In the article by L. He and A. M. Kulminski, entitled “Fast Algorithms for Conducting Large-Scale GWAS of Age-at-Onset Traits Using Cox Mixed-Effects Models” (GENETICS 215: 41–58), the authors noted that the pseudo-inverse method for handling the semipositive definite relatedness matrix proposed in this article has some limitations. Although the authors originally pointed out this issue at the end of the Discussion, they now provide a revised solution to the problem. The conclusions of the article remain unaffected.
On p. 46, before the section “Constructions of relatedness matrices for COXMEG,” the following has been added:
The above GPPL ignores penalties with respect to zero eigenvalues in , and thus it can be used when the SPSD matrix originates from biologically meaningless singularities (e.g., singularity originating from calculating a covariance matrix). However, when the singularity is biologically meaningful (e.g., for MZ twins), such zero eigenvalues would strongly penalize the difference between random effects within MZ twins and they should not be ignored. In this case, we propose a modified PPL by replacing all zero eigenvalues in with a small positive number (e.g., 10−6) and keeping the other eigenvalues unchanged, which makes positive definite, and preserves the strong penalties.
On pp. 46–47, the following sentences were deleted, starting from “The raw GRM…” to “…valid for COXMEG.”
On p. 56, the last three sentences of the Discussion were removed, starting from “In addition, we point out that although COXMEG…”.