10.1 Introduction to lm_ibdtests

The program lm_ibdtests uses identity-by-descent (ibd) based and likelihood-ratio based statistics to construct linkage detection tests. The current version allows only discrete trait data (affected or unaffected or unknown phenotypic status).

The ibd scoring approach involves construction of an ibd measure (S) that is a function of the inheritance vectors and affectation status of the individuals in pedigrees. The program uses realizations of the inheritance vectors conditional only on the marker data (Y) to compute a Monte Carlo estimate of the test statistic E(S|Y). Four different ibd measures are implemented in the program. Two of these measures, Slambda and Saffunaff (developed by Saonli Basu), allow incorporation both of affected and of unaffected individuals in the analysis. The test statistic is used to test the null hypothesis of no linkage between the trait and a set of markers. For this approach, two different testing options have been implemented; one is a normality-based test and the other is a permutation test. The permutation test keeps the observed marker data unchanged and permutes the affectation status. In the normality-based test, test statistics (Spairs, for example) are computed for each realization and averaged over realizations. The program then reports the p-values from each test at the marker loci. For more details of these methods see Basu et al. (2008) Annals of Human Genetics 72: 676-682

A new (lambda,p) model has been implemented in lm_ibdtests. The (lambda,p) model models the trait-dependent segregation of inheritance vectors at a locus given the trait data on individuals and constructs a chi-square test for linkage detection. The (lambda,p) model incorporates both affected and unaffected individuals in the analysis. The delta model is also implemented in the program. The current version of lm_ibdtests only allows the ibd measure Spairs in the delta model set-up. The program returns the p-values of the likelihood-ratio statistics under each of these two models. (For a detailed description of the (lambda,p) and delta models, see Basu et al (2009) Biometrics 66: 205-213;for a real data analysis using lm_ibdtests, see Sieh et al. 2005. Comparison of marker types and map assumptions using Markov chain Monte Carlo-based linkage analysis of COGA data. BMC Genetics 2005, 6 Suppl 1 S11)