Fast methods for spatially correlated multilevel functional data

Biostatistics

Volumn 11, Issue 2, 2010, Pages 177-194

  Staicu, Ana Maria ^a   Crainiceanu, Ciprian M ^b   Carroll, Raymond J ^c  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b JOHNS HOPKINS UNIVERSITY   (United States)

^c TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Colon carcinogenesis; Covariogram estimation; Functional data analysis; Hierarchical modeling; Mixed models; Spatial modeling

Indexed keywords

BUTYRIC ACID DERIVATIVE; CYCLIN DEPENDENT KINASE INHIBITOR 1B;

ALGORITHM; ANALYSIS OF VARIANCE; ANIMAL; ARTICLE; BIOMETRY; CHEMICALLY INDUCED DISORDER; COLON TUMOR; COMPUTER PROGRAM; COMPUTER SIMULATION; DIET; HUMAN; METABOLISM; METHODOLOGY; NONPARAMETRIC TEST; PRINCIPAL COMPONENT ANALYSIS; STATISTICAL MODEL;

ALGORITHMS; ANALYSIS OF VARIANCE; ANIMALS; BIOMETRY; BUTYRATES; COLONIC NEOPLASMS; COMPUTER SIMULATION; CYCLIN-DEPENDENT KINASE INHIBITOR P27; DIET; HUMANS; LIKELIHOOD FUNCTIONS; MODELS, STATISTICAL; PRINCIPAL COMPONENT ANALYSIS; SOFTWARE; STATISTICS, NONPARAMETRIC;

EID: 77749242738     PISSN: 14654644     EISSN: 14684357     Source Type: Journal    
DOI: 10.1093/biostatistics/kxp058     Document Type: Article

References (39)

