A Comparison of Population Average and Random-Effect Models for the Analysis of Longitudinal Count Data with Base-Line Information

Abstract

The generalized estimating equation (GEE) approach to the analysis of longitudinal data has many attractive robustness properties and can provide a`population average' characterization of interest, for example, to clinicians who have to treat patients on the basis of their observed characteristics. However, these methods have limitations which restrict their usefulness in both the social and the medical sciences. This conclusion is based on the premise that the main motivations for longitudinal analysis are insight into microlevel dynamics and improved control for omitted or unmeasured variables. We claim that to address these issues a properly formulated random-effects model is required. In addition to a theoretical assessment of some of the issues, we illustrate this by reanalysing data on polyp counts. In this example, the covariates include a base-line outcome, and the effectiveness of the treatment seems to vary by base-line. We compare the random-effects approach with the GEE approach and conclude that the GEE approach is inappropriate for assessing the treatment effects for these data.

Dynamic modelling in a study of surgical error management

“…Although there may be problems with GEE methodology with endogenous explanatory variables [16], in our example this produces qualitative conclusions very similar to the dynamic conditional logistic regression analysis. Point estimates and robust confidence intervals of regression parameters had comparable magnitude to our conditional maximum-likelihood estimates.…”

“…However, conventional random effects models assume that individual effects are uncorrelated with the explanatory variables. If instead, unobserved individual effects are correlated with the explanatory variables, which would then be termed endogenous, and cluster sizes are small, the random effects estimator is inconsistent [16]. This is a potential problem with the estimation of dynamic models with random effects and is discussed in the econometrics literature.…”

Variance component models for longitudinal count data with baseline information: epilepsy data revisited

“…We would not be able to address whether a significant parameter estimate for the baseline count is due to an effective role of this variable in determining post-randomization counts or, rather, to the dependence between this term and the individual-specific random effects which has been left out of the model. In this latter case, the estimates will be probably biased and the resulting inferences could be wrong, as proved by Crouchley and Davies (1999). This is usually known in the literature as endogeneity bias (see e.g.…”

A finite mixture model for multivariate counts under endogenous selectivity

“…As can be easily noticed, the likelihood is defined integrating with respect to G(u i | y i0 ); if the selection variable is predetermined or, at least, independent of the random effects in the primary outcomes equations, we have that G(u i |y i0 ) = G(u i ). Otherwise, the dependence between the random effects and the selection variable has to be taken explicitly into account; integrating with respect to G(u i ) rather than with respect to G(u i | y i0 ) may produce biased and inconsistent estimates, as remarked by Crouchley and Davies (1999), Fotohui (2005), Alfò and Aitkin (2006). This is usually known in the literature as endogeneity bias, see Davidson and Mackinnon (1993) for a thorough discussion of the topic.…”

“…If the selection mechanism depends on unobservable heterogeneity sources influencing the (primary) counted outcomes, and estimation is based on the model for the primary outcomes only, parameter estimates for the selection variable and for all variables depending on the selection, could be severely biased; Crouchley and Davies (1999) discuss this topic in the biostatistical context. In this case, parameter distinctiveness does not hold and the likelihood can not be factorized; therefore, we need to account for potential dependence of the selection variable on the random effects in the primary outcomes equations.…”