Inferential procedures on log-normal model for left-truncated and case-k interval censored data with covariates

The aim of the research is to study the performance of a parametric model in the presence of left-truncation and case-k interval censored data with time-dependent covariates. The log-normal distribution is focused in this study as this model has a wide usage in clinical survival study specifically involving cancer survival research. The log-normal distribution is extended to incorporate left-truncation, case-k interval censored data where left-censored, right-censored and exact lifetimes are observed as special cases among the prevalence and incidence cohorts with covariates. The research begins with the extension of the log-normal to incorporate fixed covariates with left-truncated and right-censored data. The performance of this model is compared at different percentages of left-truncation and right-censoring through a simulation study. A coverage probability study is conducted to compare the performance of asymptotic based confidence intervals with bootstrap intervals. In the next step, the log-normal model is extended to incorporate left-truncated and case-k interval censored data with fixed covariates. The robustness of the extended model is compared with the model based on midpoint imputation using a simulation study. The suitability of asymptotic and bootstrap intervals for the parameters of the extended and midpoint imputed model is determined through a coverage probability study. In the following step, the log-normal distribution is extended to accommodate timedependent covariates in the presence of left-truncation and case-k interval censoring where model based on midpoint imputation is equally considered. A simulation methodology is proposed to study the optimality of these models and suitable inferential procedures are recommended particularly when the complexity of these models increases due to different percentages of of left-truncation, censoring mechanisms with the presence of time-dependent covariates. All the recommended models behaves well particularly at lower percentage of truncation and censoring or shorter width of inspection times where the parametric bootstrap confidence interval method is recommended as the suitable inferential procedure for all the parameters. In the final step, the performance of the local influential diagnostics on detecting potentially influential observations on the parameters of the extended time-dependent log-normal model are equally explored . The local diagnostics based on the curvature values outperformed the global diagnostics on identifying influential observations. The proposed models, inferential and influential diagnostics applied to a lung-cancer data further emphasizes the importance of accounting for left-truncation specifically if the left-truncation times are longer.

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