re: st: Mixed ANOVA

[David Airey <david.airey@vanderbilt.edu>]

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:
>
> Hello,
>
> 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.
> Thanks,
> Kristin

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.

http://www.meb.ki.se/genestat/tl/genass_ldmap/gen_ass_stud_rel_ind/ 
sibpairs_twins.htm

From this page:

---snip---
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 http://www.sph.umich.edu/csg/ 
abecasis/QTDT.

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

TDT/S-TDT
Performs the test described by Spielman and Ewens (1998). Available  
for PC use from http://genomics.med.upenn.edu/spielman/TDT.htm.

References
- 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.

---snip---


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