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Marginal analysis using the generalized estimating equation approach is widely applied to correlated observations, as occur in studies with clusters and in longitudinal follow-up of individuals. In this article, we investigate the effect of confounding in such models. We assume that a risk factor x and a confounder z are related by a generalized linear model to the outcome y, which can be binary or ordinal. In order to investigate confounding arising from the omission of z, a joint structure for x and z must be specified. Modeling normally distributed (x,z) as sums of between- and within-individual (or cluster) components allows us to incorporate different degrees of between- and within-individual correlation. Such a structure includes, as special cases, cohort and period effects in longitudinal settings and random intercept models. The latter situation corresponds to allowing z to vary only on the between-individual (or cluster) level and to be uncorrelated with x, and leads to attenuation of the coefficient of x in marginal models with the logit and probit links. More complex situations occur when z is allowed to also vary on the within-individual (or cluster) level and when z is correlated with x. We examine the model specification and the expected bias when fitting a marginal model in the presence of the omitted confounder z. We derive general formulas and interpret the parameters and results in an ongoing cohort study. Testing for omitted covariates is also discussed.

AIM: To investigate the association of electrocardiographic (ECG) left and/or right ventricular hypertrophy (LVH and RVH) with physical fitness of military males.METHODS: We used a military cohort of 2587 males, who were on average 29.1 years of age, from the cardiorespiratory fitness and hospitalization events in armed forces (CHIEF) study in Taiwan for the analysis. Isolated ECG-LVH (n = 779) was diagnosed by either the Sokolow-Lyon or Cornell voltage criteria. Isolated ECG-RVH (n = 234) was defined by either the Sokolow-Lyon or Myers et al. voltage criteria. Combined ECG-LVH/RVH (n = 140) was defined as those who met the voltage criteria for both LVH and RVH. The other ECGs were defined as unaffected (n = 1434). Physical fitness was evaluated by the upper and lower 16% exercise performance (beyond 1-standard deviation) in 3000-meter run, 2-minute sit-ups, and 2-minute push-ups. All procedures were standardized and monitored by unified computerized scoring systems. A multiple logistic regression was used to determine the relationship.RESULTS: Compared with unaffected participants, those with an isolated ECG-LVH were tended to have a better 3000meter run performance (odds ratio (OR) and 95% confidence intervals: 1.22 [0.99-1.50], p-value = 0.064) after adjusting for age, service specialty, body mass index, mean blood pressure, smoking status, alcohol intake, hemoglobin level, and exercise frequency. By contrast, those with an isolated ECG-RVH were tended to have a worse 2-minute sit-up performance (OR: 1.46 [0.99-2.16], p-value = 0.054).CONCLUSION: Military males with ECG-LVH and/or ECG-RVH compared to unaffected participants may have diverse exercise performances. However, these observations narrowly failed to reach statistical significance.

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