Principal interactions analysis for repeated measures data: Application to gene-gene and gene-environment interactions

Statistics in Medicine

Volumn 31, Issue 22, 2012, Pages 2531-2551

  Mukherjee, Bhramar ^a   Ko, Yi An ^a   Vanderweele, Tyler ^b   Roy, Anindya ^c   Park, Sung Kyun ^a   Chen, Jinbo ^d  

^a UNIVERSITY OF MICHIGAN   (United States)

^b HARVARD UNIVERSITY   (United States)

^c UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

^d UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Biplot; Column interaction; Eigenvalue; Epistasis; Intraclass correlation; Likelihood ratio test; Non additivity; Permutation tests; Pseudo F test; Row interaction; Singular vector; Wishart matrix

Indexed keywords

ARTICLE; CLASSIFICATION; COHORT ANALYSIS; GENE INTERACTION; GENETIC EPISTASIS; GENOTYPE ENVIRONMENT INTERACTION; GEOMETRY; HUMAN; LONGITUDINAL STUDY; OUTCOME ASSESSMENT; PRINCIPAL INTERACTIONS ANALYSIS; QUANTITATIVE ANALYSIS; SAMPLING; STATISTICAL ANALYSIS; STATISTICAL MODEL; STRUCTURE ANALYSIS; UNITED STATES; VETERAN;

AGE FACTORS; BIOLOGICAL MARKERS; COMPUTER SIMULATION; DATA INTERPRETATION, STATISTICAL; GENE-ENVIRONMENT INTERACTION; HEARING; HUMANS; LONGITUDINAL STUDIES; MODELS, STATISTICAL; OXIDATIVE STRESS;

EID: 84866182623     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.5315     Document Type: Article

References (41)

