?rt? ??t?r???????t s?r ??s ??????s???s ?? ??tt? t?ès? ?? r??r????t ????? s????? ??s ?s???ts ????rt??ts ???s ?? ?st é???????t ??????s??? ??é??q??r ??s ???ér??t?s ??rs???t???s s????t??q??s q?????? ???r?? ???? ???s ??ôt?r??s ?? ????s?r?t ??r ??? ??s??s? s??? ?é?ér??? ??s ét???s ???ss????t??r r???r? ????t? ?? ?? ??????té ?t ?? ?? ??????té ??s rés??t?ts ??t???s? ?? ??r?s ?? ?? ????s?r?t t??r?? ??t??r ??s ???? ?r???s ???s ?? ???????s? st?t?st?q?? ?? ????é?s ???ss????t??? ? ???????s? s????????rq???r ?t ???????s? ???t????rq???rs? ???????s? s????????rq???r ??s? à ????t???r ??s ??rq???rs ?ss???és à ?? ??????? ?? ???r ?????q???t ???????????????t ?? ?ê?? t?st ???ss????t???? ???? q?? ????????té ????? t???? str?té??? ???ss? êtr? r???s? ?? q??st??? ???s ?? ???t??t? ??s ???????s, ?rq???rs à t?st?r ?t ??s ???ts ????st?s q?? ???? ???r??? à ?é? t??t?r? ?? ?st ????rt??t q?? ???????s? s????????rq???r s??t ???é? ???? ?ré???t??? q???t ??? ??ss????s ????s q?? ??????t ????t?r ?? q????té ??s rés??t?ts? ??tr? ??s ???s??ér?t???s ???r?r? st?t?st?q?? t??s q?? ?? ??t?r? ?? t?st ?t???sé ???r t?st?r ?? ?ê ,
?é?s? ??s st?? t?st?????s ?t ??s ????r??t?????s s? s??t ???? ?????és s?r ??s ???r????s ???t????rq???rs q?? ?? s??t ????????t ??s s??s ??s?r ??s ?r???è??s ?ét????????q??s é?????t ??és à ????s ?? s?s???t?????té? ?t ??s ???r????s ???t??????s q?? ???s??èr??t ?? ??s????? ?? ??r? q???rs ???s ?? ??t ??????t???r ???s???rs ????s ?? s?s???t?????té? ??t??t????????t ??st??ts? ???st à ??s ??r??èr?s q?? ???s ???s s????s ??tér?ssés? ??s ???r????s ??r ré?r?ss??? ??? ??st?q??? ??r s????s ?? st?t?st?q??s? ???????t??r?s ?t ??r ??rt?t????????ts ré??rs??s q?? ??? ?? ??????s???s ???s ????s é??q?é?s ???st?t???t ??s ?r????????s s???t???s ?r???sé?s ???s ?? ??ttér?t?r?? ???s ?r???s??s?s?st? à ???trô??r ????tr?s q???t?tés st?t?st?q??s r???t???s à ?? ??? ????? ?? t?sts ré???sés? ?? ???? ???trô?? ?? ?r???????té ????t???r??????r? s??s?????té à ?ét??t?r ??s ?r??s???s?t??s? ???s s? ??r ???????? ???s ??? ??t?q?? ?? ???trô?? q????té? ?? ?é???? ?? r?t?r?r ?? ??ét??? ??s ??r? q???rs q?? s?é??rt??t s???????t??????t ?? ??éq?????r? ????r?????????r? ???? ??s té????s? ???????t?? ?st ???? r?t?r?r ?? ????s ??ss????? ?? ???trô?? ?? ???? ????r?ît ???rs t??t à ???t ????té? ??? tr??s?è?? q???t?té ? été ??tr????t? ré??????t ?t ??rr?s???? à ?? ?r???????té ???? ??????s???s ?é?ér???s ,
? ??s ré????s t??t q??????s s??t s???????t???s à ?? ?????? ??é? ????? ???? ?st ?r???sé ???s ?? t?ès? ?? ????? ???????? ??tt? ?é??r??? ?? t?sts séq???t???s s?r ??s ??r?????s ?r????é?s ???? ??s ???r?s ??s tr??s ???r????s ?? t?r??s ?? ???ss????? ?? s??s?????té ?t ?? s?é?????té ??s rés??t?ts? ??t??s q?? ??tt? ?r???é??t?q?? ? ??s ???????t???s ???s ??r??s q?? ??s ét???s ???ss????t??? ???sq?? ?? q??st??? ?? ?? sé???t??? ??s ré????s ?ss???é?s ,
