Estimation for multistate models subject to reporting delays and incomplete event adjudication

Complete observation of event histories is often impossible due to sampling effects such as right-censoring and left-truncation, but also due to reporting delays and incomplete event adjudication. This is for example the case during interim stages of clinical trials and for health insurance claims. In this paper, we develop a parametric method that takes the aforementioned effects into account, treating the latter two as partially exogenous. The method, which takes the form of a two-step M-estimation procedure, is applicable to multistate models in general, including competing risks and recurrent event models. The effect of reporting delays is derived via thinning, extending existing results for Poisson models. To address incomplete event adjudication, we propose an imputed likelihood approach which, compared to existing methods, has the advantage of allowing for dependencies between the event history and adjudication processes as well as allowing for unreported events and multiple event types. We establish consistency and asymptotic normality under standard identifiability, integrability, and smoothness conditions, and we demonstrate the validity of the percentile bootstrap. Finally, a simulation study shows favorable finite sample performance of our method compared to other alternatives, while an application to disability insurance data illustrates its practical potential.