# A combined overdispersed and marginalized multilevel model

TL;DR: It turns out that by explicitly allowing for overdispersion random effect, the model significantly improves and is applied to two clinical studies and compared to the existing approach.

Abstract: 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

## 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

53 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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28 citations

26 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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