?è?? ??s ???ts ??é?t??r?s ?? ???s ??s ???ts ??ts ???s? ??s ???è??s ?? ?é?r?ss??? ????st?q?? à ???ts ???t?s ?????? ??????t êtr? ?t???sés ???r ?ré??r? ??s ??r?????s ??s?rèt?s ???s ??s ??s?r??t???s ??rré?é?s s?????t???r ??s ???????s?t??s ??s ?r??s s?????? ???ss????t???? ?? ?r?t?q??? ?? t????s ré?????t???s s???s?r???t ??????????t? ?? ???à ??s ???t??rs ??és à ?? q????té ??s ????é?s ?t ??s rés??t?ts? ??s ??????s???s ???tr????t??r?s ??tr? ???? ??????t???s ??????t ?r?????r ?? ré????s ???ér????s ???????q??s ??tr? ??s ??????t???s? ?? ??rt??????r? ?? ??r??t??? ?? ??tt?r? ?? ?éséq?????r? ?? ????s?? ?t ??s ?r???rt???s ???é??q??s ??tr? ??s ??????t???s ???r?????s ???ér??t?s ??s? ?? ?é? ?????r ???r ?? ?é?????rt? ?? ???????? ????s ?? s?s???t?????té? P??tôt q?? ?? s???tér?ss?r à ??s ré?????t???s ?? s??s str??t ?? t?r?? ??ê?? ????s? ?ê??s ???è??s ?ss???és?? ???s ?r???s??s ?? ???s??ér?r ?? ré?????t??? ?? ré????s ???tôt q?? ??s ??rq???rs ,
Genome-wide association studies for common diseases and complex traits, Nature Reviews Genetics, vol.158, issue.2, pp.95-108, 2005. ,
DOI : 10.1086/339258
Family-based association studies, Statistical Methods in Medical Research, vol.9, issue.6, pp.563-587, 2000. ,
DOI : 10.1191/096228000668447080
Detecting Marker-Disease Association by Testing for Hardy-Weinberg Disequilibrium at a Marker Locus, The American Journal of Human Genetics, vol.63, issue.5, pp.1531-1540, 1999. ,
DOI : 10.1086/302114
Tests for Linear Trends in Proportions and Frequencies, Biometrics, vol.11, issue.3, pp.375-386, 1955. ,
DOI : 10.2307/3001775
From Genotypes to Genes: Doubling the Sample Size, Biometrics, vol.53, issue.4, pp.1253-1261, 1997. ,
DOI : 10.2307/2533494
The $\chi^2$ Test of Goodness of Fit, The Annals of Mathematical Statistics, vol.23, issue.3, pp.315-345, 1952. ,
DOI : 10.1214/aoms/1177729380
Accurate power approximations for chi2-tests in case-control association studies of complex disease genes, Annals of Human Genetics, vol.66, issue.4, pp.307-321, 2002. ,
DOI : 10.1046/j.1469-1809.2002.00120.x
Blased Tests of Association: Comparisons of Allele Frequencies when Departing from Hardy-Weinberg Proportions, American Journal of Epidemiology, vol.149, issue.8, pp.706-711, 1999. ,
DOI : 10.1093/oxfordjournals.aje.a009878
Numerical recipies in C. Error, Accuracy, and Stability Genotyping over 100,000 snps on a pair of oligonucleotide arrays, Nature Methods, vol.1, issue.10, pp.109-111, 1992. ,
Detection of genotyping errors by Hardy???Weinberg equilibrium testing, European Journal of Human Genetics, vol.12, issue.5, pp.395-399, 2004. ,
DOI : 10.1038/sj.ejhg.5201164
Controlling the false discovery rate: A practical and powerful approach to multiple testing, J R Stat Soc B, vol.57, pp.289-300, 1995. ,
Complexity and Power in Case-Control Association Studies, The American Journal of Human Genetics, vol.68, issue.5, pp.1229-1237, 2001. ,
DOI : 10.1086/320106
Impact of Violations and Deviations in Hardy-Weinberg Equilibrium on Postulated Gene-Disease Associations, American Journal of Epidemiology, vol.163, issue.4, pp.300-309, 2006. ,
DOI : 10.1093/aje/kwj046
Statistical significance for genomewide studies, Proceedings of the National Academy of Sciences, vol.23, issue.1, pp.9440-9445, 2003. ,
DOI : 10.1002/gepi.1124
RE: "BIASED TESTS OF ASSOCIATION: COMPARISONS OF ALLELE FREQUENCIES WHEN DEPARTING FROM HARDY-WEINBERG PROPORTIONS", American Journal of Epidemiology, vol.154, issue.3 ,
DOI : 10.1093/aje/154.3.287
???Are We There Yet????: Deciding When One Has Demonstrated Specific Genetic Causation in Complex Diseases and Quantitative Traits, The American Journal of Human Genetics, vol.73, issue.4, pp.711-719, 2003. ,
DOI : 10.1086/378900
