Inference and diagnostics for generalized exponential distribution with fixed and time-dependent covariates and interval censored data - Al Hakeem, Hussein Ali Ghaffoori (2022)
The aim of this research is to analyse the Generalized Exponential distribution in the presence of interval-censored data with fixed and time-dependent covariates. The analysis starts with a thorough simulation study to compare the performance of the estimation procedure by evaluating the bias, standard error (SE) and root mean square error (RMSE) of the maximum likelihood estimates (MLE) with and without imputation at various censoring proportions and sample sizes. The results clearly indicate that the estimates, based on the random imputation method, work slightly better than the traditional method when dealing with the interval censored data and fixed covariate. Thereafter, we assessed the goodness of fit for this model by comparing the performances of the Cox-Snell and modified Cox-Snell residuals based on the empirical geometric and harmonic means via simulation study at various censoring proportions and sample sizes. The results indicate that the residuals based on the harmonic mean perform slightly better than other residuals, especially when sample sizes in the data are high. Subsequently, the Generalized Exponential distribution is further extended to incorporate time-dependent covariates with interval-censored data as well as uncensored data. The model is then investigated thoroughly via a comprehensive simulation study at various sample sizes and attendance probabilities when the timedependent covariate has two levels, before and after update time. Following that, comparison using the values of RMSE is made when a fixed covariate model was fitted wrongly to a data set with time-dependent covariate. The results clearly indicate that the estimates, based on the time dependent covariate, work slightly better than the time dependent covariate when dealing with the interval censored data time dependent covariate. Then we studied two methods of constructing confidence interval estimates namely the Wald and jackknife for the parameters of this model with time-dependent covariate and conclusions were drawn based on the results of the coverage probability study. The results indicate that the Wald technique works slightly better than the jackknife technique when dealing with interval censored data and time dependent covariate. Finally, the methods in the simulation study were applied to real interval-censored data from Diabetic Nephropathy (DN) study with fixed and time-dependent covariates. The results indicate that the Generalized Exponential distribution performs well with interval censored data, fixed, and time-dependent covariates while providing a good fit for dataset. The modified Cox-Snell residual using the harmonic mean was also very useful at assessing the model adequacy using fixed covariates. The Wald confidence interval outperformed the jackknife confidence interval estimation technique was applied to the parameters of model and was useful at indicating the significance of both the fixed and time-dependent covariate parameters.