A general model for detecting genetic determinants underlying longitudinal traits with unequally spaced measurements and nonstationary covariance structure

Biostatistics

Volumn 6, Issue 3, 2005, Pages 420-433

  Hou, Wei ^a   Garvan, Cynthia W ^a   Zhao, Wei ^a   Behnke, Marylou ^b   Eyler, Fonda Davis ^b   Wu, Rongling ^a  

^a University of Florida ^*  (United States)

^b UNIVERSITY OF FLORIDA COLLEGE OF MEDICINE   (United States)

Author keywords

EM algorithm; Genetic determinant; Longitudinal trait; Mixture model

Indexed keywords

ALGORITHM; ALLELE; ARTICLE; BIOLOGICAL MODEL; BIOMETRY; CHILD; CHILD DEVELOPMENT; GENE FREQUENCY; GROWTH, DEVELOPMENT AND AGING; HEAD; HISTOLOGY; HUMAN; INFANT; LONGITUDINAL STUDY; NEWBORN; PRESCHOOL CHILD; QUANTITATIVE TRAIT LOCUS; STATISTICAL MODEL;

ALGORITHMS; ALLELES; BIOMETRY; CHILD; CHILD DEVELOPMENT; CHILD, PRESCHOOL; GENE FREQUENCY; HEAD; HUMANS; INFANT; INFANT, NEWBORN; LONGITUDINAL STUDIES; MODELS, GENETIC; MODELS, STATISTICAL; QUANTITATIVE TRAIT LOCI;

EID: 26444520027     PISSN: 14654644     EISSN: 14684357     Source Type: Journal    
DOI: 10.1093/biostatistics/kxi019     Document Type: Article

References (41)

