A score test for linkage using identity by descent data from sibships

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, well-characterized 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 the maximal lod score Z_max. It is well known that the maximal lod score has asymptotically a (2 ln 10)^–1 × (1/2 χ²(0) + 1/2 χ²(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_max has no simple form when more than one marker is used (multipoint analysis). In fact, the distribution of Z_max depends on the number of families, their structure, the assumed genetic model, marker denseness, and marker informativity. This means that a constant critical limit of Z_max leads to tests associated with different significance levels. Because of the above-mentioned problems, from the statistical point of view the maximal lod score should be supplemented by a p-value when results are reported.

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“…In (1) the same asymptotic limit distribution also appears when ψ is misspecified, cf. [11] and [12]. Hence the significance level…”

Section: Parametric Linkage Analysismentioning

confidence: 95%

On Computation of p-Values in Parametric Linkage Analysis

Kurbasic

Hössjer²

2004

Hum Hered

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“…Dudoit and T. P. Speed (1999). A score test for linkage using identity by descent data from sibships.…”

Section: Human Pedigreesmentioning

confidence: 99%

“…For sibships of size k, label locus (1, 2) and maternally derived alleles (3,4). The inheritance vector at a given locus is the vector x = (x 1 , x 2 , ..., x 2k−1 , x 2k ), where for sib i, x 2i−1 is the label of the paternally inherited allele (1 or 2) and x 2i is that of the maternally inherited allele (3 or 4) at the locus.…”

Section: Inheritance Vectormentioning

confidence: 99%

“…However, using their formulation of the problem, Dudoit and Speed [4] show rigorously that for affected sibships of a given size, the second-order Taylor series expansion of the log likelihood around the null of no linkage is independent of the genetic inheritance model. They thus provide a mathematically justified basis for affected sib-pair methods, which do not require an assumed mode of inheritance.…”

Section: Score Test For Linkagementioning

confidence: 99%

See 1 more Smart Citation

Statistical Genetics

Goldstein¹

2012

Selected Works of Terry Speed

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Terry Speed has produced many interesting and important contributions to the field of statistical genetics, with work encompassing both experimental crosses and human pedigrees. He has been instrumental in uncovering and elucidating algebraic structure underlying a diverse range of statistical problems, providing new and unifying insights.Here, I provide a brief commentary and introduction to some of the key building blocks for an understanding of the papers. Some readers may also find useful a refresher on group action (see e.g. Fraleigh [6]) and hidden Markov models [13]. Linkage mappingLinkage analysis studies inheritance of traits in families, with the aim of determining the chromosomal location of genes influencing the trait. The analysis proceeds by tracking patterns of coinheritance of the trait of interest and other traits or genetic markers, relying on the varying degree of recombination between trait and marker loci to map the loci relative to one another.A measure of the degree of linkage is the recombination fraction θ , the chance of recombination occurring between two loci. For unlinked genes, θ = 1/2; for linked genes, 0 ≤ θ < 1/2.

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“…However, Knapp et al [1994a, b] showed that (i) for all (f 2 , f 1 , f 0 , p), the mean test is locally (in ) most powerful; (ii) in case 22 Hum Hered 2005;59:21-25 Knapp that the penetrances satisfy the condition f 1 2 = f 2 W f 0 , the mean test is uniformly (in ) most powerful, and (iii) if parametric linkage analysis is conducted for a sample of ASPs for which the disease status of the parents is unknown and if the inheritance model assumed for this parametric linkage analysis satisfies f 1 2 = f 2 W f 0 , then the resulting maximum lod score is a monotone function of the total number of alleles shared ibd in the sample. Subsequently, Dudoit and Speed [1999] generalized (i) to samples of affected sibships of any (but constant) size k, i.e., they showed that the test based on the total number of alleles shared ibd in a sample of nuclear families with k affected children is locally (in ) most powerful, irrespective of the mode of inheritance. The purpose of the present note is to generalize (ii) and (iii) to samples of affected sib triplets.…”

Section: Introductionmentioning

confidence: 99%

A Note on Linkage Analysis with Affected Sib Triplets

Knapp

2005

Hum Hered

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Previously, it has been shown for affected sib pairs that the mean test is the uniformly (in Θ) most powerful test in case of a multiplicative mode of inheritance and that the mean test is equivalent to parametric linkage analysis calculated under an assumed multiplicative mode of inheritance. Here, these two results are extended to samples consisting of affected sib triplets. For affected sib quadruplets, however, it is shown that these results are no longer valid.

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A score test for linkage using identity by descent data from sibships

Cited by 20 publications

References 26 publications

On Computation of p-Values in Parametric Linkage Analysis

On Computation of p-Values in Parametric Linkage Analysis

Statistical Genetics

A Note on Linkage Analysis with Affected Sib Triplets

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