based on the cumulative martingale residuals for the interval-censored observations
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