General Considerations in the Multiple-Trial Setting
The choice of trial-level units
An important issue that arises in the multiple-trial surrogate evaluation setting pertains to the choice of the cluster-level unit of the analysis (Molenberghs et al., 2010). Viable choices are clinical trial, treating physician, country, or hospital (Burzykowski, Molenberghs, and Buyse, 2005; Cortinas et al., 2004).
As a general paradigm, clinical trial is taken as the level of replication (hence the terminology “trial-level surrogacy” and the Rrial notation), but this is not always possible or sensible. For example, it may occur that only a few clinical trials are available (see also Chapter 15). When the number of clustering units is too small, convergence problems tend to occur when mixed- effects models are fitted to the data. The use of a simplified two-stage modeling strategy (see Section 4.3.1) provides no viable alternative in this situation, because Model (4.11) that is fitted in the second stage of the analysis would then be based on only a few data points. This could result in an overestimation of the trial-level surrogacy.
The other extreme situation, where the number of clusters is high and the number of participants per cluster is low, is also not ideal. Indeed, this situation is convenient to explain the between-cluster variability but not the within-cluster variability. The use of a simplified two-stage approach is again not an ideal alternative, because the estimation of the fixed cluster-specific treatment effects for S and T would be based on relatively few observations per cluster, which impacts the precision of these estimates. This problem can be remedied to some extent by using a weighted regression procedure at the second stage of the analysis (see Section 4.3.4), but some other issues still remain. For example, when the number of participants per cluster is low, it may occur that only one type of treatment is administered within certain clusters. The cluster-specific treatment effects cannot be estimated in such clusters, and thus data are lost from the analyses.
In general, the choice for a particular clustering unit will depend on several considerations, such as the information that is available in the dataset, experts’ opinion regarding the most suitable clustering unit, and the number of patients per clustering unit. Importantly, simulation studies have shown that the impact of shifting between (hierarchical) clustering units, e.g., using hospital instead of trial, on the estimated Rrial is small when the magnitude of the variability in the treatment effects at the different levels (trial, hospital) is roughly similar. However, when there are large differences in the magnitude of this variability, the impact of shifting between clustering units on the estimated R?rial can be substantial and thus caution is needed (Cortinas et al., 2004).