A complete enumeration and classification of two-locus disease models

Human Heredity

Volumn 50, Issue 6, 2000, Pages 334-349

  Li, Wentian ^a   Reich, Jens ^b  

^a ROCKEFELLER UNIVERSITY   (United States)

^b MAX DELBRÜCK CENTER FOR MOLECULAR MEDICINE   (Germany)

Author keywords

Correlation; Epistasis; Identity by descent; Two locus model

Indexed keywords

ARTICLE; DISEASE MODEL; EPISTASIS; GENE LOCUS; GENETIC DISORDER; GENETIC LINKAGE; GENETIC MODEL; PENETRANCE; PROBABILITY;

EID: 0033940280     PISSN: 00015652     EISSN: None     Source Type: Journal    
DOI: 10.1159/000022939     Document Type: Article

References (94)

1. Agresti A: An Introduction to Categorical Data Analysis. New York, Wiley, 1996.
2. Badner JA, Gershon ES, Goldin LR: Optimal ascertainment strategies to detect linkage to common disease alleles. Am J Hum Genet 1998;63:880-888.
3. Bishop CM: Neural Networks for Pattern Recognition. Oxford, Oxford University Press, 1995.
4. Clerget-Darpoux F. Babron MC: Testing genetic models for IDDM by the MASC method. Genet Epidemiol 1989;6:59-64.
5. Cotterman CW: Regular two-allele and three-allele phenotype systems. Am J Hum Genet 1953;5:193-235.
6. Defrise-Gussenhoven PE: Hypothèses de dimérie et de non-pénétrance. Acta Genet Stat Med (Basel) 1961;12:65-69.
7. Campbell MA, Elston RC: Relatives of probands: Models for preliminary genetic analysis. Ann Hum Genet 1971;35:225-236.
8. Cockerham CC: An extension of the concept of partitioning hereditary variance for analysis of covariances among relatives when epistasis is present. Genetics 1954;39:859-882.
9. Cordell HJ, Todd JA, Bennett ST, Kawaguchi Y, Farrall M: Two-locus maximum lod score analysis of a multifactorial trait: Joint consideration of IDDM2 and IDDM4 with IDDM1 in type I diabetes. Am J Hum Genet 1995;57: 920-934.
10. Cox NJ, Frigge M, Nicolac DL, Concannon P, Hanis CL, Bell GI, Kong A: Loci on chromosomes 2 (NIDDM1) and 15 interact to increase susceptibility diabetes in Mexican Americans. Nat Genet 1999;21:213-215.
11. Davis S, Schroeder M, Goldin LR, Weeks DE: Nonparametric simulation-based statistics for detecting linkage in general pedigrees. Am J Hum Genet 1996:58:867-880.
12. Davis S, Weeks DE: Comparison of nonparametric statistics for detection of linkage in nuclear families: Single-marker evaluation. Am J Hum Genet 1997;61:1431-1444.
13. de Bruijn NG: Pólya theory of counting; in Beckenbach EF (ed): Applied Combinatorial Mathematics. New York, Wiley, 1964, pp 144-184.
14. 2 method. Am J Hum Genet 1994; 55:1042-1049.
15. Dizier MH, Babron MC, Clerget-Darpoux F: Conclusion of LOD-score analysis for family data generated under two-locus models. Am J Hum Genet 1996;58:1338-1346.
16. Dizier MH, Bonaiti-Pellie C, Clerget-Darpoux F: Conclusions of segregation analysis for family data generated under two-locus models. Am J Hum Genet 1993;53:1338-1346.
17. Dizier MH, Clerget-Darpoux F: Two-disease locus model: Sib pair method using information on both HLA and Gm. Genet Epidemiol 1986;3:343-356.
18. Dizier MH, Clerget-Darpoux F, Hochez J: Segregation analysis of two genetic markers in IDDM families under two-locus models. Genet Epidemiol 1989;6:71-75.
19. Dizier MH, Clerget-Darpoux F, Hochez J: Two-disease-locus model: Segregation analysis using information on two markers in nuclear families. Application to IDDM. Tissue Antigens 1990;36:1-7.
