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Debashis Ghosh, Jeremy M. G. Taylor, Daniel J. Sargent, Rejoinder for “Meta-analysis for Surrogacy: Accelerated Failure Time Models and Semicompeting Risks Modeling”, Biometrics, Volume 68, Issue 1, March 2012, Pages 245–247, https://doi.org/10.1111/j.1541-0420.2011.01638.x
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1. Introduction
We would first like to express our appreciation to coeditor David Zucker and the Associate Editor for organizing this discussion. We also thank the discussants for their comments on our article. They have raised many excellent points, and in our response, we only deal with a subset of them.
Geert Molenberghs (M) and John O'Quigley and Philippe Flandre (OF) accurately describe the methodology in our article as joint regression and association modeling of the surrogate and true endpoints in which a constraint is placed on the type of data that are used (the “wedge” region). As OF noted, this constraint leads to the multistate model of Fix and Neyman (1951). This data structure complicates the standard estimation procedures that were developed by Burzykowski, Molenberghs, and Buyse (2005, Ch. 11). However, much of the model formulation is very similar to what was described there. The constraints in our approach can be viewed as a different model for the error distribution. Our focus is not on predictions, as advocated by Edward Korn (K), partly because it is very hard with censored data to estimate the intercept parameter in a linear model well without making strong assumptions (Ying, Jung, and Wei, 1995). K is suspicious of the standard errors in our semicompeting risks analysis, but our application of the methodology to data from Ghosh (2009) yielded essentially identical answers to those reported there (data not shown). An implication of the artificial censoring strategy we propose here is that we are throwing away information on recurrences. Consequently, the standard errors for the treatment effects on the surrogate endpoint will increase in our approach relative to approaches that do not throw away that information (e.g., the analyses in Table 1 of K's discussion). An implication of the semicompeting risks approach will be that the magnitude of the treatment effect on the surrogate endpoint will be less than or equal to that on the true endpoint because of the wedge contstraint.
