Conditional and marginal models

 Statistical analyses of related data need to take the relations into account to avoid misleading results. Two main types of statistical models are used, conditional and marginal models (1). A conditional model can be fitted within the framework of generalized linear mixed models (GLMM) and a marginal model using generalized estimating equations (GEE).

Analyses based on conditional and marginal models give answers to different questions. While a conditional model can be used to estimate the outcome within a subject or cluster after conditioning on covariates, a marginal model can estimate the average outcome for the population accounting group-specific effects.

For example, in a longitudinal study comparing patients receiving diet recommendations (treated) with patients receiving exercise recommendations (controls), uncontrolled blood pressure at repeated visits can be modelled using both a conditional and marginal model.

Neither of these two models is automatically more correct than the other. Which of the models is the most useful depends on the estimand.

A conditional model should be chosen if the aim is to estimate treatment effects for a given patient, accounting for the patient's characteristics, a marginal model if the aim is to estimate the expected average outcome of a broadly implemented treatment.

References

1. Muff, S., Held, L. and Keller, L.F. (2016), Marginal or conditional regression models for correlated non-normal data?. Methods Ecol Evol, 7: 1514-1524. https://doi.org/10.1111/2041-210X.12623

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