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Concluding Remarks

The approach to evaluation of a failure-time surrogate for a failure-time true endpoint, presented in the current chapter, has already been applied multiple times in oncology. Table 5.1 provides details of several applications.

The results of the analysis, presented in the current chapter, suggest that PFS does not seem to be a useful surrogate for OS in advanced gastric cancer, although, given the imprecision of the estimation of Rriai(r), this statement may need to be treated with caution. These findings parallel those in advanced breast cancer (Burzykowski et al., 2008). They are at variance with those in advanced colorectal cancer and advanced ovarian cancer, where PFS seemed a good surrogate for OS (Burzykowski et al., 2001; Buyse et al., 2007). In advanced lung cancer, the value of PFS as a surrogate for OS is questionable (Laporte et al., 2013). It seems difficult to draw general conclusions about the surrogacy of PFS as a surrogate for OS in advanced forms of cancer.

The choice of the copula in model (5.1) requires some attention, as mis- specification of the shape of the association between S and T may lead to bias (Renfro, Shang, and Sargent, 2015). Renfro, Shang, and Sargent (2015) provide some recommendations in that respect. It should be noted that copulas (5.1) treat both endpoints symmetrically. However, if the true endpoint is, e.g., the overall survival time, there is a natural restriction that S < T. Obviously, in that case, the copula model is misspecified and it may lead to, e.g., a biased estimate of the individual-level association. A possible solution to this issue is an accelerated failure-time model that takes into account the ordering of the two endpoints as proposed by Ghosh, Taylor, and Sargent (2012).

 
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