Marginal clustered multistate models for longitudinal progressive processes with informative cluster size

Abstract

Informative cluster size (ICS) is a phenomenon where cluster size is related to the outcome. While multistate models can be applied to characterize the unit‐level transition process for clustered interval‐censored data, there is a research gap addressing ICS within this framework. We propose two extensions of multistate model that account for ICS to make marginal inference: one by incorporating within‐cluster resampling and another by constructing cluster‐weighted score functions. We evaluate the performances of the proposed methods through simulation studies and apply them to the Veterans Affairs Dental Longitudinal Study (VADLS) to understand the effect of risk factors on periodontal disease progression. ICS occurs frequently in dental data, particularly in the study of periodontal disease, as people with fewer teeth due to the disease are more susceptible to disease progression. According to the simulation results, the mean estimates of the parameters obtained from the proposed methods are close to the true values, but methods that ignore ICS can lead to substantial bias. Our proposed methods for clustered multistate model are able to appropriately take ICS into account when making marginal inference of a typical unit from a randomly sampled cluster.