Nonreplication in Genetic Studies of Complex Diseases-Lessons Learned From Studies of Osteoporosis and Tentative Remedies, Journal of Bone and Mineral Research, vol.18, issue.Suppl 1, pp.365-376, 2005. ,
DOI : 10.1359/JBMR.041129
A Transmission/Disequilibrium Test That Allows for Genotyping Errors in the Analysis of Single-Nucleotide Polymorphism Data, The American Journal of Human Genetics, vol.69, issue.2, pp.371-380, 2001. ,
DOI : 10.1086/321981
Genomic Control for Association Studies, Biometrics, vol.280, issue.4, pp.997-1004, 1999. ,
DOI : 10.1111/j.0006-341X.1999.00997.x
Use of Unlinked Genetic Markers to Detect Population Stratification in Association Studies, The American Journal of Human Genetics, vol.65, issue.1, pp.220-228, 1999. ,
DOI : 10.1086/302449
Theorical and compuational methods in genome research, chapter Evaluating the statistical significance of multiple distinct local alignments, pp.1-14, 1997. ,
Locally optimal subalignments using nonlinear similarity functions, Bulletin of Mathematical Biology, vol.20, issue.5-6, pp.633-660, 1986. ,
DOI : 10.1007/BF02462328
A nonlinear measure of subalignment similarity and its significance levels, Bulletin of Mathematical Biology, vol.82, issue.5-6, pp.617-632, 1986. ,
DOI : 10.1007/BF02462327
Basic local alignment search tool, Journal of Molecular Biology, vol.215, issue.3, pp.403-410, 1990. ,
DOI : 10.1016/S0022-2836(05)80360-2
MDR and PRP: A Comparison of Methods for High-Order Genotype-Phenotype Associations, Human Heredity, vol.58, issue.2, pp.82-92, 2004. ,
DOI : 10.1159/000083029
Controlling the false discovery rate: a practical and powerful approach to multiple testing, Journal of the Royal Statistical Society B, vol.57, pp.289-300, 1995. ,
Methods and algorithms for statistical analysis of protein sequences., Proceedings of the National Academy of Science USA, 1992. ,
DOI : 10.1073/pnas.89.6.2002
Identifying SNPs predictive of phenotype using random forests, Genetic Epidemiology, vol.19, issue.2, pp.171-182, 2005. ,
DOI : 10.1002/gepi.20041
Mapping complex disease loci in whole-genome association studies, Nature, vol.3, issue.6990, pp.446-452, 2004. ,
DOI : 10.1161/01.ATV.0000081635.96290.D3
Detecting Disease Associations due to Linkage Disequilibrium Using Haplotype Tags: A Class of Tests and the Determinants of Statistical Power, Human Heredity, vol.56, issue.1-3, pp.18-31, 2003. ,
DOI : 10.1159/000073729
Genetic and physiological data implicating the new human gene G72 and the gene for D-amino acid oxidase in schizophrenia, Proceedings of the National Academy of Science USA 99, pp.13675-13680, 2002. ,
DOI : 10.1007/s11920-996-0036-9
Use of unphased multilocus genotype data in indirect association studies, Genetic Epidemiology, vol.24, issue.4, pp.415-428, 2004. ,
DOI : 10.1002/gepi.20032
A dna polymorphism discovery resource for research on human genetic variation, Genome Research, vol.8, pp.1229-1231, 1998. ,
Strong Limit Theorems of Empirical Functionals for Large Exceedances of Partial Sums of I.I.D. Variables, The Annals of Probability, vol.19, issue.4, pp.1737-1755, 1991. ,
DOI : 10.1214/aop/1176990232
G72/G30 in Schizophrenia and Bipolar Disorder: Review and Meta-analysis, Biological Psychiatry, vol.60, issue.2, 2006. ,
