SEMIPARAMETRIC LIKELIHOOD RATIO-BASED INFERENCES FOR TRUNCATED DATA

In astronomic, demographic, epidemiologic, and other studies, the vari able of interest, say the survival time, is often truncated by an asso ciated variable. In many situations, the distribution of the truncatio n variable can be described by a parametric form. Unlike in the standa rd right-censorship model in which the censoring distribution is nonin formative, knowledge of the truncation distribution can be used to imp rove estimation of the survival distribution. This article derives lik elihood ratio-based confidence intervals for survival probabilities an d for the truncation proportion under the two models in which the trun cation distribution is assumed either to be known or to belong to a pa rametric family. Our proposed methods enable one to incorporate both t he information contained in the data and the available information on the truncation distribution and thus are expected to have better perfo rmance than fully nonparametric methods. Our approach also has applica tions to some biased sampling problems. A simulation study is done to assess the small-sample performance of the proposed methods and to com pare it with some existing nonparametric methods. An illustration is a lso given using a transfusion-related acquired immune deficiency syndr ome (AIDS) data.