The validation of surrogate endpoints has been studied by Prentice (1989). He presented a definition as well as a set of criteria, which are equivalent only if the surrogate and true endpoints are binary. Freedman et al. (1992) supplemented these criteria with the so-called 'proportion explained'. Buyse and Molenberghs (1998) proposed replacing the proportion explained by two quantities: (1) the relative effect linking the effect of treatment on both endpoints and (2) an individual-level measure of agreement between both endpoints. The latter quantity carries over when data are available on several randomized trials, while the former can be extended to be a trial-level measure of agreement between the effects of treatment of both endpoints. This approach suggests a new method for the validation of surrogate endpoints, and naturally leads to the prediction of the effect of treatment upon the true endpoint, given its observed effect upon the surrogate endpoint. These ideas are illustrated using data from two sets of multicenter trials: one comparing chemotherapy regimens for patients with advanced ovarian cancer, the other comparing interferon-alpha with placebo for patients with age-related macular degeneration.

[1] Self-potential (SP) signals that are generated under two-phase flow conditions could be used to study vadose zone dynamics and to monitor petroleum production. These streaming-potentials may also act as an error source in SP monitoring of vulcanological activity and in magnetotelluric studies. We propose a two-phase flow SP theory that predicts streaming currents as a function of the pore water velocity, the excess of charge in the pore water, and the porosity. The source currents that create the SP signals are given by the divergence of the streaming currents, and contributions are likely to be located at infiltration fronts, at the water table, or at geological boundaries. Our theory was implemented in a hydrogeological modeling code to calculate the SP distribution during primary drainage. Forward and inverse modeling of a well-calibrated 1D drainage experiment suggest that our theory can predict streaming potentials in the vadose zone. Citation: Linde, N.,

Summary. Before a surrogate end point can replace a ®nal (true) end point in the evaluation of an experimental treatment, it must be formally`validated'. The validation will typically require large numbers of observations. It is therefore useful to consider situations in which data are available from several randomized experiments. For two normally distributed end points Buyse and co-workers suggested a new de®nition of validity in terms of the quality of both trial level and individual level associations between the surrogate and true end points. This paper extends this approach to the important case of two failure time end points, using bivariate survival modelling. The method is illustrated by using two actual sets of data from cancer clinical trials.

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