DOI : 10.1016/j.biopsych.2006.01.019
Power estimation of multiple SNP association test of case-control study and application, Genetic Epidemiology, vol.81, issue.1, pp.22-30, 2004. ,
DOI : 10.1002/gepi.10293
Genome-wide association studies for common diseases and complex traits, Nature Reviews Genetics, vol.158, issue.2, pp.95-108, 2005. ,
DOI : 10.1086/339258
Scan statistics to scan markers for susceptibility genes, Proceedings of the National Academy of Science USA 97, pp.9615-9617, 2000. ,
DOI : 10.1073/pnas.96.26.15173
Mathematical multi-locus approaches to localizing complex human trait genes, Nature Reviews Genetics, vol.11, issue.9, pp.701-709, 2003. ,
DOI : 10.1093/bioinformatics/btf877
Trimming, Weighting, and Grouping SNPs in Human Case-Control Association Studies, Genome Research, vol.11, issue.12, pp.2115-2119, 2001. ,
DOI : 10.1101/gr.204001
Extreme Values in the GI/G/1 Queue, The Annals of Mathematical Statistics, vol.43, issue.2, pp.627-635, 1972. ,
DOI : 10.1214/aoms/1177692642
Statistical signals in bioinformatics, Proceedings of the National Academy of Science USA, pp.13355-13362, 2005. ,
DOI : 10.1016/S0960-9822(00)00005-1
Methods for assessing the statistical significance of molecular sequence features by using general scoring schemes., Proceedings of the National Academy of Science USA, pp.2264-2268, 1990. ,
DOI : 10.1073/pnas.87.6.2264
Applications and statistics for multiple high-scoring segments in molecular sequences., Proceedings of the National Academy of Science USA 90, pp.5873-5877, 1993. ,
DOI : 10.1073/pnas.90.12.5873
Chance and statistical significance in protein and DNA sequence analysis, Science, vol.257, issue.5066, pp.39-49, 1992. ,
DOI : 10.1126/science.1621093
Statistical Methods and Insights for Protein and DNA Sequences, Annual Review of Biophysics and Biophysical Chemistry, vol.20, issue.1, pp.175-203, 1991. ,
DOI : 10.1146/annurev.bb.20.060191.001135
Limit distributions of maximal segmental score among Markov-dependent partial sums, Advances in Applied Probability, vol.16, issue.01, pp.113-140, 1992. ,
DOI : 10.1214/aop/1176992160
Complexity and Power in Case-Control Association Studies, The American Journal of Human Genetics, vol.68, issue.5, pp.1229-1237, 2001. ,
DOI : 10.1086/320106
Association Cluster Detector: a tool for heuristic detection of significance clusters in whole-genome scans, Bioinformatics, vol.21, issue.Suppl 2, pp.180-181, 2005. ,
DOI : 10.1093/bioinformatics/bti1118
Power and efficiency of the tdt and case-control design for association scans, Behavior Genetics, vol.32, issue.2, pp.135-144, 2002. ,
DOI : 10.1023/A:1015205924326
Exact Distribution for the Local Score of One i.i.d. Random Sequence, Journal of Computational Biology, vol.8, issue.4, pp.373-380, 2001. ,
DOI : 10.1089/106652701752236197
URL : https://hal.archives-ouvertes.fr/hal-00714174
Multipoint linkagedisequilibrium mapping narrows location interval and identifies mutation heterogeneity, Proceedings of the National Academy of Science USA, vol.11, pp.13442-13446, 2003. ,
DOI : 10.1073/pnas.2235031100
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC263833
