Regression analysis of clustered interval-censored data with informative cluster size.

Interval-censored data are commonly found in studies of diseases that progress without symptoms, which require clinical evaluation for detection. Several techniques have been suggested with independent assumption. However, the assumption will not be valid if observations come from clusters. Furthermore, when the cluster size relates to response variables, commonly used methods can bring biased results. For example, in a study on lymphatic filariasis, a parasitic disease where worms make several nests in the infected person's lymphatic vessels and reside until adulthood, the response variable of interest is the nest-extinction times. As the extinction times of nests are checked by repeated ultrasound examinations, exact extinction times are not observed. Instead, data are composed of two examination points: the last examination time with living worms and the first examination time with dead worms. Furthermore, as Williamson et al. (Statistics in Medicine 2008; 27:543-555) pointed out, larger nests show a tendency for low clearance rates. This association has been denoted as an informative cluster size. To analyze the relationship between the numbers of nests and interval-censored nest-extinction times, this study proposes a joint model for the relationship between cluster size and clustered interval-censored failure data. A proportional hazard model with random effect and a mixed ordinal regression model are applied to failure times and cluster size, respectively. The joint model approach addresses both the association among failure times from the same cluster and the dependency of failure times on cluster size. Simulation studies are performed to assess the finite sample properties of the estimators and lymphatic filariasis data are analyzed as an illustration.