STATISTICS Correction for “Using distance correlation and SS-ANOVA to assess associations of familial relationships, lifestyle factors, diseases, and mortality,” by Jing Kong, Barbara E. K. Klein, Ronald Klein, Kristine E. Lee, and Grace Wahba, which appeared in issue 50, December 11, 2012, of Proc Natl Acad Sci USA (109:20352–20357; first published November 21, 2012; 10.1073/pnas.1217269109).
The authors note that: “The phrase ‘non-Euclidean pedigree dissimilarity’” on page 20355, right column, first paragraph, line 3, is not correct. As a result of the error, the text from page 20355, right column, line 1 to page 20365, right column, line 7, and Figs 3 and 4 are superfluous and should be omitted.
“The pedigree dissimilarity in the article is in fact Euclidean, a consequence of the fact that the matrix of kinship coefficients {φij} is positive definite, a fact that has been long since known. Thus, there is no reason to invoke the pedigree embedding by regularized kernel estimation (RKE), and the striking similarity between Upper and Lower of Fig. 3, and also between Figs. 2 and 4, is not surprising. In theory, they should be identical. The very minor differences can be explained by the small amount of regularization applied here in the RKE method. The rest of the paper, including results and discussion, is not affected. We thank Daniel Gianola and Gustavo de los Campos for pointing out the mistake.”