20. Durner M, Greenberg DA, Hodge SE: Inter- and intra-familial heterogeneity: Effective sampling strategies and comparison of analysis methods. Am J Hum Genet 1992;51:859-870.
21. Durner M, Vieland VJ, Greenberg DA: Further evidence for the increased power of LOD scores compared with nonparametric methods, Am J Hum Genet 1999;64:281-289.
22. Eccles DM, Forabosco P, Williams A, Dunn B, Williams C, Bishop DT, Morton NE: Segregation analysis of ovarian cancer using diathesis to include other cancers. Am J Hum Genet 1997;61:243-252.
23. Falk CT: Effect of genetic heterogeneity and assortative mating on linkage analysis: A simulation study. Am J Hum Genet 1997;61:1169-1178.
24. Farrall M: Affected sibpair linkage tests for multiple linked susceptibility genes. Genet Epidemiol 1997;14:103-115.
25. Fisher RA: The correlation between relatives on the supposition of Mendelian inheritance. Trans R Soc Edinburgh 1918;52:399-433.
26. Frankel WN, Schork NJ: Who's afraid of epistasis? Nat Genet 1996;14:371-373.
27. Goldgar DE, Oniki RS: Comparison of a multipoint identity-by-descent method with parametric multipoint linkage analysis for mapping quantitative traits. Am J Hum Genet 1992;50: 598-606.
28. Goldgar DE, Easton DF: Optimal strategies for mapping complex diseases in the presence of multiple loci. Am J Hum Genet 1997;60:1222-1232.
29. Goldin LR: Detection of linkage under heterogeneity: Comparison of the two-locus vs. admixture models. Genet Epidemiol 1992;9:61-66.
30. Goldin LR, Weeks DE: Two-locus models of disease: Comparison of likelihood and nonparametric linkage methods. Am J Hum Genet 1993;53:908-915.
31. Greenberg DA: A simple method for testing two-locus models of inheritance. Am J Hum Genet 1981;33:519-530.
32. Greenberg DA: Simulation studies of segregation analysis: Application to two-locus models. Am J Hum Genet 1984;36:167-176.
33. Greenberg DA: Linkage analysis assuming a single-locus mode of inheritance for traits determined by two loci: Inferring mode of inheritance and estimating penetrance. Genet Epidemiol 1990;7:467-479.
34. Greenberg DA, Lange KL: A maximum likelihood test of the two locus model for coeliac disease. Am J Med Genet 1982;12:75-82.
35. Greenberg DA, Delgado-Escueta AV, Maldonado HM, Widelitz H: Segregation analysis of juvenile myoclonic epilepsy. Genet Epidemiol 1988;5:81-94.
36. Greenberg DA, Hodge SE: Linkage analysis under 'random' and 'genetic' reduced penetrance. Genet Epidemiol 1989;6:259-264.
37. Greenberg DA, Abreu P, Hodge SE: The power to detect linkage in complex disease by means of simple LOD-score analyses. Am J Hum Genet 1998;63:870-879.
38. Hartl DL, Maruyama T: Phenogram enumeration: The number of regular genotype-phenotype correspondences in genetic systems. J Theor Biol 1968;20:129-163.
39. Hodge SE: Some epistatic two-locus models of disease. I. Relative risks and identical-by-descent distributions in affected sib pairs. Am J Hum Genet 1981;33:381-395.
40. Hodge SE, Abreu PC, Greenberg DA: Magnitude of type I error when single-locus linkage analysis is maximized over models: A simulation study. Am J Hum Genet 1997;60:217-227.
41. Hogben L: The genetic analysis of familial traits: II. Double gene substitutions, with special reference to hereditary dwarfism. J Gent 1932;25:211-240.
42. Johnson WG: Metabolic interference and the +/-heterozygote: A hypothetical form of simple inheritance which is neither dominant nor recessive. Am J Hum Genet 1980;32:374-386.
