Concluding Remarks

The results of the analysis, presented in the current chapter, suggest that tumor response is substantially associated with OS in patients with advanced colorectal cancer. The survival odds ratio, estimated by using the Plackett copula, is equal to 6.5 and 4.9 for the four-category and binary response, respectively. Thus, tumor response could be regarded as a valid surrogate at the individual level. However, it is not a valid surrogate at the trial level: for the four-category response, the estimated values of R(

were around


0.15, while for the binary response, they were oscillating around 0.40. The estimated confidence intervals were relatively wide, but were excluding values larger than 0.75. Note that, given the small estimated values of R2rial(r), no attempts to estimate the surrogate threshold effects (STE; Section 4.5) were made.

Unsatisfactory performance of tumor response as a surrogate for OS in advanced colorectal cancer was reported by Burzykowski, Molenberghs, and Buyse (2004) and Buyse et al. (2000). A similar conclusion was made by Burzykowski et al. (2008) regarding the validity of binary tumor response as a surrogate for OS in metastatic breast cancer.

The analyses presented in the current chapter illustrate problems that one can encounter when trying to properly adjust the analysis for the presence of the estimation error in the observed trial-specific treatment effects. The analysis weighted by the sample size offers a solution in this regard. However, its validity may be questioned, as outlined in Section Another alternative is to consider the Bayesian approach for the “adjusted” analysis, proposed by Renfro et al. (2012).

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