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re: st: Mixed ANOVA

From   David Airey <[email protected]>
To   [email protected]
Subject   re: st: Mixed ANOVA
Date   Mon, 18 Jul 2005 16:40:49 -0500

I replied earlier but it didn't post. I then tried to waste Pagano's time figured he posted for Kristin so he could relay a reply. Would have been easier if I'd been at a text only email station, or had Kristin's email posted to reply directed to...anyway my reply is below.

Dr. Pagano posted for Kristin:

For Kristin:


I have genotype and phenotype data for persons with a disease, their healthy siblings, and unrelated healthy controls. Since the genotypes between affected persons and siblings are correlated, I need to create a random effect for family membership. I am trying to run a mixed anova with fixed effect(genotype) and random effect (family). I want to get an F-test for effect of genotype on phenotype.

I have read the documentation for anova, and the description says it does mixed-effects anovas, but there's no example of it, so I am not sure how to specify the model.

You seem to have a data set that is a mixture of a population association design and a family/pedigree association design. The Allison references below are pertinent to making use of you sibs data, but it will ignore your population controls. To make use of both pedigree and population data in the same test, it seems maybe the Fulker reference is worth looking at. sibpairs_twins.htm

From this page:

Continuous phenotypes
Allison et al (1999) describe two joint tests of linkage and association for continuous phenotypes using siblings. An alternative approach to joint modeling of linkage and association, for continuous phenotypes, which is based on variance components models is described by Fulker et al. (1999). Variance components models have a long history in linkage analysis for quantitative traits, but it is first with the work of Fulker et al. (1999) that their potential for testing association, jointly with linkage, has been fully exploited. The method described by Fulker et al. (1999) utilizes the method of testing for linkage which is based on examining the identity (identical)-by-descent (IBD) relationships among genotypes of sib- pairs. The expected within covariance matrix for sib pairs can be expressed in terms of IBD shared alleles, under the null hypothesis of no linkage. Whilst linkage can be modeled in the covariance structure, association can be modeled on the means of the continuous outcomes, simultaneously in a variance components model. Since linkage and association are partitioned in this way, it is possible to perform a number of different tests within this framework. (The approaches described by Allison et al. are joint tests of linkage and association with single test statistics.) According to the Fulker et al. approach it is possible to

- jointly test for linkage and association
- test for association while simultaneously modeling linkage and controlling for population stratification
- test for the presence of population stratification
- test for linkage while simultaneously modeling association (if there is significant linkage while modeling association then it is reasonable to conclude that the locus is in linkage disequilibrium with some other locus, which is directly related to the phenotype.)

Computer programs

QTDT (Author: Abecasis)
This package includes programs for the methods of Allison (1997), Abecasis et al. (2000), Fulker et al. (1999), Monks et al. (1998) and Rabinowitz (1997). Handles families of any size, with or without parental information. Available from abecasis/QTDT.

Posthuma et al. (2004) implement the method of Fulker et al. (1999) in the program Mx.

Performs the test described by Spielman and Ewens (1998). Available for PC use from

- Allison DB (1997) Transmission-Disequilibrium tests for quantitative traits. Am. J. Hum. Genet 60:676-690.
- Allison DB, Heo M, Kaplan N, Martin ER (1999) Sibling based tests of linkage and association for quantitative traits. Am. J. Hum. Genet. 64: 1754-1764.
- Boehnke M and Langefeld CD (1998) Genetic association mapping based on discordant sib pairs: the discordant sib pair test. Am. J. Hum. Genet. 62:950-961.
- Curtis D (1997) Use of siblings as controls in case-control association studies. Ann. Hum. Genet. 61:319-333.
- Fulker DW, Cherny SS, Sham PC, Hewitt JK (1999) Combined linkage and association sib-pairs analysis for quantitative traits. Am. J. Hum. Genet. 64: 259-267.
- Horvath S and Laird NM (1998) A discordant-sibship test for disequilibrium and linkage: no need for parental data. Am. J. Hum. Genet. 63:1886-1897.
Posthuma D, de Geus EJC, Boomsma DI, Neale MC (2004) Combined linkage and association tests in Mx. Behaviour Genetics. 34:179-196.


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