A Combinatorial Partitioning Method to Identify Multilocus Genotypic Partitions That Predict Quantitative Trait Variation, Genome Research, vol.11, issue.3, pp.458-470, 2001. ,
DOI : 10.1101/gr.172901
Effect of Two- and Three-Locus Linkage Disequilibrium on the Power to Detect Marker/Phenotype Associations, Genetics, vol.168, issue.2, pp.1029-1040, 2004. ,
DOI : 10.1534/genetics.103.022335
Assessing Optimal Neural Network Architecture for Identifying Disease-associated Multi-marker Genotypes using a Permutation Test, and Application to Calpain 10 Polymorphisms Associated with Diabetes, Annals of Human Genetics, vol.54, issue.5, pp.348-356, 2003. ,
DOI : 10.1086/302889
Issues in Association Analysis: Error Control in Case-Control Association Studies for Disease Gene Discovery, Human Heredity, vol.58, issue.3-4, pp.171-174, 2004. ,
DOI : 10.1159/000083544
???Are We There Yet????: Deciding When One Has Demonstrated Specific Genetic Causation in Complex Diseases and Quantitative Traits, The American Journal of Human Genetics, vol.73, issue.4, pp.711-719, 2003. ,
DOI : 10.1086/378900
Molecular genetic studies of schizophrenia, European Journal of Human Genetics, vol.139, issue.6, pp.669-680, 2006. ,
DOI : 10.1111/j.1601-183X.2004.00078.x
Searching for genes in complex diseases: lessons from systemic lupus erythematosus, Journal of Clinical Investigation, vol.105, issue.11, pp.1503-1506, 2000. ,
DOI : 10.1172/JCI10266
The Future of Genetic Studies of Complex Human Diseases, Science, vol.273, issue.5281, pp.1516-1517, 1996. ,
DOI : 10.1126/science.273.5281.1516
A linear time algorithm for finding all maximal scoring subsequences, 7th International Conference of Intelligent Systems for Molecular Biology, pp.234-241, 1999. ,
Evaluating associations of haplotypes with traits, Genetic Epidemiology, vol.72, issue.4, pp.348-364, 2004. ,
DOI : 10.1002/gepi.20037
Advanced sequencing technologies: methods and goals, Nature Reviews Genetics, vol.11, issue.5, pp.335-344, 2004. ,
DOI : 10.1016/S0014-5793(02)03275-1
The tdt and other family-based tests for linkage disequilibrium and association, American Journal of Human Genetics, vol.59, pp.983-989, 1996. ,
A new algorithm for haplotype-based association analysis: the Stochastic-EM algorithm, Annals of Human Genetics, vol.85, issue.2, pp.165-177, 2004. ,
DOI : 10.1159/000048602
On the Identification of Disease Mutations by the Analysis of Haplotype Similarity and Goodness of Fit, The American Journal of Human Genetics, vol.72, issue.4, pp.891-902, 2003. ,
DOI : 10.1086/373881
Sum statistics for the joint detection of multiple disease loci in case-control association studies with SNP markers, Genetic Epidemiology, vol.19, issue.4, pp.350-359, 2003. ,
DOI : 10.1002/gepi.10263
Systems of mating, Genetics, vol.6, pp.111-178, 1921. ,
Analysis of Multiple Single Nucleotide Polymorphisms of Candidate Genes Related to Coronary Heart Disease Susceptibility by Using Support Vector Machines, Clinical Chemistry and Laboratory Medicine, vol.41, issue.4, pp.529-534, 2003. ,
DOI : 10.1515/CCLM.2003.080
Tests for Linear Trends in Proportions and Frequencies, Biometrics, vol.11, issue.3, pp.375-386, 1995. ,
DOI : 10.2307/3001775
Asymptotic Power of Chi Square Tests for Linear Trends in Proportions, Biometrics, vol.24, issue.2, pp.315-327, 1968. ,
