Concluding Remarks

The results of the analysis presented in the current chapter suggest that (the logarithm of) PSA at 28 days is very weekly associated with OS in patients with advanced prostate cancer. Also, the association between treatment effects on (the logarithm of) PSA and OS is very weak. Thus, PSA is not a valid surrogate at the individual or at the trial level. Note that, given the small estimated values of R^riatfr), no attempts to estimate the surrogate threshold effects (STE; Section 4.5) were made.

Unsatisfactory performance of PSA as a surrogate for OS in advanced prostate cancer was reported, among others, by Buyse et al. (2003) and Collette et al. (2005).

The analyses presented in the current chapter illustrate problems that one can encounter when trying to evaluate a surrogate when using a limited dataset. In such a situation, the “natural” grouping of patients by trial may not be feasible due to an insufficient number of trials. Considering other grouping, e.g., by countries (as in our example) or centers, may be possible, but raises several issues (Cortinas et al., 2004; Renfro et al., 2014). One of them is related to the smaller sample size of the groups, which, in turn, implies a larger estimation error in the estimated group-specific treatment effects. In such a situation, an analysis adjusted for the estimation error is of special importance. Yet, it is often difficult to conduct, as it requires a considerable between-group variability of the treatment effects for the association between the true random treatment effects to become estimable. The analysis weighted by the sample size offers a solution in this regard. However, its validity may be questioned, as outlined in Section An alternative is to consider the Bayesian approach, proposed by Renfro et al. (2012).

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