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A CORRECTION TO TDT STATISTICS FOR MAPPING QUANTITATIVE TRAIT LOCI

A CORRECTION TO TDT STATISTICS FOR MAPPING QUANTITATIVE TRAIT LOCI Ann. Hum. Genet. (1999), 63, 469 469 Printed in Great Britain Letter to the Editor Xiong et al. (1998) proposed a general transmission disequilibrium test (TDT) for quantitative traits. Their TDT for quantitative traits permits more than one child and more than one heterozygous parent per family. This TDT is also appropriate for the situation where the trait and marker loci are at varying degrees of linkage and linkage disequilibrium. Their generalized TDT statistic for a multi-allele marker locus may be more useful in practice. However, there are several mistakes in their mathematical presentation for this generalized TDT statistic for a multi-allele marker locus, and it confuses readers. Here, we present a corrected TDT statistic for a multi-allele marker locus with a clearer presentation. We hope that this new presentation will remove some confusion for readers. Suppose there are m alleles M ;:::;M at the marker locus. Consider the ith allele M and sampled 1 m i parents with genotype M M (j  i and 1 6 j 6 m). Denote the number of heterozygous parents i j who transmitted the allele M to a child by n (j  i and 1 6 j 6 m), the child's trait value of i ij the kth such parent is denoted by Y (1 6 k 6 n , j  i and 1 6 j 6 m). Denote the number of ijk ij heterozygous parents who transmitted the allele M (j i and 1 6 j 6 m) to a child by n (j i j ji and 1 6 j 6 m), the child's trait value of the kth such parent is denoted by Y (1 6 k 6 n , ji jik ji P P m m and 1 6 j 6 m). Let n = n and n = n . De ne i ij i ji j=1;ji j=1;ji m ij XX Y = Y ; i ijk j=1 k=1 ji m ji XX Y = Y ; i jik j=1 k=1 ji 2 3 n n m ij m ji XX XX 6 7 2 2 2 S = (Y Y ) + (Y Y ) : 4 ijk i jik i 5 n + n 2 i i j=1 j=1 k=1 k=1 ji ji The TDT statistic for a multi-allele marker locus is then of the form m 1 (Y Y ) i i TDT = : 1 1 m 2 + S i=1 n n i i references Xiong, M. M., Krushkal, J. & Boerwinkle, E. (1998). TDT statistics for mapping quantitative trait loci. Ann. Hum. Genet. 62, 431{452. J. Wang and J. Cohen Center for Human Nutrition, UT Southwestern Medical Center, 5323 Harry Hines Blvd, Dallas, Texas 75235-9052, USA Tel: 214-648-8734; Fax: 214-648-7150; E-mail: wang@crcdec.swmed.edu This communication has been seen by Dr Xiong and accepted as an appropriate correction to the paper published in 1998 (Ann. Hum. Genet. 62, 431{452). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Human Genetics Wiley

A CORRECTION TO TDT STATISTICS FOR MAPPING QUANTITATIVE TRAIT LOCI

Wang, J.; Cohen, J.
Annals of Human Genetics , Volume 63 (5) – Jan 1, 1999
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References (1)

Publisher
Wiley
Copyright
Copyright © 1999 Wiley Subscription Services
ISSN
0003-4800
eISSN
1469-1809
DOI
10.1046/j.1469-1809.1999.6350469.x
Publisher site
See Article on Publisher Site

Abstract

Ann. Hum. Genet. (1999), 63, 469 469 Printed in Great Britain Letter to the Editor Xiong et al. (1998) proposed a general transmission disequilibrium test (TDT) for quantitative traits. Their TDT for quantitative traits permits more than one child and more than one heterozygous parent per family. This TDT is also appropriate for the situation where the trait and marker loci are at varying degrees of linkage and linkage disequilibrium. Their generalized TDT statistic for a multi-allele marker locus may be more useful in practice. However, there are several mistakes in their mathematical presentation for this generalized TDT statistic for a multi-allele marker locus, and it confuses readers. Here, we present a corrected TDT statistic for a multi-allele marker locus with a clearer presentation. We hope that this new presentation will remove some confusion for readers. Suppose there are m alleles M ;:::;M at the marker locus. Consider the ith allele M and sampled 1 m i parents with genotype M M (j  i and 1 6 j 6 m). Denote the number of heterozygous parents i j who transmitted the allele M to a child by n (j  i and 1 6 j 6 m), the child's trait value of i ij the kth such parent is denoted by Y (1 6 k 6 n , j  i and 1 6 j 6 m). Denote the number of ijk ij heterozygous parents who transmitted the allele M (j i and 1 6 j 6 m) to a child by n (j i j ji and 1 6 j 6 m), the child's trait value of the kth such parent is denoted by Y (1 6 k 6 n , ji jik ji P P m m and 1 6 j 6 m). Let n = n and n = n . De ne i ij i ji j=1;ji j=1;ji m ij XX Y = Y ; i ijk j=1 k=1 ji m ji XX Y = Y ; i jik j=1 k=1 ji 2 3 n n m ij m ji XX XX 6 7 2 2 2 S = (Y Y ) + (Y Y ) : 4 ijk i jik i 5 n + n 2 i i j=1 j=1 k=1 k=1 ji ji The TDT statistic for a multi-allele marker locus is then of the form m 1 (Y Y ) i i TDT = : 1 1 m 2 + S i=1 n n i i references Xiong, M. M., Krushkal, J. & Boerwinkle, E. (1998). TDT statistics for mapping quantitative trait loci. Ann. Hum. Genet. 62, 431{452. J. Wang and J. Cohen Center for Human Nutrition, UT Southwestern Medical Center, 5323 Harry Hines Blvd, Dallas, Texas 75235-9052, USA Tel: 214-648-8734; Fax: 214-648-7150; E-mail: wang@crcdec.swmed.edu This communication has been seen by Dr Xiong and accepted as an appropriate correction to the paper published in 1998 (Ann. Hum. Genet. 62, 431{452).

Journal

Annals of Human Genetics – Wiley

Published: Jan 1, 1999

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