Flexible modeling of left-truncated and interval-censored competing risks data with missing event types

Interval-censored competing risks data arise in many cohort studies in clinical research, where multiple types of events subject to interval censoring are included and the occurrence of the primary event of interest may be censored by the occurrence of other events. The presence of missing event types and left truncation poses challenges to the regression analysis of such data. We propose a new two-stage estimation procedure under a class of semiparametric generalized odds rate transformation models to overcome these challenges. Our method first facilitates the estimation of both the probability of response and the probability of occurrence of each type of event under the missing at random assumption, using either parametric or non-parametric methods. An augmented inverse probability weighting likelihood based on the complete-case likelihood and data from subjects with missing type of event is then maximized for estimating regression parameters. We provide desirable asymptotic properties and construct a concordance index to evaluate the model's discriminative ability. The proposed method is demonstrated through extensive simulations and the analysis of data from the Amsterdam cohort study on HIV infection and AIDS.