On Computation of Pvalues in Parametric Linkage Analysis
Azra Kurbasic and Ola Hössjer
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2003
ISSN 14039338

Abstract:

Parametric linkage analysis is usually used to find chromosomal regions linked
to a disease (phenotype) that is described with a specific genetic model.
This is done by investigating the relations between the disease and genetic
markers, that is, loci of known position with a clear Mendelian mode of
inheritance. Assume we have found an interesting region on a chromosome that
we suspect is linked to the disease. Then we want to test the hypothesis
of no linkage versus the alternative one of linkage. As a measure we use
a maximal lod score $Z_{\mbox{\scriptsize max}}$. It is well known that the
maximal lod score has asymptotically a $(2 \ln 10)^{1}\times
(\frac{1}{2}\chi^{2}(0)+\frac{1}{2}\chi^{2}(1))$ distribution under the null
hypothesis of no linkage when only one point (one marker) on the chromosome
is studied. In this paper, we show, both by simulations and theoretical
arguments, that the null hypothesis distribution of $Z_{\mbox{\scriptsize
max}}$ has no simple form when more than one marker is used (multipoint
analysis). In fact, the distribution of $Z_{\mbox{\scriptsize max}}$ depends
both on the number of families, their structure, the genetic model, marker
denseness, and marker informativity. This means

that a constant critical limit of $Z_{\mbox{\scriptsize max}}$ leads to tests
associated with different significance levels. Because of the abovementioned
problems from the statistical point of view a pvalue is a more desirable
measure of significance than the maximal lod score.



Key words:


Linkage analysis, lod score distribution, pointwise/genomwide pvalue.