Erratum

Erratum Michael Knapp n and Konstantin Strauch In the May 2004 issue of the Journal, in the article ‘‘Affected-Sib-Pair Test for Linkage Based on Constraints for Identical-by-Descent Distribu- tions Corresponding to Disease Models With Imprinting’’ by Knapp and Strauch [Genet. Epi- demiol. 26:273–285], we proposed an affected-sib- pair linkage test that takes genomic imprinting into account. The null distribution of the statistic of this test is a mixture P 3 k¼0 w k w 2 k of w 2 distributions with 0, 1, 2, and 3 df. The weights depend on Fisher’s information matrix. We provided an exact expression for w 3 , but resorted to a simulation procedure for obtaining approx- imate values of the weights because we thought that ‘‘it seems impossible to obtain exact expres- sions for the remaining weights w 2 , w 1 ,w 0 .’’ This statement, however, is not correct. Let I(v 0 ) denote the Fisher information [cf. Appendix A in Knapp and Strauch, 2004], X ¼ðX 1 ; X 2 ; X 3 Þ Nð0; I 1 ðv 0 ÞÞ, V ¼ðV 1 ; V 2 ; V 3 Þ Nð0; I ðv 0 ÞÞ, r ij denote the correlation between X i and X j , and ~ r ij denote the correlation between V i and V j . Then, formula (3.44) provided by Kudo ˆ [1963] makes it straightforward to show that w 3 ¼ 1 4p ð2p cos 1 r 12 cos 1 r 13 cos 1 r 23 Þ; w 2 ¼ 1 4p ðcos 1 ~ r 12 þ cos 1 ~ r 13 þ cos 1 ~ r 23 Þ; w 1 ¼ 1 2 w 3 ; w 0 ¼ 1 2 w 2 : We implemented this result in our software (http://www.uni-bonn.de/Bumt70e/soft.htm), thereby avoiding time-consuming simulations for the determination of weights and simplifying the analysis. REFERENCES Kudo ˆ A. 1963. A multivariate analogue of the one-sided test. Biometrika 50:403–418. Genetic Epidemiology 28: 288 (2005) n Correspondence to: Michael Knapp, Institute for Medical Biometry, Informatics and Epidemology, University of Bonn, Sigmund-Freud- Str. 25, D-53105 Bonn, Germany. E-mail: [email protected] Received 16 September 2004; Accepted 20 September 2004 Published online 2 December 2004 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/gepi.20053 & 2004 Wiley-Liss, Inc.

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Erratum

Michael Knappn and Konstantin Strauch

In the May 2004 issue of the Journal, in thearticle ‘‘Affected-Sib-Pair Test for Linkage Basedon Constraints for Identical-by-Descent Distribu-tions Corresponding to Disease Models WithImprinting’’ by Knapp and Strauch [Genet. Epi-demiol. 26:273–285], we proposed an affected-sib-pair linkage test that takes genomic imprintinginto account. The null distribution of the statisticof this test is a mixture

P3k¼0 wk � w2k of w2

distributions with 0, 1, 2, and 3 df. The weightsdepend on Fisher’s information matrix. Weprovided an exact expression for w3, but resortedto a simulation procedure for obtaining approx-imate values of the weights because we thoughtthat ‘‘it seems impossible to obtain exact expres-sions for the remaining weights w2, w1, w0.’’ Thisstatement, however, is not correct. Let I(v0)denote the Fisher information [cf. Appendix A inKnapp and Strauch, 2004], X ¼ ðX1;X2;X3Þ �Nð0; I�1ðv0ÞÞ, V ¼ ðV1;V2;V3Þ � Nð0; Iðv0ÞÞ, rij

denote the correlation between Xi and Xj, and~rrij denote the correlation between Vi and Vj. Then,formula (3.44) provided by Kudo [1963] makes itstraightforward to show that

w3 ¼ 14pð2p� cos�1 r12 � cos�1 r13 � cos�1 r23Þ;

w2 ¼ 14pðcos

�1 ~rr12 þ cos�1 ~rr13 þ cos�1 ~rr23Þ;w1 ¼1

2 � w3;

w0 ¼12 � w2:

We implemented this result in our software(http://www.uni-bonn.de/Bumt70e/soft.htm),thereby avoiding time-consuming simulations forthe determination of weights and simplifying theanalysis.

REFERENCES

Kudo A. 1963. A multivariate analogue of the one-sided test.Biometrika 50:403–418.

Genetic Epidemiology 28: 288 (2005)

nCorrespondence to: Michael Knapp, Institute for Medical Biometry, Informatics and Epidemology, University of Bonn, Sigmund-Freud-Str. 25, D-53105 Bonn, Germany. E-mail: [email protected] 16 September 2004; Accepted 20 September 2004Published online 2 December 2004 in Wiley InterScience (www.interscience.wiley.com)DOI: 10.1002/gepi.20053

& 2004 Wiley-Liss, Inc.