Linkage analysis in the presence of errors IV: joint pseudomarker analysis of linkage and/or linkage disequilibrium on a mixture of pedigrees and singletons when the mode of inheritance cannot be accurately specified.

There is a lot of confusion in the literature about the "differences" between "model-based" and "model-free" methods and about which approach is better suited for detection of the genes predisposing to complex multifactorial phenotypes. By starting from first principles, we demonstrate that the differences between the two approaches have more to do with study design than statistical analysis. When simple data structures are repeatedly ascertained, no assumptions about the genotype-phenotype relationship need to be made for the analysis to be powerful, since simple data structures admit only a small number of df. When more complicated and/or heterogeneous data structures are ascertained, however, the number of df in the underlying probability model is too large to have a powerful, truly "model-free" test. So-called "model-free" methods typically simplify the underlying probability model by implicitly assuming that, in some sense, all meioses connecting two affected individuals are informative for linkage with identical probability and that the affected individuals in a pedigree share as many disease-predisposing alleles as possible. By contrast, "model-based" methods add structure to the underlying parameter space by making assumptions about the genotype-phenotype relationship, making it possible to probabilistically assign disease-locus genotypes to all individuals in the data set on the basis of the observed phenotypes. In this study, we demonstrate the equivalence of these two approaches in a variety of situations and exploit this equivalence to develop more powerful and efficient likelihood-based analogues of "model-free" tests of linkage and/or linkage disequilibrium. Through the use of a "pseudomarker" locus to structure the space of observations, sib-pairs, triads, and singletons can be analyzed jointly, which will lead to tests that are more well-behaved, efficient, and powerful than traditional "model-free" tests such as the affected sib-pair, transmission/disequilibrium, haplotype relative risk, and case-control tests. Also described is an extension of this approach to large pedigrees, which, in practice, is equivalent to affected relative-pair analysis. The proposed methods are equally applicable to two-point and multipoint analysis (using complex-valued recombination fractions).

[1]  Blackwelder Wc,et al.  A comparison of sib-pair linkage tests for disease susceptibility loci , 1985 .

[2]  M. Boehnke,et al.  Loss of information due to ambiguous haplotyping of SNPs , 1999, Nature Genetics.

[3]  Jurg Ott,et al.  Handbook of Human Genetic Linkage , 1994 .

[4]  G. Mendel,et al.  Versuche Uber Pflanzenhybriden , 1960 .

[5]  D. Siegmund,et al.  Statistical methods for linkage analysis of complex traits from high-resolution maps of identity by descent. , 1995, Genetics.

[6]  J. Terwilliger A powerful likelihood method for the analysis of linkage disequilibrium between trait loci and one or more polymorphic marker loci. , 1995, American journal of human genetics.

[7]  D. Weeks,et al.  Comparison of nonparametric statistics for detection of linkage in nuclear families: single-marker evaluation. , 1997, American journal of human genetics.

[8]  C. Falk,et al.  Haplotype relative risks: an easy reliable way to construct a proper control sample for risk calculations , 1987, Annals of human genetics.

[9]  J. Suvisaari,et al.  A genomewide screen for schizophrenia genes in an isolated Finnish subpopulation, suggesting multiple susceptibility loci. , 1999, American journal of human genetics.

[10]  J. Ott,et al.  Strategies for multilocus linkage analysis in humans. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[11]  S A Seuchter,et al.  Linkage analysis in nuclear families. 2: Relationship between affected sib-pair tests and lod score analysis. , 1994, Human heredity.

[12]  D. Siegmund,et al.  Combining information within and between pedigrees for mapping complex traits. , 1997, American journal of human genetics.

[13]  B S Weir,et al.  Tests for linkage and association in nuclear families. , 1997, American journal of human genetics.

[14]  R C Elston,et al.  Lods, wrods, and mods: The interpretation of lod scores calculated under different models , 1994, Genetic epidemiology.

[15]  Q. Mcnemar Note on the sampling error of the difference between correlated proportions or percentages , 1947, Psychometrika.

[16]  R. Spielman,et al.  High-resolution linkage mapping for susceptibility genes in human polygenic disease: insulin-dependent diabetes mellitus and chromosome 11q. , 1991, American journal of human genetics.

[17]  L. Penrose THE DETECTION OF AUTOSOMAL LINKAGE IN DATA WHICH CONSIST OF PAIRS OF BROTHERS AND SISTERS OF UNSPECIFIED PARENTAGE , 1935 .

[18]  C. Nechemias,et al.  HLA antigens and islet cell antibodies in gestational diabetes. , 1981, Human immunology.

