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Methods for observed-cluster inference when cluster size is informative: a review and clarifications.

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Seaman, Shaun R 
Pavlou, Menelaos 
Copas, Andrew J 


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.



Bridge distribution, Immortal cohort inference, Informative missingness, Missing not at random, Mortal cohort inference, Semi-continuous data, Arthritis, Psoriatic, Biometry, Cluster Analysis, Epidemiologic Methods, Female, Humans, Male, Models, Statistical

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MRC (unknown)
SRS is funded by MRC grants U1052 60558 and MC_US_A030_0015, AJC and MP by MRC grant G0600657.