DOI : 10.2307/2528037
The chi-square test of goodness of fit, Annals of Human Genetics, vol.23, pp.315-345, 1952. ,
Numerical inversion of a characteristic function, Biometrika, vol.60, issue.2, pp.481-482, 1973. ,
DOI : 10.1093/biomet/60.2.415
Algorithm AS 155: The Distribution of a Linear Combination of ?? 2 Random Variables, Applied Statistics, vol.29, issue.3, pp.323-333, 1980. ,
DOI : 10.2307/2346911
Power and Sample Size Calculations for Case-Control Genetic Association Tests when Errors Are Present: Application to Single Nucleotide Polymorphisms, Human Heredity, vol.54, issue.1, pp.22-33, 2002. ,
DOI : 10.1159/000066696
Accurate power approximations for chi2-tests in case-control association studies of complex disease genes, Annals of Human Genetics, vol.66, issue.4, pp.307-321, 2002. ,
DOI : 10.1046/j.1469-1809.2002.00120.x
What SNP genotyping errors are most costly for genetic association studies?, Genetic Epidemiology, vol.164, issue.2, pp.132-141, 2004. ,
DOI : 10.1002/gepi.10301
Complexity and Power in Case-Control Association Studies, The American Journal of Human Genetics, vol.68, issue.5, pp.1229-1237, 2001. ,
DOI : 10.1086/320106
Improving the numerical techniqie for computing the accumulated distribution of a quadratic form in normal variables, Econometric review 21, pp.149-165, 2002. ,
On the Limiting Power Function of the Frequency Chi-Square Test, The Annals of Mathematical Statistics, vol.29, issue.4, pp.1221-1233, 1958. ,
DOI : 10.1214/aoms/1177706453
Searching for genes in complex diseases: lessons from systemic lupus erythematosus, American society for clinical investigation 105, pp.1503-1506, 2000. ,
DOI : 10.1172/JCI10266
Power of Linkage versus Association Analysis of Quantitative Traits, by Use of Variance-Components Models, for Sibship Data, The American Journal of Human Genetics, vol.66, issue.5, pp.1616-1630, 2000. ,
DOI : 10.1086/302891
Case-Control Studies of Genetic Markers: Power and Sample Size Approximations for Armitage???s Test for Trend, Human Heredity, vol.52, issue.3, pp.149-153, 2001. ,
DOI : 10.1159/000053370
Family-based association studies, Statistical Methods in Medical Research, vol.9, issue.6, pp.563-587, 2000. ,
DOI : 10.1191/096228000668447080
(h) ) 0 ?t z P(z|X, ? (h) ) = 1 ,
(h) ) = log z P(X|z, ?)P(z|?) ? log P(X|?) = log z P(X|z, ?)P(z|?) × P(z|X ,
h) ) ?t L(?) s??t é????s? ??tr? ?????t?? ?st ?? ????s?r ??? ?????r ?? ? q?? ??????s? L(?)? ???s ????s ???tré q?? ?? ????t??? l(?|? (h) ) ?st ????ré? ??r L(?) ?t q?? ??s ???? s??t é????s ???r ??? ?ê?? ?????r ?? ?? P?r ???séq???t? t??t ? q?? ???r?ît l(?|? (h) ) ???r?ît é???????t L(?)? ?? ??ç?? à ré???s?r ?? ???????r ???r??ss????t ??ss???? ?? L(?)? ??????r?t??? ?? ?ré????s? ?? ????s?r ? t?? q?? l(?|? (h) ,
?st??ts ??r r????rt à ? ? ? (h+1) = arg max ? z P(z|X, ? (h) ) log P(X|z, ?)P(z|?) = arg max ? z P(z|X, ? (h) ) log P(X, z, ?) P(z, ?) ,
(?)? ??s ????t???s s??t é????s ???r ? = ? (h) ? ??????r?t??? ?? ????s?t ? (h+1) t?? q?? l(?|? (h) ) ?st ????, ) ) ????????t?r ??r ?? ?ê?? ????s??? L(?) à ???q?? ét???? ,
??s q?? ??s séq?????s ?? t????? ? ? ?? ré???s? ?st k t?? q?? n = 2 k ? ?? s????s??t q?? ?? séq????? s??t ????? t????? q?? s??t(n) s??t O(n log, ?é???t q?? k = log 2 (n)? ?ù log 2 ?st ,