Simplified modeling strategies for surrogate validation with multivariate failure-time data

The linear mixed effects model 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 unavoidable computational problems. In the context of surrogate markers, this problem has appeared when using an estimation and prediction-based approach for the evaluation of surrogate endpoints. Convergence problems can occur mainly due to small between-trial variability or small number of trials. A number of alternative strategies has been proposed and studied for normally distributed data, but not such study has been conducted for other types of endpoints. The idea is to study if such simplified strategies, which always ignore individual level surrogacy, can also be applied when both surrogate and true endpoints are of failure-time types. It is shown via simulations that the 3 simplified strategies produced biased estimates, especially for the cases in which the strength of individual level association is different from the strength of trial level association. For this reason, it is recommended not to use simplified strategies when dealing with failure-time data, in contrast to the case of normally distributed data, for which simplified strategies are recommended. Possible reasons for this discrepancy might be that, in this case, ignoring the individual level association influences estimates of the mean structure parameters, what results in distorted estimates of the trial level association.