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.
MRC Biostatistics Unit, Cambridge CB2 0SR, UK.
Shaun R
SR
Seaman
Menelaos
M
Pavlou
Andrew J
AJ
Copas
D015535:Arthritis, Psoriatic / Q000453:epidemiology; D001699:Biometry / Q000379:methods*; D016000:Cluster Analysis; D004812:Epidemiologic Methods; D005260:Female; D006801:Humans; D008297:Male; D015233:Models, Statistical
Bridge distribution; Immortal cohort inference; Informative missingness; Missing not at random; Mortal cohort inference; Semi-continuous data