Application of robust estimating equations to the analysis of quantitative longitudinal data

A model fit by general estimating equations (GEE) has been used extensively for the analysis of longitudinal data in medical studies. To some extent, GEE tries to minimize a quadratic form of the residuals, and therefore is not robust in the sense that it, like least squares estimates, is sensitive to heavy-tailed distributions, contaminated distributions and extreme values. This paper describes the family of truncated robust estimating equations and its properties for the analysis of quantitative longitudinal data. Like GEE, the robust estimating equations aim to assess the covariate effects in the generalized linear model in the complete population of observations, but in a manner that is more robust to the influence of aberrant observations. A simulation study has been conducted to compare the finite-sample performance of GEE and the robust estimating equations under a variety of error distributions and data structures. It shows that the parameter estimates based on GEE and the robust estimating equations are approximately unbiased and the type I errors of Wald tests do not tend to be inflated. GEE is slightly more efficient with pure normal data, but the efficiency of GEE declines much more quickly than the robust estimating equations when the data become contaminated or have heavy tails, which makes the robust estimating equations advantageous with non-normal data. Both GEE and the robust estimating equations are applied to a longitudinal analysis of renal function in the Diabetes Control and Complications Trial (DCCT). For this application, GEE seems to be sensitive to the working correlation specification in that different working correlation structures may lead to different conclusions about the effect of intensive diabetes treatment. On the other hand, the robust estimating equations consistently conclude that the treatment effect is highly significant no matter which working correlation structure is used. The DCCT Research Group also demonstrated a significant effect using a mixed-effects longitudinal model.