Assessing surrogates as trial endpoints using mixed models

Having a surrogate for a definitive endpoint in a clinical trial can sometimes be useful when it is impractical, invasive or very time consuming to obtain the definitive endpoint. This paper discusses methods for assessing whether the surrogate-endpoint results of a trial can be used in place of definitive-endpoint results. It is important when examining this trial-level surrogacy to include the possibility of trial-level effects and to distinguish whether the treatment arms are naturally ordered, e.g. A vs A+B rather than A vs B. Methods using mixed models of trial-level summaries are discussed and compared to fixed-effects models and to the possibility of using models of individual-level data. We give estimators for definitive-endpoint results of a trial that are predicted from the surrogate-endpoint results of the trial and a set of results from previous trials in which both the definitive and surrogate trial results were available. Graphical displays are also suggested. Two sets of trial results previously analysed for trial-level surrogacy are used as examples.