Videoconferência (VC): A Flexible Modeling Framework for Overdispersed, Hierarchical Data of a Combined Nature

Geert Molenberghs - Interuniversity Institute for Biostatistics and Statistical Bioinformatics

(1) Hasselt University, Diepenbeek, Belgium

(2) Katholieke Universiteit Leuven, Belgium

Abstract: Non-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson regression. Two of the main reasons for extending this family are (1) the occurrence of overdispersion, meaning that the variability in the data is not adequately described by the models, which often exhibit a prescribed mean-variance link, and (2) the accommodation of hierarchical structure in the data, stemming from clustering in the data which, in turn, may result from repeatedly measuring the outcome, for various members of the same family, etc. The first issue is dealt with through a variety of overdispersion models, such as, for example, the beta-binomial model for grouped binary data and the negative-binomial model for counts. Clustering is often accommodated through the inclusion of random subject-specific effects. Though not always, one conventionally assumes such random effects to be normally  distributed. While both of these phenomena may occur simultaneously, models combining them are uncommon. We propose a broad class of generalized linear models accommodating overdispersion and clustering through two separate sets of random effects. The binary, count, and time-to-event cases are given particular emphasis. A consequence of using this type of models is that one is confronted with non-constant cluster sizes, a feature shared with, for example, group sequential trials; it aggravates when data are incomplete. The implications of this are discussed.

Collaborators: Geert Verbeke (K.U.Leuven, Belgium), Michael G. Kenward (London School of Hygiene and Tropical Medicine, U.K.), Clarice G.B. Demétrio (ESALQ, Piracicaba, SP, Brazil), Edmund Njeru Njagi (UHasselt, Belgium), Elasma Milanzi (UHasselt, Belgium), Ariel Alonso (Univ. Maastricht, the Netherlands).