9.1 Introduction to lm_auto and lm_pval

The MORGAN programs lm_auto and lm_pval are referred to as "Autozyg" programs, as they estimate autozygosity, or identity by descent (ibd). The Autozyg programs use MCMC to perform multipoint linkage analysis on large pedigrees where many individuals may be unobserved and exact computation is infeasible. The data are the genotypes at marker loci of observed individuals in pedigrees and affectation status (affected / unaffected / unknown) for the trait of interest. lm_auto and lm_pval estimate conditional probabilities of gene ibd states, given the trait and marker data.

lm_auto uses the LM-sampler to realize ibd configurations from their conditional distribution given the marker data. Given marker data, it estimates conditional probabilities of genome sharing patterns (gene ibd) among specified haplotypes, usually from affected individuals. The marker data are used jointly in the sampling, but the resulting ibd is scored marginally at each marker locus.

lm_pval also uses LM-sampling to provide the conditional distribution of an ibd measure given marker data. In principle it can be used to provide Monte Carlo estimates of any NPL (Non-Parametric Linkage) statistics for detecting linkage. Trait information provided to the program consists of the list of affected members of the pedigree, provided either as a list of names in the parameter file or as the phenotypic status in the pedigree file.

The version of the program lm_pval released in MORGAN V.2.8 and subsequent, and described in this tutorial, uses the latent p-value distribution of Thompson & Geyer (2007, Biometrika). In lm_pval, marker data are assumed available on some pedigree members, at some of the marker loci. The distribution of the ibd measure conditional on marker data is compared to the unconditional distribution under the null hypothesis of no linkage to produce quantiles of a latent (fuzzy) p-value distribution. A latent p-value distribution corrected for multiple testing is also produced, by scoring the maximum of the ibd measure over loci.

Additional programs using latent p-values are under development, including programs for the distribution of latent lod scores obtained in MCMC sampling (lm_fuzlod), p-values and randomized tests based on latent lod score statistics (lm_fzplod), and randomized confidence sets for the location of a trait locus (lm_fzconf). These are working names only; versions of the programs will be released under MORGAN 3. The methods are described in Thompson (2008: JSM 2007 proceedings, Pp. 3751-3758). The MORGAN 3 program civil also uses latent p-values (Di and Thompson, 2009, Human Heredity 68: 139-150).