The null distribution of the heterogeneity lod score does depend on the assumed genetic model for the trait

Jian Huang, Veronica J. Vieland

Research output: Journal article publicationJournal articleAcademic researchpeer-review

13 Citations (Scopus)


It is well known that the asymptotic null distribution of the homogeneity lod score (LOD) does not depend on the genetic model specified in the analysis. When appropriately rescaled, the LOD is asymptotically distributed as 0.5 χ02 + 0.5 χ12, regardless of the assumed trait model. However, because locus heterogeneity is a common phenomenon, the heterogeneity lod score (HLOD), rather than the LOD itself, is often used in gene mapping studies. We show here that, in contrast with the LOD, the asymptotic null distribution of the HLOD does depend upon the genetic model assumed in the analysis. In affected sib pair (ASP) data, this distribution can be worked out explicitly as (0.5 - c)χ02 + 0.5χ12 + cχ22, where c depends on the assumed trait model. E.g., for a simple dominant model (HLOD/D), c is a function of the disease allele frequency p: for p = 0.01, c = 0.0006; while for p = 0.1, c = 0.059. For a simple recessive model (HLOD/R), c = 0.098 independently of p. This latter (recessive) distribution turns out to be the same as the asymptotic distribution of the MLS statistic under the possible triangle constraint, which is asymptotically equivalent to the HLOD/R. The null distribution of the HLOD/D is close to that of the LOD, because the weight c on the χ22 component is small. These results mean that the cutoff value for a test of size α will tend to be smaller for the HLOD/D than the HLOD/R. For example, the α = 0.0001 cutoff (on the lod scale) for the HLOD/D with p = 0.05 is 3.01, while for the LOD it is 3.00, and for the HLOD/R it is 3.27. For general pedigrees, explicit analytical expression of the null HLOD distribution does not appear possible, but it will still depend on the assumed genetic model.
Original languageEnglish
Pages (from-to)217-222
Number of pages6
JournalHuman Heredity
Issue number4
Publication statusPublished - 3 Dec 2001
Externally publishedYes


  • Heterogeneity lod score
  • Mixture of χ distributions 2
  • Trait model

ASJC Scopus subject areas

  • General Medicine
  • Genetics
  • Genetics(clinical)


Dive into the research topics of 'The null distribution of the heterogeneity lod score does depend on the assumed genetic model for the trait'. Together they form a unique fingerprint.

Cite this