Simplified hierarchical linear models for the evaluation of surrogate endpoints

The linear mixed-effects model (Verbeke and Molenberghs, 2000) has become a standard tool for the analysis of continuous hierarchical data such as, for example, repeated measures or data from meta-analyses. However, in certain situations the model does pose insurmountable computational problems. Precisely this has been the experience of Buyse et al. (2000a) who proposed an estimation- and prediction-based approach for evaluating surrogate endpoints. Their approach requires fitting linear mixed models to data from several clinical trials. In doing so, these authors built on the earlier, single-trial based, work by Prentice (1989), Freedman et al. (1992), and Buyse and Molenberghs (1998). While Buyse et al. (2000a) claim their approach has a number of advantages over the classical single-trial methods, a solution needs to be found for the computational complexity of the corresponding linear mixed model. In this paper, we propose and study a number of possible simplifications. This is done by means of a simulation study and by applying the various strategies to data from three clinical studies: Pharmacological Therapy for Macular Degeneration Study Group (1977), Ovarian Cancer Meta-analysis Project (1991) and Corfu-A Study Group (1995).