A model for repeated clustered data with informative cluster sizes

Many chronic diseases or health conditions manifest with recurring episodes, each of which can be characterized by a measure of intensity or severity. Both the number of episodes and the severity of each episode can depend on the latent severity of an individual's underlying condition. Data such as this are commonly gathered repeatedly at fixed follow-up intervals. An example is a study of the association between stressful life events and the onset of depression. Stress exposure is assessed through the frequency and intensity of stressful life events occurring each month. Both the number of events and the intensity of each event at each measurement occasion are informative about the underlying severity of stress over time. One might hypothesize that people that approach the onset of a depressive episode have worse stress profiles than the controls, reflected by both more frequent and more intense stressors. We propose models to analyze data collected repeatedly on both the frequency of an event and its severity when both of these are informative about the underlying latent severity. Maximum likelihood estimators are developed, and simulations with small to moderate sample sizes show that the estimators also have good finite sample properties, and they are robust against misspecification of the model. This method is applied to a psychiatric data set.