Abstract
The semi-competing risks data model is a special type of disease-state model that focuses on studying the association between an intermediate event and a terminal event and proves to be a useful tool in modeling disease progression. The study of the semi-competing risk data model not only allows us to evaluate whether a disease episode is related to death but also provides a toolkit to predict death, given that the episode occurred at a certain time. However, the computation of the semi-competing risk models is a numerically challenging task. The Gamma-Frailty conditional Markov model has been shown to be an efficient computation model for studying semi-competing risks data. Building on recent advances in studying semi-competing risks data, this work proposes a non-parametric pseudo-likelihood method equipped with an EM-like algorithm to study semi-competing risks data with event misascertainment under the restricted Gamma-Frailty conditional Markov model. A thorough simulation study is conducted to demonstrate the inference validity of the proposed method and its numerical stability. The proposed method is applied to a large HIV cohort study, EA-IeDEA, that has a severe death under-reporting issue to assess the degree of adverse impact of the interruption of ART care on HIV mortality.