Inferential procedures for the generalized exponential model having covariate, with right and interval censored data

In literature, there are various studies that incorporate censoring mechanisms to the generalized exponential model (GEM). This research aims to analyse generalized exponential models in the presence of right and interval-censored data with fixed covariates. The analysis starts with the extension of the GEM to incorporate fixed covariates in the presence of right and interval censored data. Parameters of the models under both censoring were estimated using the maximum likelihood estimation (MLE) method. The performance of these estimates were assessed at various sample sizes (n) and censoring proportion (cp) via the bias, standard error (SE) and root mean square error (RMSE). Next the model was extended to incorporate interval censored data with covariate. The performance of the MLE using the midpoint, right, left, random imputations were compared at various sample sizes and censoring proportions via a simulation study. In addition, three asymptotic confidence interval procedures which included Wald, likelihood ratio, and score confidence intervals procedures were investigated through a coverage probability study when the data were both right and interval censored at various n and cp. Then, five alternative confidence intervals procedures, which included the jackknife, bootstrap-normal, bootstrap-t, bootstrap-p, bias correction acceleration bootstrap procedures were studied via a coverage probability study. This simulation study showed that overall, the Wald asymptotic and bootstrap normal alternative confidence intervals methods are recommended as a suitable inferential to estimate the parameters of the model using different sample sizes, interval length and censoring proportions. In summary, the simulation studies for each category indicate that the bias, standard error, and root mean square error are large when the cp is high, which indicates that the estimators perform better when the sample size is large, and the cp is low. Furthermore, the performance of the asymptotic confidence interval estimate indicates that the Wald confidence interval for the parameter β1 in the generalized exponential model, under both right and interval censoring, represent the most effective approach. In comparison to alternative confidence intervals, the bootstrap normal (b-n) method yields results significantly closer to the nominal error probability for parameters β0 and β1. Finally, to further support the findings of the simulation studies, we employ two real datasets with right and interval-censored data from lung and breast cancer datasets, respectively. The first dataset is an interval censored data from a breast cancer study with age as the covariate. The second dataset consists of right censored lung cancer data with age as the covariate. The results indicated that the GEM was a better fit for both datasets compared to the exponential distribution. The confidence interval estimation techniques were obtained for the covariate parameter of both models. Additionally, the findings of the real data indicate that theWald method for the covariate β1 is significant within the context of the lung cancer data. For the breast censer data with age as the covariate, the bootstrap normal, bootstrap-t, BCa and the jackknife have a similar confidence interval for μ, α, β0 and β1. The results indicate that the generalized exponential model outperforms the submodel based on the exponential distribution.

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