Adjusted predictions for generalized estimating equations

Generalized estimating equations (GEEs) are a popular statistical method for longitudinal data analysis, requiring specification of the first 2 marginal moments of the response along with a working correlation matrix to capture temporal correlations within a cluster. When it comes to prediction at future/new time points using GEEs, a standard approach adopted by practitioners and software is to base it simply on the marginal mean model. In this article, we propose an alternative approach to prediction for independent cluster GEEs. By viewing the GEE as solving an iterative working linear model, we borrow ideas from universal kriging to construct an adjusted predictor that exploits working cross-correlations between the current and new observations within the same cluster. We establish theoretical conditions for the adjusted GEE predictor to outperform the standard GEE predictor. Simulations and an application to longitudinal data on the growth of sitka spruces demonstrate that, even when we misspecify the working correlation structure, adjusted GEE predictors can achieve better performance relative to standard GEE predictors, the so-called "oracle" GEE predictor using all time points, and potentially even cluster-specific predictions from a generalized linear mixed model.