1. ATCHLEY, W. R. AND ZHU, J. (1997). Developmental quantitative genetics, conditional epigenetic variability and growth in mice. Genetics 147, 765-776.
2. BARRET, W. (1979). A theorem on inverse of tridiagonal matrices. Linear Algebra and Its Applications 27, 211-217.
3. BOX, G. E. P. AND COX, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society: Series B 26, 211-252.
4. CARROLL, R. J. AND RUPPERT, D. (1984). Power-transformations when fitting theoretical models to data. Journal of the American Statistical Association 79, 321-328.
5. CHURCHILL, G. A. AND DOERGE, R. W. (1994). Empirical threshold values for quantitative trait mapping. Genetics 138, 963-971.
6. DEMPSTER, A. P., LAIRD, N. M. AND RUBIN, D. B. (1977). Maximum likelihood from incomplete data via EM algorithm. Journal of the Royal Statistical Society: Series B 39, 1-38.
7. DIGGLE, P. J., HEAGERTY, P., LIANG, K. Y. AND ZEGER, S. L. (2002). Analysis of Longitudinal. Data. Oxford, UK: Oxford University Press.
8. EYLER, F. D., BEHNKE, M., CONLON, M., WOODS, N. S. AND WOBIE, K. (1998a). Birth outcome from a prospective matched study of prenatal crack/cocaine use. Part I: Interactive and dose effects on health and growth. Pediatrics 101, 229-237.
9. EYLER, F. D., BEHNKE, M., CONLON, M., WOODS, N. S. AND WOBIE, K. (1998b). Birth outcome from a prospective, matched study of prenatal crack/cocaine use. Part II: Interactive and dose effects on neurobehavioral assessment. Pediatrics 101, 237-241.
10. GABRIEL, K. R. (1962). Antedependence analysis of an ordered set of variables. Annals of Mathematical Statistics 33, 201-212.
11. GONG, Y., WANG, Z. H., ZHU, Y. AND WU, R. L. (2004). A statistical model for high-resolution mapping of quantitative trait loci affecting pharmacodynamic processes. The Pharmacogenomics Journal 4, 315-321.
12. JENSS, R. M. AND BAYLEY, N. ( 1937). A mathematical method for studying the growth of a child. Human Biology 9, 556-563.
13. LAGARIUS, J. C., REEDS, J. A., WRIGHT, M. H. AND WRIGHT, P. E. (1998). Convergence properties of the Neler-Mead simplex method in low dimensions. SIAM Journal of Optimization 9, 112-147.
14. LANDER, E. S. AND BOTSTEIN, D. (1989). Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics 121, 185-199.
15. Lou, X.-Y., CASELLA, G., LITTELL, R. C., YANG, M. K. C. AND WU, R. L. (2003). A haplotype-based algorithm for multilocus linkage disequilibrium mapping of quantitative trait loci with epistasis in natural populations. Genetics 163, 1533-1548.
16. LOUIS, T. A. (1982). Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society, Series B 44, 226-233.
17. LYNCH, M. AND WALSH, B. (1998). Genetics and Analysis of Quantitative Traits. Sunderland, MA: Sinauer.
18. MA, C.-X., CASELLA, G. AND WU, R. L. (2002). Functional mapping of quantitative trait loci underlying the character process: a theoretical framework. Genetics 161, 1751-1762.
19. MA, C.-X., WU, R. L. AND CASELLA, G. (2004). FunMap: functional mapping of complex traits. Bioinformatics 20, 1808-1811.
20. MACCHIAVELLI, R. E. AND ARNOLD, S. F. (1994). Variable order antedependence models. Commuications in Statistics: Theory and Methods 23, 2683-2699.
21. MENG, X.-L. AND RUBIN, D. B. (1991). Using EM to obtain asymptotic variance-covariance matrices: the SEM algorithm. Journal of the American Statistical Association 86, 899-909.
22. NELDER, J. A. AND MEAD, R. (1965). A simplex method for function minimization. Computer Journal 7, 308-313.
23. NÚÑEZ-ANTÓN, V. (1997). Longitudinal data analysis: non-stationary error structures and antedependence models. Applied Stochastic Models and Data Analysis 13, 279-287.
24. NÚÑEZ-ANTÓN, V. AND WOODWORTH, G. G. (1994). Analysis of longitudinal data with unequally spaced observations and time-dependent correlated errors. Biometrics 50, 445-456.
25. NÚÑEZ-ANTÓN, V. AND ZIMMERMAN, D. L. (2000). Modeling nonstationary longitudinal data. Biometrics 56, 699-705.
26. SAMUELSEN, S. O., STENE, L. C. AND BAKKETEIG, L. S. (2004). Association of head circumference at birth among sibling pairs. Paediatric and Perinatal Epidemiology 18, 26-34.
27. VENABLES, W. N. AND RIPLEY, B. D. (2002). Modern Applied Statistics with S, 4th edition. New York: Springer.
28. VON BERTALANFFY, L. (1957). Quantitative laws in metabolism and growth. Quarterly Review of Biology 32, 217-231.
29. WANG, Z. H. AND WU, R. L. (2004). A statistical model for high-resolution mapping of quantitative trait loci determining human HIV-1 dynamics. Statistics in Medicine 23, 3033-3051.
30. WEST, G. B., BROWN, J. H. AND ENQUIST, B. J. (2001). A general model for ontogenetic growth. Nature 413, 628-631.
31. WOLFINGER, R. D. (1996). Heterogeneous variance-covariance structures for repeated measures. Journal of Agricultural, Biological, and Environmental Statistics 1, 205-230.
32. WU, R. L., MA, C.-X., CHANG, M., LITTELL, R. C., WU, S. S., YIN, T. M., HUANG, M. R., WANG, M. X. AND CASELLA, G. (2002a). A logistic mixture model for characterizing genetic determinants causing differentiation in growth trajectories. Genetical Research 19, 235-245.
33. WU, R. L., MA, C.-X., LIN, M. AND CASELLA, G. (2004a). A general framework for analyzing the genetic architecture of developmental characteristics. Genetics 166, 1541-1551.
34. WU, R. L., MA, C.-X., LIN, M., WANG, Z. H. AND CASELLA, G. (2004b). Functional mapping of quantitative trait loci underlying growth trajectories using a transform-both-sides logistic model. Biometrics 60, 729-738.
35. WU, R. L., MA, C.-X., LITTELL, R. C. AND CASELLA, G. (2002b). A statistical model for the genetic origin of allometric scaling laws in biology. Journal of Theoretical Biology 217, 275-287.
36. WU, R. L., MA, C.-X., YANG, M. C. K., CHANG, M., SANTRA, U., WU, S. S., HUANG, M., WANG, M. AND CASELLA, G. (2003a). Quantitative trait loci for growth in Populus. Genetical Research 81, 51-64.
37. WU, R. L., MA, C.-X., ZHAO, W. AND CASELLA, G. (2003b). Functional mapping of quantitative trait loci underlying growth rates: a parametric model. Physiological Genomics 14, 241-249.
38. ZHAO, W., WU, R. L., MA, C.-X. AND CASELLA, G. (2004). A fast algorithm for functional mapping of complex traits. Genetics 167, 2133-2137.
39. ZIMMERMAN, D. L. AND NÚÑEZ-ANTÓN, V. (1997). Structured antedependence models for longitudinal data. In Gregoire, G., Brillinger, D. R., Diggle, P. J., Russek-Cohen, E., Warren, W. G., and Wolfinger R. D. (eds), Modelling Longitudinal and Spatially Correlated Data: Methods, Applications, and Future Directions. Lecture Notes Series in Statistics No. 122. New York: Springer, pp. 63-76.
40. ZIMMERMAN, D. L. AND NÚÑEZ-ANTÓN, V. (2001). Parametric modeling of growth curve data: an overview (with discussion). Test 10, 1-73.
41. ZIMMERMAN, D. L., NÚÑEZ-ANTÓN, V. AND EL BARMI, H. (1998). Computational aspects of likelihood-based estimation of first-order antedependence models. Journal of Statistical Computation and Simulation 60, 67-84.