A Note On Marginal Linear Regression With Correlated Response Data

Correlated response data often arise in longitudinal and familial studies The marginal regression model and its associated generalized estimating equation GEE method are becoming more and more popular in handling such data Pepe and Anderson pointed out that there is an important yet implicit assumption behind the marginal model and GEE If the assumption is violated and a non diagonal working correlation matrix is used in GEE biased estimates of regression coe cients may result On the other hand if a diagonal correlation matrix is used irrespective of whether the assumption is violated the resulting estimates are nearly unbiased A straightforward interpretation of this phenomenon is lacking in part due to the unavailability of a closed form for the resulting GEE estimates In this note we show how the bias may arise in the context of linear regression where the GEE estimates of regression coe cients are the ordinary or generalized least squares LS estimates Also we explain why the generalized LS estimator may be biased in contrast to the well known result that it is usually unbiased In addition we discuss the bias properties of the sandwich variance estimator of the ordinary LS estimate