A goodness of fit test for left-truncated and right-censored data

Survival data in many follow-up studies are often collected using cross-sectional sampling designs. Data of this type are often subject to left-truncation and right-censoring. The product limit estimator is the most commonly used nonparametric estimator for the variable of interest. However, under certain assumptions, it is known to be less efficient than the parametric or semiparametric estimator. A chi-square test is proposed for testing the hypothesis that the truncation distribution follows a parametric family.