Effect of Confounding and Other Misspecification in Models for Longitudinal Data

Abstract

Confounding, measurement error and selection bias are major concerns in observational studies. In a study of sleep disorders motivating our research, it was suspected that one or more of these problems were the cause of inconsistencies between regression coefficients obtained by different methods. We discuss such possibilities by examining the effect of omitted confounding variables on the generalized estimating equation (GEE) approach and on conditional logistic regression. Assuming that a covariate z _ij is unmeasured or otherwise omitted, we specify a structure with normally distributed x _i and z _i that allows their relationship to be different within and between individuals. This may arise, for example, from differences between persons entering the study at different ages or from time trends. The structure may also be interpreted as describing certain types of measurement error and selection bias.

We find that fitting a model which includes $\overline {{x_{i.}}}$ yields the correct mean structure, hence the same limit with any working correlation for GEE. However, fitting a model without $\overline {{x_{i.}}}$, using exchangeable working correlation in certain situations yields different results for different assumed correlations. When the working correlation approaches 1, the coefficient of x _ij approaches the one in the model with $\overline {{x_{i.}}}$ . This latter coefficient, for the logit link, can be converted into the one for conditional logistic regression by a scale change.