[19]  L. Peltonen,et al.  Refined assignment of the infantile neuronal ceroid lipofuscinosis (INCL, CLN1) locus at 1p32: incorporation of linkage disequilibrium in multipoint analysis. , 1993, Genomics.

[20]  S. Chow,et al.  On the Performance of a Likelihood Ratio Test for Genetic Linkage , 1984 .

[21]  N Risch,et al.  The Future of Genetic Studies of Complex Human Diseases , 1996, Science.

[22]  L. Excoffier,et al.  Incorporating genotypes of relatives into a test of linkage disequilibrium. , 1998, American journal of human genetics.

[23]  J. J. Tai,et al.  Asymptotic distribution of the lod score for familial data. , 1989, Proceedings of the National Science Council, Republic of China. Part B, Life sciences.

[24]  J. Ott,et al.  An allele of COL9A2 associated with intervertebral disc disease. , 1999, Science.

[25]  Courtney A. Harper,et al.  A genomic screen of autism: evidence for a multilocus etiology. , 1999, American journal of human genetics.

[26]  H H Göring,et al.  Linkage analysis in the presence of errors II: marker-locus genotyping errors modeled with hypercomplex recombination fractions. , 2000, American journal of human genetics.

[27]  B. Suarez,et al.  A simple method to detect linkage for rare recessive diseases: An application to juvenile diabetes , 1979, Clinical genetics.

[28]  L. Peltonen,et al.  Evidence for involvement of the type 1 angiotensin II receptor locus in essential hypertension. , 1999, Hypertension.

[29]  H H Göring,et al.  Linkage analysis in the presence of errors III: marker loci and their map as nuisance parameters. , 2000, American journal of human genetics.

[30]  Leena Peltonen,et al.  A putative vulnerability locus to multiple sclerosis maps to 5p14–p12 in a region syntenic to the murine locus Eae2 , 1996, Nature Genetics.

[31]  J D Terwilliger,et al.  Two-locus linkage analysis in multiple sclerosis (MS). , 1994, Genomics.

[32]  J. Browne,et al.  Identification of a major susceptibility locus on chromosome 6p and evidence for further disease loci revealed by a two stage genome-wide search in psoriasis. , 1997, Human molecular genetics.

[33]  S. S. Wilks The Likelihood Test of Independence in Contingency Tables , 1935 .

[34]  H H Göring,et al.  Linkage analysis in the presence of errors I: complex-valued recombination fractions and complex phenotypes. , 2000, American journal of human genetics.

[35]  K. Weiss,et al.  Linkage disequilibrium mapping of complex disease: fantasy or reality? , 1998, Current opinion in biotechnology.

[36]  R. Elston,et al.  A comparison of sib‐pair linkage tests for disease susceptibility loci , 1985, Genetic epidemiology.

[37]  Alejandro A. Schäffer,et al.  Inverse inbreeding coefficient problems with an application to linkage analysis of recessive diseases in inbred populations , 2000, SODA '99.

[38]  W. Ewens,et al.  Transmission test for linkage disequilibrium: the insulin gene region and insulin-dependent diabetes mellitus (IDDM). , 1993, American journal of human genetics.

[39]  A A Schäffer,et al.  Faster sequential genetic linkage computations. , 1993, American journal of human genetics.

[40]  P. Holmans,et al.  Asymptotic properties of affected-sib-pair linkage analysis. , 1993, American journal of human genetics.

[41]  J. Terwilliger,et al.  Two stage genome–wide search in inflammatory bowel disease provides evidence for susceptibility loci on chromosomes 3, 7 and 12 , 1996, Nature Genetics.

[42]  Tai Jj,et al.  Asymptotic distribution of the lod score for familial data. , 1989 .

[43]  M. Farrall LOD wars: the affected-sib-pair paradigm strikes back! , 1997, American journal of human genetics.

[44]  J. Terwilliger,et al.  A haplotype-based 'haplotype relative risk' approach to detecting allelic associations. , 1992, Human heredity.

[45]  L. Kruglyak Nonparametric linkage tests are model free. , 1997, American journal of human genetics.

[46]  David L. Rimoin,et al.  Principles and Practice of Medical Genetics , 1990 .

[47]  S E Hodge,et al.  Affecteds-only linkage methods are not a panacea. , 1996, American journal of human genetics.

[48]  J. Ott Statistical properties of the haplotype relative risk , 1989, Genetic epidemiology.

[49]  A S Whittemore,et al.  Genome scanning for linkage: an overview. , 1996, American journal of human genetics.

[50]  D. Hartl,et al.  Principles of population genetics , 1981 .