Methods for Observed-Cluster Inference When Cluster Size Is Informative: A Review and Clarifications

Clustered data commonly arise in epidemiology. We assume each cluster member has an outcome Y and covariates X . When there are missing data in Y, the distribution of Y given X in all cluster members (“complete clusters”) may be different from the distribution just in members with observed Y (“observed clusters”). Often the former is of interest, but when data are missing because in a fundamental sense Y does not exist (e.g., quality of life for a person who has died), the latter may be more meaningful (quality of life conditional on being alive). Weighted and doubly weighted generalized estimating equations and shared random‐effects models have been proposed for observed‐cluster inference when cluster size is informative, that is, the distribution of Y given X in observed clusters depends on observed cluster size. We show these methods can be seen as actually giving inference for complete clusters and may not also give observed‐cluster inference. This is true even if observed clusters are complete in themselves rather than being the observed part of larger complete clusters: here methods may describe imaginary complete clusters rather than the observed clusters. We show under which conditions shared random‐effects models proposed for observed‐cluster inference do actually describe members with observed Y. A psoriatic arthritis dataset is used to illustrate the danger of misinterpreting estimates from shared random‐effects models.