A combined overdispersed and marginalized multilevel model
Summary (1 min read)
Summary
- Overdispersion and correlation are two features often encountered when modeling non-Gaussian dependent data, usually as a function of known covariates.
- Methods that ignore the presence of these phenomena are often in jeopardy of leading to biased assessment of covariate effects.
- The beta-binomial and negative binomial models are well known in dealing with overdispersed data for binary and count data, respectively.
- Similarly, generalized estimating equations (GEE) and the generalized linear mixed models (GLMM) are popular choices when analyzing correlated data.
- A so-called combined model simultaneously acknowledges the presence of dependency and overdispersion by way of two separate sets of random effects.
- A marginally specified logistic-normal model for longitudinal binary data which combines the strength of the marginal and hierarchical models has been previously proposed.
- These two are brought together to produce a marginalized longitudinal model which brings together the comfort of marginally meaningful parameters and the ease of allowing for overdispersion and correlation.
- Apart from model formulation, estimation methods are discussed.
- The proposed model is applied to two clinical studies and compared to the existing approach.
- It turns out that by explicitly allowing for overdispersion random effect, the model significantly improves.
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Citations
66 citations
Cites methods from "A combined overdispersed and margin..."
...Iddi S, Molenberghs G....
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...By combining overdispersion, random effects, and marginalized model methods, Iddi and Molenberghs [8] obtain population-averaged interpretations for discrete outcomes....
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29 citations
Cites background or methods from "A combined overdispersed and margin..."
...Hence, Iddi and Molenberghs [15] merged the concepts of the combined model of Molenberghs et al. [7] and the MMM of Heagerty [13] and proposed a marginalized combined model, so that the resulting estimates have a direct marginal interpretation, together with corresponding inferences....
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...Based on [17] and [15], specifying a logit link for the marginal model and a probit link for the conditional model leads to computational advantages from the probit-normal relationship, with the marginal parameters still having the odds-ratio interpretation....
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...In practice, both overdispersion and correlation can occur simultaneously, which led Molenberghs et al. [7] to formulate a flexible and unified modeling framework, which they termed the combined model, to handle a wide range of hierarchical data, including count, binary, and time-to-events....
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...Hence, the connector functions, as shown in [15], are as follows....
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...Third, zeros in excess to what can be expected based on the commonly used count distributions may be observed. aDepartment of Epidemiology and Biostatistics, Jimma University, Ethiopia bI-BioStat, CenStat, Universiteit Hasselt, B-3590 Diepenbeek, Belgium cI-BioStat, L-BioStat, Katholieke Universiteit Leuven, B-3000 Leuven, Belgium *Correspondence to: Geert Molenberghs, I-BioStat, Universiteit Hasselt, Martelarenlaan 42, 3000 Hasselt, Belgium....
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References
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