Conditional Generalized Estimating Equations for the Analysis of Clustered and Longitudinal Data

Abstract

A common and important problem in clustered sampling designs is that the effect of within-cluster exposures (i.e., exposures that vary within clusters) on outcome may be confounded by both measured and unmeasured cluster-level factors (i.e., measurements that do not vary within clusters). When some of these are ill/not accounted for, estimation of this effect through population-averaged models or random-effects models may introduce bias. We accommodate this by developing a general theory for the analysis of clustered data, which enables consistent and asymptotically normal estimation of the effects of within-cluster exposures in the presence of cluster-level confounders. Semiparametric efficient estimators are obtained by solving so-called conditional generalized estimating equations. We compare this approach with a popular proposal by Neuhaus and Kalbfleisch (1998, Biometrics 54, 638-645) who separate the exposure effect into a within- and a between-cluster component within a random intercept model. We find that the latter approach yields consistent and efficient estimators when the model is linear, but is less flexible in terms of model specification. Under nonlinear models, this approach may yield inconsistent and inefficient estimators, though with little bias in most practical settings.

Fixed and random effects models: making an informed choice

“…How big a problem is this? Brumback et al (2010Brumback et al ( :1651 found that, in running simulations, "it was difficult to find an example in which the problem is severe" (see also Goetgeluk and Vansteelandt 2008). In a later paper, however, Brumback et al (2013) did identify one such example, but only with properties unlikely to be found in real life data (Allison 2014)-x i and i very highly correlated, and few observations per level-2 entity.…”

Association Between Medication Use and Performance on Higher Education Entrance Tests in Individuals With Attention-Deficit/Hyperactivity Disorder

“…We tested the association between medication use and the test scores using a conditional generalized estimation equation (CGEE), conditioning on the individual patient. 29,30 The analyses were performed with and without the adjustment of time-varying confounders including age and the number of previous tests. Because each individual serves as his or her own control in this design, all the time-invariant confounders were implicitly adjusted for.…”

Within-Subject Mediation Analysis in AB/BA Crossover Designs

“…approach is expected when there are no random slopes [37]. Lastly, the joint modelling approach performs rather well in terms of bias, except for the estimators obtained under the third simulation setting (where assumption (vi) is violated) for the larger sample size, where we find significant bias for all three parameters.…”

“…The question of whether or not the approach of Imai et al [11] yields unbiased estimators for the direct and indirect effects in the presence of unmeasured subject-level confounders in non-linear settings remains to be explored. However, separating within-and between-effects in mixed models with log-or logit-links may yield inconsistent within-subject effects in the presence of unmeasured subject-specific confounders [37]. We conjecture that the mediation package approach in the multilevel setting may require assumptions that are too stringent, even if centred predictors were used.…”

“…Within-effects (effects of the deviations from the subject means) and between-effects (effects of the subject means) can be different and even opposite in [35,36]. This can result from unmeasured upper-level confounding, which is absorbed in the between-subject effect [37]. In view of this, allowing both effects in the outcome equation will not dictate a "forced average" of within-and between-effects, as demanded by the single parameter coefficient when no centring of the mediator is used.…”