1. BALADANDAYUTHAPANI, V., MALLICK, B. K., HONG, M. Y., LUPTON, J. R., TURNER, N. D. AND CARROLL, R. J. (2008). Bayesian hierarchical spatially correlated functional data analysis with application to colon carcino-genesis. Biometrics 64, 64-73.
2. BRUMBACK, B. A. AND RICE, J. A. (1998). Smoothing spline models for the analysis of nested and crossed samples of curves (with discussion). Journal of the American Statistical Association 93, 961-976.
3. CHRISTAKOS, G. (1984). On the problem of permissible covariance and variogram models. Water Resources Research 20, 251-265.
4. CRAINICEANU, C. M. (2008). Likelihood ratio testing for zero variance components in linear mixed models. In: David B. Dunson (editor), Model Uncertainty in Random Effects and Latent Variable Models. New York: Springer.
5. CRAINICEANU, C. M. AND RUPPERT, D. (2004). Likelihood ratio tests in linear mixed effects with one variance component. Journal of the Royal Statistical Society, Series B 66, 165-185.
6. CRAINICEANU, C. M., RUPPERT, D., CLAESKENS, G. AND WAND, M. P. (2005). Likelihood ratio tests of polynomial regression against a general nonparametric alternative. Biometrika 92, 91-103.
7. CRESSIE, N. A. C. (1991). Statistics for Spatial Data. New York: Wiley.
8. DI, C., CRAINICEANU, C. M., CAFFO, B. S. AND PUNJABI, N. M. (2009). Multilevel functional principal component analysis. Annals of Applied Statistics 3, 458-488.
9. FAN, J. AND ZHANG, J. T. (2000). Two-step estimation of functional linear models with applications to longitudinal data. Journal of the Royal Statistical Society, Series B 62, 303-322.
10. GRAMBSCH, P. M., RANDALL, B. L., BOSTICK, R. M., POTTER, J. D. AND LOUIS, T. A. (1995). Modeling the labeling index distribution: an application of functional data analysis. Journal of the American Statistical Association 90, 813-821.
11. GREVEN, S., CRAINICEANU, C. M., KUECHENHOFF, H. AND PETERS, A. (2008). Restricted likelihood ratio testing for zero variance components in linear mixed models. Journal of Computational and Graphical Statistics 17, 870-891.
12. GUO, W. (2002). Functional mixed effects models. Biometrics 58, 121-128.
13. HALL, P., MÜ LLER, H.-G. AND YAO, F. (2008). Modeling sparse generalized longitudinal observations with latent Gaussian processes. Journal of the Royal Statistical Society, Series B 70, 703-723.
14. JOURNEL, A. G. AND HUJIBREGTS, C. J. (1978). Mining Geostatistic. London: Academic Press.
15. LI, Y., WANG, N., HONG, M., TURNER, N. D., LUPTON, J. R. AND CARROLL, R. J. (2007). Nonparametric estimation of correlation functions in longitudinal and spatial data, with application to colon carcinogenesis experiments. The Annals of Statistics 35, 1600-1643.
16. LIANG, H., WU, H. AND CARROLL, R. J. (2003). The relationship between virologic and immunologic responses in AIDS clinical research using mixed-effects varying-coeffcient models with measurement error. Biostatistics 4, 297-312.
17. MARTINEZ, J. G., HUANG, J. Z., BURGHARDT, R. C., BARHOUMI, R. AND CARROLL, R. J. (2010). Use of multiple singular value decompositions to analyze complex intracellular calcium ion signals. Annals of Applied Statistics (in press).
18. MATHERON, G. (1962). Traité de Geostatistique Appliqué e, Tome 1. Paris: Technip.
19. MORRIS, J. S. AND CARROLL, R. J. (2006). Wavelet-based functional mixed models. Journal of the Royal Statistical Society, Series B 68, 179-199.
20. MORRIS, J. S., VANNUCCI, M., BROWN, P. J. AND CARROLL, R. J. (2003). Wavelet-based nonparametric modeling of hierarchical functions in colon carcinogenesis (with discussion). Journal of the American Statistical Association 98, 573-583.
21. MORRIS, J. S., WANG, N., LUPTON, J. R., CHAPKIN, R. S., TURNER, N. D., HONG, M. Y. AND CARROLL, R. J. (2001). Parametric and nonparametric methods for understanding the relationship between carcinogen-induced DNA adduct levels in distal and proximal regions of the colon. Journal of the American Statistical Association 96, 816-826.
22. MÜ LLER, H.-G. (2005). Functional modelling and classifcation of longitudinal data. Scandivanian Journal of Statistics 32, 223-240.
23. MÜ LLER, H.-G. AND STADTMÜ LLER, U. (2005). Generalized functional linear models. The Annals of Statistics 33, 774-805.
24. RAMSAY, J. O. AND SILVERMAN, B. W. (2005). Functional Data Analysis. New York: Springer.
25. RICE, J. A. AND WU, C. (2001). Nonparametric mixed effects models for unequally sampled noisy curves. Biometrics 57, 253-269.
26. RONCUCCI, L., PEDRONI, M., VACCINA, F., BENATTI, P., MARZONA, L. AND DE POL, A. (2000). Aberrant crypt foci in colorectal carcinogenesis: cell and crypt dynamics. Cell Proliferation 33, 1-18.
27. RUPPERT, D., WAND, M. P. AND CARROLL, R. J. (2003). Semiparametric Regression. Cambridge: Cambridge University Press.
28. SGAMBATO, A., CITTADINI, A., FARAGLIA, B. AND WEINSTEIN, I. B. (2000). Multiple functions of p27kip1 and its alterations in tumor cells: a review. Journal of Cell Biology 183, 18-27.
29. SHI, M., WEISS, R. E. AND TAYLOR, J. M. G. (1996). An analysis of paediatric CD4 counts for acquired immune defciency syndrome using fexible random curves. Applied Statistics 45, 151-163. (Pubitemid 126331741)
30. STANISWALIS, J. G. AND LEE, J. J. (1998). Nonparametric regression analysis of longitudinal data. Journal of the American Statistical Association 93, 1403-1418.
31. STRAM, D. O. AND LEE, J. W. (1994). Variance components testing in the longitudinal mixed effects model. Biometrics 50, 1171-1177.
32. WANG, Y. (1998). Mixed effects smoothing spline analysis of variance. Journal of the Royal Statistical Society, Series B 60, 159-174.
33. WU, H. AND LIANG, H. (2004). Backftting random varying-coeffcient models with time-dependent smoothing covariates. Scandianavian Journal of Statistics 31, 3-20.
34. WU, H. AND ZHANG, J. T. (2002). Local polynomial mixed-effects models for longitudinal data. Journal of the American Statistical Association 97, 883-897.
35. WU, H. AND ZHANG, J. T. (2006). Nonparametric Regression Methods for Longitudinal Data Analysis: Mixed-Effects Modeling Approaches. New York: John Wiley & Sons.
36. XIAO, G., REILLY, C. AND KHODURSKY, A. B. (2009). Improved detection of differentially expressed genes through incorporation of gene locations. Biometrics 65, 805-814.
37. YAO, F. AND LEE, T. C. M. (2006). Penalized spline models for functional principal component analysis. Journal of the Royal Statistical Society, Series B 68, 3-25.
38. YAO, F., MÜ LLER, H.-G., CLIFFORD, A. J., DUEKER, S. R., FOLLETT, J., LIN Y., BUCHHOLZ, B. A. AND VOGEL, J. S. (2003). Shrinkage estimation for functional principal component scores with application to the population kinetics of plasma folate. Biometrics 59, 676-685.
39. YAO, F., MÜ LLER, H.-G. AND WANG, J.-L. (2005). Functional data analysis for sparse longitudinal data. Journal of the American Statistical Association 100, 577-590.