### Abstract

Case-control studies compare marker-allele distributions in affected and unaffected individuals, and significant results suggest linkage but may simply reflect population structure. For markers with m alleles (m ≤ 2), a McNemar-like statistic, I, estimates the level of population association between marker and disease loci. To test for linkage after significant case- control tests, within-family tests are performed. These operate on the contingency table, with i, jth element equal to the number of parents that transmit marker allele M(i) and do not transmit marker allele M(j) to an affected offspring. The dimension of the table is the number of alleles at the marker locus. Three test statistics have recently been proposed in the literature: T(c) compares symmetric pairs of cells (i, j) and (j, i), T(m) compares row and column totals for the same marker allele, and a likelihood ratio statistic T(l) uses all the cells in the table. In addition, we consider a new statistic, T(mhet), that uses only the heterozygous parents and is approximately χ^{2} with (m - 1) df. We use a Monte Carlo test to guarantee valid tests and to demonstrate the inferiority of T(c) and the equality of T(m) and T(l) in terms of power. The power of the T(mhet) test is close but not always equal to the power of the T(m) test. We also show that under the alternative hypothesis of linkage, T(m) is approximately noncentral χ^{2} with (m - 1) df and noncentrality parameter 2N(T)(1 - 2θ)^{2}I*, when data on single affecteds in N(T) families are used. If the disease has a low population frequency, then I* is estimated using the case-control statistic I. This offers a basis for choosing sample size, or choosing a marker system.

Original language | English |
---|---|

Pages (from-to) | 691-702 |

Number of pages | 12 |

Journal | American Journal of Human Genetics |

Volume | 60 |

Issue number | 3 |

State | Published - Mar 1 1997 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Genetics

### Cite this

*American Journal of Human Genetics*,

*60*(3), 691-702.

**Power studies for the transmission/disequilibrium tests with multiple alleles.** / Kaplan, N. L.; Martin, Eden R; Weir, B. S.

Research output: Contribution to journal › Article

*American Journal of Human Genetics*, vol. 60, no. 3, pp. 691-702.

}

TY - JOUR

T1 - Power studies for the transmission/disequilibrium tests with multiple alleles

AU - Kaplan, N. L.

AU - Martin, Eden R

AU - Weir, B. S.

PY - 1997/3/1

Y1 - 1997/3/1

N2 - Case-control studies compare marker-allele distributions in affected and unaffected individuals, and significant results suggest linkage but may simply reflect population structure. For markers with m alleles (m ≤ 2), a McNemar-like statistic, I, estimates the level of population association between marker and disease loci. To test for linkage after significant case- control tests, within-family tests are performed. These operate on the contingency table, with i, jth element equal to the number of parents that transmit marker allele M(i) and do not transmit marker allele M(j) to an affected offspring. The dimension of the table is the number of alleles at the marker locus. Three test statistics have recently been proposed in the literature: T(c) compares symmetric pairs of cells (i, j) and (j, i), T(m) compares row and column totals for the same marker allele, and a likelihood ratio statistic T(l) uses all the cells in the table. In addition, we consider a new statistic, T(mhet), that uses only the heterozygous parents and is approximately χ2 with (m - 1) df. We use a Monte Carlo test to guarantee valid tests and to demonstrate the inferiority of T(c) and the equality of T(m) and T(l) in terms of power. The power of the T(mhet) test is close but not always equal to the power of the T(m) test. We also show that under the alternative hypothesis of linkage, T(m) is approximately noncentral χ2 with (m - 1) df and noncentrality parameter 2N(T)(1 - 2θ)2I*, when data on single affecteds in N(T) families are used. If the disease has a low population frequency, then I* is estimated using the case-control statistic I. This offers a basis for choosing sample size, or choosing a marker system.

AB - Case-control studies compare marker-allele distributions in affected and unaffected individuals, and significant results suggest linkage but may simply reflect population structure. For markers with m alleles (m ≤ 2), a McNemar-like statistic, I, estimates the level of population association between marker and disease loci. To test for linkage after significant case- control tests, within-family tests are performed. These operate on the contingency table, with i, jth element equal to the number of parents that transmit marker allele M(i) and do not transmit marker allele M(j) to an affected offspring. The dimension of the table is the number of alleles at the marker locus. Three test statistics have recently been proposed in the literature: T(c) compares symmetric pairs of cells (i, j) and (j, i), T(m) compares row and column totals for the same marker allele, and a likelihood ratio statistic T(l) uses all the cells in the table. In addition, we consider a new statistic, T(mhet), that uses only the heterozygous parents and is approximately χ2 with (m - 1) df. We use a Monte Carlo test to guarantee valid tests and to demonstrate the inferiority of T(c) and the equality of T(m) and T(l) in terms of power. The power of the T(mhet) test is close but not always equal to the power of the T(m) test. We also show that under the alternative hypothesis of linkage, T(m) is approximately noncentral χ2 with (m - 1) df and noncentrality parameter 2N(T)(1 - 2θ)2I*, when data on single affecteds in N(T) families are used. If the disease has a low population frequency, then I* is estimated using the case-control statistic I. This offers a basis for choosing sample size, or choosing a marker system.

UR - http://www.scopus.com/inward/record.url?scp=0031018304&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031018304&partnerID=8YFLogxK

M3 - Article

C2 - 9042930

AN - SCOPUS:0031018304

VL - 60

SP - 691

EP - 702

JO - American Journal of Human Genetics

JF - American Journal of Human Genetics

SN - 0002-9297

IS - 3

ER -