University of Michigan Center for Statistical 


Non-parametric statistics for quantitative traits

This page provides a brief overview of the non-parametric quantitative trait linkage statistics implemented in MERLIN. These statistics are accessed through the --qtl and --deviates command line options.

The two non-parametric quantitative trait statistics are implemented in the general framework of Whittemore and Halpern (1994) and Kong and Cox (1997). The basic idea in this framework is do define some function S(v) that allows alternative inheritance vectors for one pedigree to be ranked according to the evidence for linkage they provide.

Thus, a suitable function should be such that S(v1) > S(v2) indicates that inheritance pattern v1 is more suggestive of linkage than v2. For example, for affected sib pairs, one suitable definition is S(v)=π(v) where π(v) denotes the number of alleles shared for inheritance vector v. For discordant sib-pairs, an alternative definition might be S(v)=-π(v).

For quantitative traits, MERLIN uses the following defintion:

Here, the score for each inheritance vector S(v) is calculated by summing squared scores for each founder allele. This sum will take larger values when the scores for individual founder alleles are more extreme. The score for each founder allele is calculated by simply mean deviates (yi-μ) for all individuals i who carry the founder allele. Note that yi is the phenotype for individual i, μ is the population mean and the list of individuals who carry a particular founder allele is implied by v.

When the --qtl option is selected MERLIN uses the sample mean to estimate μ. When the --deviates option is selected, MERLIN fixes μ at 0 (zero). The later option is suitable for the analysis of selected samples if the sample mean is subtracted from individual phenotypes prior to analysis.

The procedure for converting scores for individual inheritance vectors into Z-scores for a single or multiple pedigrees is described in detail by Whittemore and Halpern (1994). These Z-scores are used by MERLIN to construct a likelihood ratio test for linkage and define a LOD score statistic using the procedure described by Kong and Cox (1997).

MERLIN also implements variance components (--vc option) and regression-based (MERLIN-REGRESS package) tests of linkage for quantitative traits. Both of these tests are designed for traits which are normally distributed in the population and are likely to be more powerful for such traits. Detailed descriptions of these alternatives are available elsewhere (see for example, Amos, 1994; Sham et al, 2002).


Amos (1994) Robust variance-components approach for assessing genetic linkage in pedigrees. American Journal of Human Genetics 54535-543

Kong and Cox (1997) Allele-sharing models: LOD scores and accurate linkage tests. American Journal of Human Genetics 61:1179-1188

Sham, Purcell, Cherny and Abecasis (2002) Powerful regression-based quantitative-trait linkage analysis of general pedigrees. American Journal of Human Genetics 71:238-253

Whittemore and Halpern (1994) A class of tests for linkage using affected pedigree members. Biometrics 50118-127


University of Michigan | School of Public Health | Abecasis Lab