LTMLM  version 2.0, 1/1/2017 (for Linux only)

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In addition to LTMLM statistic we introduce a family-based association statistic 
(LT-Fam) that is robust to the problem or family-biased case-control ascertainment, 
where case and control subjects are ascertained non-randomly with respect to
family relatedness. A simple exampe of this would be a discordant sibling trial for
a case control disease. 

Similar to LTMLM, LT-Fam is computed from  posterior mean liabilities (PML) 
under a liability threshold model; however, LT-Fam uses published narrow-sense 
heritability estimates to avoid the problem of biased heritability estimation, 
enabling correct calibration. So, The LT-Fam statistic is recommended to use 
published narrow-sense heritability estimates as well as genetic relatedness 
using a threshold, as opposed to LTMLM which uses SNP-heritability estimates 
and calibration based on phenotypic covariance without thresholding.

Liability Threshold Mixed Linear Model (LTMLM) association 
statistic and software for ascertained case-control studies that increases 
power vs. existing mixed model methods, with a well-controlled 
false-positive rate.  Recent work has shown that existing mixed model 
methods suffer a loss in power under case-control ascertainment, but no 
solution has been proposed.  

Here, we solve this problem using a chi-square score statistic computed 
from posterior mean liabilities (PML) under the liability threshold model. 
Each individual’s PML is conditional not only on that individual’s 
case-control status, but also on every individual’s case-control status 
and on the genetic relationship matrix obtained from the data.  
The PML are estimated using a multivariate Gibbs sampler, with the 
liability-scale phenotypic covariance matrix based on the genetic 
relationship matrix (GRM) and a heritability parameter estimated via 
Haseman-Elston regression on case-control phenotypes followed by 
transformation to liability scale.  More details can be found at:

Mixed Model Association with Family-Biased Case-Control Ascertainment 
American Journal of Human Genetics 2017
Tristan J. Hayeck, Po-Ru Loh, Samuela Pollack, Alexander Gusev, Nick Patterson,
Noah A. Zaitlen, and Alkes L. Price

Tristan J. Hayeck, Noah Zaitlen, Po-Ru Loh, Bjarni Vilhjalmsson, 
Samuela Pollack, Alexander Gusev, Jian Yang, Guo-Bo Chen, 
Michael E. Goddard, Peter M. Visscher, Nick Patterson, Alkes Price 
“Mixed Model with Correction for Case-Control Ascertainment 
Increases Association Power” American Journal of Human Genetics 2015

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For more information please contact: Tristan J. Hayeck (Tristan.Hayeck@gmail.com) 
or Samuela Pollack (SPOLLACK@hsph.harvard.edu)


This software also uses:
GCTA http://www.complextraitgenomics.com/software/gcta/manipulation_grm.html
(GCTA source code under is released under GPL and the binary code under MIT)
Eigenstrat convertf http://www.hsph.harvard.edu/alkes-price/software/

For detailed examples see the *.docx and *.pdf Read me and tutorial files

Acknowledgements:
LTMLM was written by Tristan J. Hayeck, Samuela Pollack, and Alkes Price
We thank Jian Yang and Peter Visscher for use of GCTA and additional 
assistance on this project. 
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SOFTWARE COPYRIGHT NOTICE AGREEMENT
This software and its documentation are copyright (2010) by Harvard University 
and The Broad Institute. All rights are reserved. This software is supplied 
without any warranty or guaranteed support whatsoever. Neither Harvard 
University nor The Broad Institute can be responsible for its use, misuse, or 
functionality. The software may be freely copied for non-commercial purposes, 
provided this copyright notice is retained.