1. Khoury M, Wacholder S. Invited commentary: from genome-wide association studies to gene-environment-wide interaction studies-challenges and opportunities. American Journal of Epidemiology 2009; 169(2):227.
2. Verbeke G, Molenberghs G. Linear Mixed Models for Longitudinal Data. Springer Verlag: New York, 2009.
3. Fitzmaurice G, Laird N, Ware J. Applied Longitudinal Analysis. Wiley-IEEE: New Jersey, 2004.
4. Lin X, Zhang D. Inference in generalized additive mixed models by using smoothing splines. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 1999; 61(2):381-400.
5. Tukey J. One degree of freedom for non-additivity. Biometrics 1949; 5(3):232-242.
6. Mandel J. Non-additivity in two-way analysis of variance. Journal of the American Statistical Association 1961; 56(296):878-888.
7. Gollob H. A statistical model which combines features of factor analytic and analysis of variance techniques. Psychometrika 1968; 33(1):73-115.
8. Mandel J. The partitioning of interaction in analysis of variance. Journal of Research of the National Bureau of Standards-B. Mathematical Sciences 1969; 73(4):309-328.
9. Mandel J. A new analysis of variance model for non-additive data. Technometrics 1971; 13(1):1-18.
10. Johnson D, Graybill F. An analysis of a two-way model with interaction and no replication. Journal of the American Statistical Association 1972; 67(340):862-868.
11. Johnson D, Graybill F. Estimation of σ 2 in a two-way classification model with interaction. Journal of the American Statistical Association 1972; 67(338):388-394.
12. Corsten L, Eijnsbergen A. Multiplicative effects in two-way analysis of variance. Statistica Neerlandica 1972; 26(3):61-68.
13. Hegemann V, Johnson D. On analyzing two-way AoV data with interaction. Technometrics 1976; 18(3):273-281.
14. Marasinghe M, Johnson D. A test of incomplete additivity in the multiplicative interaction model. Journal of the American Statistical Association 1982; 77(380):869-877.
15. Cornelius P. Statistical tests and retention of terms in the additive main effects and multiplicative interaction model for cultivar trials. Crop science 1993; 33(6):1186-1193.
16. Piepho H. Robustness of statistical tests for multiplicative terms in the additive main effects and multiplicative interaction model for cultivar trials. TAG Theoretical and Applied Genetics 1995; 90(3):438-443.
17. Barhdadi A, Dubé MP. Testing for gene-gene interaction with AMMI models. Statistical Applications in Genetics and Molecular Biology 2010; 9(1).
18. Alin A, Kurt S. Testing non-additivity (interaction) in two-way ANOVA tables with no replication. Statistical Methods in Medical Research 2006; 15(1):63.
19. Oman S. Multiplicative effects in mixed model analysis of variance. Biometrika 1991; 78(4):729.
20. Gogel B, Cullis B, Verbyla A. REML estimation of multiplicative effects in multienvironment variety trials. Biometrics 1995; 51(2):744-749.
21. Piepho H. Analyzing genotype-environment data by mixed models with multiplicative terms. Biometrics 1997; 53(2):761-766.
22. Meyer K. Factor-analytic models for genotype x environment type problems and structured covariance matrices. Genetics Selection Evolution 2009; 41(1):21.
23. Jung J, Sun B, Kwon D, Koller D, Foroud T. Allelic-based gene-gene interaction associated with quantitative traits. Genetic Epidemiology 2009; 33(4):332-343.
24. Chatterjee N, Kalaylioglu Z, Moslehi R, Peters U, Wacholder S. Powerful multilocus tests of genetic association in the presence of gene-gene and gene-environment interactions. The American Journal of Human Genetics 2006; 79(6):1002-1016.
25. Maity A, Carroll R, Mammen E, Chatterjee N. Testing in semiparametric models with interaction, with applications to gene-environment interactions. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 2009; 71(1):75-96.
26. Tukey J. The future of data analysis. The Annals of Mathematical Statistics 1962; 33(1):1-67.
27. Eckart C, Young G. The approximation of one matrix by another of lower rank. Psychometrika 1936; 1(3):211-218.
28. Hanumara R, Thompson W. Percentage points of the extreme roots of a Wishart matrix. Biometrika 1968; 55(3):505.
29. GauchJr H. Model selection and validation for yield trials with interaction. Biometrics 1988; 44(3):705-715.
30. Gauch H, Zobel R. Predictive and postdictive success of statistical analyses of yield trials. TAG Theoretical and Applied Genetics 1988; 76(1):1-10.
31. Piepho H. On tests for interaction in a nonreplicated two-way layout. Australian & New Zealand Journal of Statistics 1994; 36(3):363-369.
32. Gabriel K. The biplot graphic display of matrices with application to principal component analysis. Biometrika 1971; 58(3):453.
33. Bradu D, Gabriel K. The biplot as a diagnostic tool for models of two-way tables. Technometrics 1978; 20(1):47-68.
34. Bell B, Rose C, Damon A. The Veterans Administration longitudinal study of healthy aging. The Gerontologist 1966; 6(4):179.
35. Cruickshanks K, Wiley T, Tweed T, Klein B, Klein R, Mares-Perlman J, Nondahl D. Prevalence of hearing loss in older adults in Beaver Dam, Wisconsin. American Journal of Epidemiology 1998; 148(9):879.
36. Mordukhovich I, Wilker E, Suh H, Wright R, Sparrow D, Vokonas P, Schwartz J. Black carbon exposure, oxidative stress genes, and blood pressure in a repeated-measures study. Environmental Health Perspectives 2009; 117(11):1767.
37. Park S, Elmarsafawy S, Mukherjee B, SpiroIII A, Vokonas P, Nie H, Weisskopf M, Schwartz J, Hu H. Cumulative lead exposure and age-related hearing loss: the VA normative aging study. Hearing Research 2010; 269(1-2):48-55.
38. Lee E. Statistical analysis software for multiplicative interaction models, 2004. Unpublished Doctoral Dissertation.
39. Nothnagel M. Simulation of LD block-structured SNP haplotype data and its use for the analysis of case-control data by supervised learning methods. The American Journal of Human Genetics 2002; 71(suppl 4):A2363.
40. Culverhouse R, Klein T, Shannon W. Detecting epistatic interactions contributing to quantitative traits. Genetic Epidemiology 2004; 27(2):141-152.
41. Viele K, Srinivasan C. Parsimonious estimation of multiplicative interaction in analysis of variance using Kullback-Leibler Information. Journal of Statistical Planning and Inference 2000; 84(1-2):201-219.