43. Juo SH, Beaty TH, Xu J, Prenger VL, Coresh J, Kwiterovich PO Jr: Segregation analysis of two-locus models regulating apolipoprotein-A1 levels. Two-locus models of diseases. Genet Epidemiol 1998;15:73-86.
44. Kempthorne O: The correlation between relatives in a random mating population. Trans R Soc Lond (B) 1954;143:103-113.
45. Kempthorne O: An Introduction to Genetic Statistics. New York, Wiley, 1957.
46. Knapp M, Scuchter SA, Baur MP: Two-locus disease models with two marker loci: The power of affected-sib-pair tests. Am J Hum Genet 1994;55:1030-1041.
47. Kullback S: Information Theory and Statistics. New York, Wiley, 1959.
48. Lathrop GM, Ott J: Analysis of complex diseases under oligogenic models and intrafamilial heterogeneity by the LINKAGE program (abstract). Am J Hum Genet 1990;47(suppl): A188.
49. Levy J, Nagylaki T: A model for the genetics of handedness. Genetics 1972;72:117-128.
50. Li CC: 'Some general properties of recessive inheritance'. Am J Hum Genet 1953;5:269-279.
51. Li CC (1955): Population Genetics; First Course in Population Genetics. Pacific Grove, Boxwood Press, 1976, 1978, chapt 4.
52. Li CC, Sacks L: The derivation of joint distribution and correlation between relatives by the use of stochastic matrices. Biometrics 1954;10: 347-360.
53. Li H, Helling R, Tang C, Wingreen N: Emergence of preferred structures in a simple model of protein folding. Science 1996;273:666-669.
54. Li W: Mutual information functions versus correlation functions. J Stat Phys 1990;60: 823-837.
55. Li W, Packard N: The structure of the elementary cellular automata rule space. Complex Syst 1990;4:281-297.
56. Li W: A complete listing and classification of two-locus two-allele fully-penetrant disease model (abstract). Am J Hum Genet 1997; 61(suppl):A204.
57. Li W: An exact calculation of the probability of identity-by-descent in two-locus models using an extention of the Li-Sacks' method (abstract). Am J Hum Genet 1998;63(suppl):A297.
58. Li W, Haghighi F. Falk CT: Design of artificial neural network and its applications to the analysis of alcoholism data. Genet Epidemiol, in press.
59. Lucek P, Hanke J, Reich J, Solla SA, Ott J: Multi-locus nonparametric linkage analysis of complex trait loci with neural networks. Hum Hered 1998;48:275-284.
60. MacLean CJ, Sham PC, Kendler KS: Joint linkage of multiple loci for a complex disorder. Am J Hum Genet 1993;53:353-366.
61. Majumder PP: Strategies and sample-size considerations for mapping a two-locus autosomal recessive disorder. Am J Hum Genet 1989;45: 412-423.
62. Majumder PP, Ramesh A, Chinnappan D: On the genetics of prelingual deafness. Am J Hum Genet 1989;45:412-423.
63. Malécot G: Les Mathématiques de l'Hérédité. Paris, Masson, 1948.
64. Merry A: Disease inheritance: Some 2-loci symmetric viability models, MSc diss, University of Reading, 1977.
65. Merry A, Roger JH, Curnow RN: A two-locus model for the inheritance of a familiar disease. Ann Hum Genet 1979;43:71-80.
66. Moran PAP: On the theory of selection dependent on two loci. Ann Hum Genet 1968;32: 183-190.
67. Neuman RJ, Rice JP: Two-locus models of diseases. Genet Epidemiol 1992;9:347-365.
68. Ober C: Current topic: HLA and reproduction: Lessons from studies in the Hutterites. Placenta 1995;16:569-577.
69. Olson JM: Multipoint linkage analysis using sib pairs: an interval mapping approach for dichotomous outcomes. Am J Hum Genet 1995;56:788-798.
70. Olson JM, Boehnke M, Neiswanger K, Roche AF, Siervogel RM: Alternative genetic models for the inheritance of the phenylthiocarbamide taste deficiency. Genet Epidemiol 1989;6:423-434.
