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...
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| Format: | Thesis |
| Language: | English English |
| Published: |
2023
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| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/111572/1/IPM%202023%202%20-%20IR.pdf |
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| Summary: | 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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