Estimating hazard functions in the presence of double truncation in statistical data analysis

The motivation for studying the incompletely observed doubly truncated data arises from its prevalence in various fields such as actuarial science, engineering and astronomy. For example, in medical research the analysis of AIDS data and that of childhood cancer remains two of significant challenge for the worldwide, in these cases, only patients infected during a specific period who subsequently developed the disease are studied. Thus, the age at diagnosis is doubly truncated. In this paper, we’ll provide tow smooth estimators of the cumulative distribution function and that of hazard function under doubly truncated data. Also, we’ll conduct both numerical and theoretical comparisons between our proposed estimators and other existing estimators. A simulation study is carried out to examine the bias and root mean square error of the proposed estimators. Furthermore, an application to a real childhood cancer data set, is presented to demonstrate that our newly estimator fits better than known existing estimators.