71. Pólya G: Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chcmische Verbindungen. Acta Math 1937;68:145-254.
72. Press WH, Teukolsky SA, Vetterling WT, Flannery BP: Numerical Recipies in C, cd 2. Cambridge, Cambridge University Press, 1992.
73. Rapoport A, Guyer M, Gordon D: The 2 × 2 Game. Ann Arbor, University of Michigan Press, 1976.
74. Risch N: Linkage strategies for genetically complex traits. I. Multilocus models. Am J Hum Genet 1990;46:222-228.
75. Risch N: Linkage strategies for genetically complex traits. II. The power of affected relative pairs. Am J Hum Genet 1990;46:229-241.
76. Scapoli C, Collins A, Benatti P, Percesepe A, Roncucci L, de Leon MP: A two-locus model for hereditary non-polyposis colorectal cancer in Modena, Italy. Ann Hum Genet 1997;61: 109-119.
77. Schork NJ, Boehnke M, Terwilliger JD, Ott J: Two-trait-locus linkage analysis: A powerful strategy for mapping complex linkage genetic traits. Am J Hum Genet 1993;53:1127-1136.
78. Schork NJ, Boehnke M, Terwilliger JD, Ott J: Reply to Sham et al (letter to the editors). Am J Hum Genet 1994;55:856-858.
79. Sham PC, MacLean CJ, Kendler KS: Two-locus versus one-locus lods for complex traits (letter to the editors). Am J Hum Genet 1994; 55:855-856.
80. Sokal RR, Rohlf FJ: Biometry, ed 3. New York, Freeman, 1995.
81. Steinberg AG, Becker SW Jr, Fitzpatrick TB, Kierland RR: A further note on the genetics of psoriasis. Am J Hum Genet 1952;4:373-375.
82. Stoesz MR, Cohen JC, Mooser V, Marcovina S, Guerra R: Extension of the Haseman-Elston method to multiple alleles and multiple loci: Theory and practice for candidate genes. Am J Hum Genet 1997;61:263-274.
83. Strickberger MW: Genetics, ed 3. New York, Macmillan, 1985.
84. Tiwari HK, Elston RC: Deriving components of genetic variance for multilocus models. Gen Epidemiol 1997;14:1131-1136.
85. Tiwari HK, Elson RC: Linkage of multilocus components of variance to polymorphic markers. Ann Hum Genet 1997;61:253-261.
86. Tiwari HK, Elston RC: Restrictions on components of variance for epistatic models. Theor Popul Biol 1998;54:161-174.
87. Todorov AA, Borecki IB, Rao DC: Linkage analysis of complex traits using affected sib-pairs: Effects of single-locus approximations on estimates of the required sample size. Genet Epidemiol 1997;14:389-401.
88. Trojak JE, Murphy EA: Recurrence risks for autosomal, epistatic two-locus systems: The effects of linkage disequilibrium. Am J Med Genet 1981;9:219-229.
89. Vieland VJ, Hodge SE, Greenberg DA: Adequacy of single-locus approximations for linkage analyses of oligogenic traits. Genet Epidemiol 1992;9:45-59.
90. Vieland VJ, Greenberg DA, Hodge SE: Adequacy of single-locus approximations for linkage analyses of oligogenic traits: Extension to multigenerational pedigree structures. Hum Hered 1993;43:329-336.
91. Welshons WJ: Genetics basis for two types of recessive lethality at the notch locus of Drosophila. Genetics 1971;68:259-268.
92. Wilkie AOM: The molecular basis of genetic dominance. J Med Genet 1994;31:89-98.
93. Xu J, Taylor EW, Panhuysen CI, Prenger VL, Koskela R, Kiemeney B, LaBuda MC, Maestri NE, Meyers DA: Two-locus approach of segregation and linkage analysis in the study of complex traits. Genet Epidemiol 1995;12:825-830.
94. Zinn-Justin A, Abel L: Two-locus developments of the weighted pairwise correlation method for linkage analysis. Genet Epidemiol 1998;15:491-510.