Proportional Hazard Model and Proportional Odds Model under Dependent Truncated Data

Truncation data arise when the interested event time can be observed only if it satisfies a certain condition. Most of the existing approaches analyze this kind of data by assuming the truncated variable is quasi-independent of the interested event time. However, in many situations, the quasi-independence assumption may be not suitable. In this article, the authors consider the copulas to relax the quasi-independence assumption. Additionally, the survival function of the interested event time is estimated by a copula-graphic approach. Then, the authors propose two estimation procedures for the proportional hazard (PH) model and the proportional odds (PO) model, which can be applied to the right-truncated data, and the left-truncated and right-censoring data. Subsequently, the performance of the proposed estimation approaches is assessed via simulation studies. Finally, the proposed methodologies are applied to analyze two real datasets (the retirement center dataset and the transfusion-related AIDS dataset).