Parametric and nonparametric inference for partly interval-censored failure time data

Survival analysis is used in many fields for analysis of data, particularly in medical and biological science. In this context the event of interest is often death, the onset of disease or the disappearance of disease's symptoms. The time to event is called failure time, and this failure time may be observed exactly and recorded or may occurred between two inspection times. Data that include both exact failure data and interval-censored data is called partly interval-censored data. This phenomenon often happens in clinical trials and health studies that are followed by periodic follow-ups. Comparison of survival functions is one of the main objectives in survival studies. Thus, this thesis focuses on the aspect of inferential comparison problem for survival functions in the existence of partly interval-censored failure time data. The research is divided into two parts, parametric and nonparametric inferences. The parametric maximum likelihood estimator, and a score test and likelihood ratio test for this kind of failure time data are constructed under Weibull distributions by using direct approach (without imputation) and indirect approach (with multiple imputation technique). The nonparametric maximum likelihood estimator and the development of nonparametric test approach for comparison of survival function of two samples or more in the existence of partly interval-censored failure time data are constructed where the Turnbull self-consistency equation is modified and then subsequently used in the multiple imputation technique. The behavior of parametric and nonparametric maximum likelihood estimators, and the development of parametric and nonparametric tests approach for comparison of survival function of two samples in the existence of this type of censored data are also studied under the non-proportional hazard by using Piecewise exponential distribution. Simulation studies are carried out to assess the performance of the method and approach that have been developed. The simulation results indicate that the developed tests statistics work well and the good points of a certain method depend on a special situation. A modified secondary data set from breast cancer study has been used to illustrate the proposed tests.

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