1022-7954/03/3908- $25.00 © 2003
Russian Journal of Genetics, Vol. 39, No. 8, 2003, pp. 948–954. Translated from Genetika, Vol. 39, No. 8, 2003, pp. 1128–1135.
Original Russian Text Copyright © 2003 by Zorkoltseva, Axenovich.
Mapping of the genes for widespread human dis-
eases is one of the main tasks of genetics. Among the
methods of gene localization, the approach based on
studying allelic associations and linkage disequilibrium
is becoming increasingly more popular [1–4]. When
applied to simple Mendelian characters, association
analysis is successfully used for a more precise local-
ization of genes discovered with the use of linkage
analysis, because association-based mapping has con-
siderably higher resolution [1, 5–7]. The region of gene
location estimated using this approach varies from sev-
eral to about a hundred kilobases, which approximately
corresponds to 0.0001 cM on a genetic map. This
approach was used for mapping some Mendelian dis-
eases, e.g., cystic ﬁbrosis, Huntington’s disease, and
Wilson’s disease . In addition, this approach was
successfully used for the localization of the genes of
some complex diseases. One example is early-onset
Alzheimer’s disease, for which the major gene effect
has been demonstrated . Analysis of population
associations was decisive for studying the HLA com-
plex and demonstrated its involvement in the etiology of
more 100 diseases related to immune imbalance [10, 11].
These are type I diabetes [12–14], rheumatoid arthritis
, multiple sclerosis, and tolerance to some infec-
tions (e.g., malaria, tuberculosis, and AIDS) .
Many researchers believe that analysis of associa-
tions is the most effective strategy for mapping genes of
complex diseases [2, 16–19].
Although many laboratories are involved in map-
ping and identiﬁcation of human genes, the progress in
this ﬁeld is slower than could be expected. One possible
reason is the so-called “publication bias,” when only
positive results are published. Indeed, if the researchers
cannot localize a gene to a certain genomic region, they
often decide not to publish the results at all, because it
is sometimes unclear whether the data are insufﬁcient
or the gene is merely located in another genomic
region. To choose between these two explanations, it is
necessary to know the power of the mapping method. In
this case, the given locus can be excluded from further
analysis if the method has been sufﬁciently powerful.
We developed a method for estimating the power of
the transmission disequilibrium test (TDT), one of the
most popular tests used for analysis of associations.
Here, we ﬁrst describe the general principles of analysis of
associations and testing genetic hypotheses, then obtain
analytical expression for estimating the power of the TDT,
and ﬁnally illustrate this method using actual data.
ANALYSIS OF ALLELIC ASSOCIATIONS
Analysis of associations is based on the search for
correlations between allele frequencies. If alleles of
two loci segregate independently, the frequency of each
haplotype is equal to the product of allele frequencies.
If this rule is not complied with, then the two alleles are
associated with each other or the loci display linkage
disequilibrium. Linkage disequilibrium may be
accounted for by different factors, that main causes
being population mixing, close linkage between loci,
interaction between loci, and data clustering . Only
the associations that result from close linkage between
the loci are important for mapping.
There are various methods of association analysis.
The most popular and logically simple method for
studying associations between a disease and a marker
locus is comparison of the allele frequencies of the
marker gene in random samples of affected and healthy
subjects from the same general population. However,
the disadvantage of this approach is difﬁculties with the
interpretation of the results, because linkage is not the
Analysis of Allelic Association:
Estimation of the Power of the TDT
I. V. Zorkoltseva and T. I. Axenovich
Institute of Cytology and Genetics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090 Russia;
fax: (3832)33-12-78; e-mail: firstname.lastname@example.org
Received June 24, 2002
—Analysis of allelic associations is an increasingly more widely used approach to ﬁne mapping of
genes of various diseases. To interpret the results correctly, it is necessary to estimate the power of the statistical
test used. The principle of the analysis of associations and testing of hypothesis are described, and analytically
obtained estimates of the power of the transmission disequilibrium test (TDT), one of the most popular methods
of analysis of allelic associations, are presented. These estimates are applicable to arbitrary models of inherit-
ance formulated in terms of genotypic relative risk. The proposed method is illustrated by analysis of the asso-
ciations of idiopathic scoliosis and aggrecan gene alleles.
MODELS AND METHODS