Response-Adaptive Regression for Longitudinal Data

Biometrics

Volumn 67, Issue 3, 2011, Pages 852-860

  Wu, Shuang ^a   Müller, Hans Georg ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

AIDS clinical trials; Functional data analysis; Functional linear regression; Growth curves; Kiwi growth; Prediction; Repeated measurements; Sparse data; Viral load

Indexed keywords

LINEAR REGRESSION; TRAJECTORIES;

AIDS CLINICAL TRIAL; FUNCTIONAL DATA ANALYSIS; FUNCTIONAL LINEAR REGRESSION; FUNCTIONAL REGRESSION; GROWTH CURVES; KIWI GROWTH; LONGITUDINAL DATA; REPEATED MEASUREMENTS; SPARSE DATA; VIRAL LOAD;

FORECASTING;

ACQUIRED IMMUNE DEFICIENCY SYNDROME; BIOMETRY; BIRD; DATA SET; DATABASE; ERROR ANALYSIS; GROWTH CURVE; LIFE SCIENCE; NUMERICAL MODEL; PREDICTION; REGRESSION ANALYSIS; VIRUS; WEIGHT;

EID: 80052790467     PISSN: 0006341X     EISSN: 15410420     Source Type: Journal    
DOI: 10.1111/j.1541-0420.2010.01518.x     Document Type: Article

References (28)

1. Ash, R. B. and Gardner, M. F. (1975). Topics in Stochastic Processes, Probability and Mathematical Statistics, Vol. 27. New York Academic Press.
2. Cai, T. and Hall, P. (2006). Prediction in functional linear regression. The Annals of Statistics 34, 2159-2179.
3. Cardot, H., Ferraty, F., and Sarda, P. (1999). Functional linear model. Statistics and Probability Letters 45, 11-22.
4. Cardot, H., Ferraty, F., and Sarda, P. (2003). Spline estimators for the functional linear model. Statistica Sinica 13, 571-591.
5. Cardot, H., Crambes, C., Kneip, A., and Sarda, P. (2007). Smoothing splines estimators in functional linear regression with errors-in-variables. Computational Statistics and Data Analysis 51, 4832-4848.
6. Colbourne, R., Bassett, S., Billing, T., McCormick, H., McLennan, J., Nelson, A., and Robertson, H. (2005). The development of operation nest egg as a tool in the conservation management of kiwi. Science for Conservation 259.
7. Crambes, C., Kneip, A., and Sarda, P. (2009). Smoothing splines estimators for functional linear regression. The Annals of Statistics 37, 35-72.
8. Draper, N. R. and Smith, H. (1998). Applied Regression Analysis. New York John Wiley & Sons.
9. Faraway, J. J. (1997). Regression analysis for a functional response. Technometrics 39, 254-261.
10. Hall, P. and Horowitz, J. L. (2007). Methodology and convergence rates for functional linear regression. The Annals of Statistics 35, 70-91.
11. He, G., Müller, H.-G., and Wang, J.-L. (2000). Extending correlation and regression from multivariate to functional data. In Asymptotics in Statistics and Probability, M. L. Puri (ed), 301-315. Amsterdam: VSP International Science Publishers.
12. James, G. M. and Silverman, B. W. (2005). Functional adaptive model estimation. Journal of the American Statistical Association 100, 565-576.
13. Jones, G., Leung, J., and Robertson, H. (2009). A mixed model for investigating a population of asymptotic growth curves using restricted b-splines. Journal of Agricultural, Biological, and Environmental Statistics 14, 66-78.
14. Lederman, M. M., Connick, E., Landay, A., Kuritzkes, D. R., Spritzler, J., Clair, M. S., Kotzin, B. L., Fox, L., Chiozzi, M. H., Leonard, J. M., Rousseau, F., Wade, M., D'Arc Roe, J., Martinez, A., and Kessler, H. (1998). Immunologic responses associated with 12 weeks of combination antiretroviral therapy consisting of zidovudine, lamivudine, and ritonavir: Results of AIDS Clinical Trials Group Protocol 315. Journal of Infectious Diseases 178, 70-79.
15. Liang, H., Wu, H., and Carroll, R. J. (2003). The relationship between virologic and immunologic responses in AIDS clinical research using mixed-effects varying-coefficient models with measurement error. Biostatistics 4, 297-312.
16. Liu, B. and Müller, H.-G. (2008). Functional data analysis for sparse auction data. In Statistical Methods in eCommerce Research, W. Jank and G. Shmueli (eds), 269-290. New York Wiley.
17. Liu, B. and Müller, H.-G. (2009). Estimating derivatives for samples of sparsely observed functions, with application to on-line auction dynamics. Journal of the American Statistical Association 104, 704-714.
18. Malfait, N. and Ramsay, J. O. (2003). The historical functional linear model. Canadian Journal of Statistics, La Revue Canadienne de Statistique 31, 115-128.
19. Müller, H.-G. and Yao, F. (2008). Functional additive models. Journal of the American Statistical Association 103, 1534-1544.
20. Müller, H.-G., Chiou, J.-M., and Leng, X. (2008). Inferring gene expression dynamics via functional regression analysis. BMC Bioinformatics 9, 60.
21. Ramsay, J. O. and Dalzell, C. J. (1991). Some tools for functional data analysis. Journal of the Royal Statistical Society, Series B (Statistical Methodology) 53, 539-572.
22. Ramsay, J. O. and Silverman, B. W. (2005). Functional Data Analysis, 2nd edition. New York Springer.
23. Rice, J. A. and Silverman, B. W. (1991). Estimating the mean and covariance structure nonparametrically when the data are curves. Journal of the Royal Statistical Society, Series B (Statistical Methodology) 53, 233-243.
24. Rice, J. A. and Wu, C. O. (2001). Nonparametric mixed effects models for unequally sampled noisy curves. Biometrics 57, 253-259.
25. Sy, J. P., Taylor, J. M. G., and Cumberland, W. G. (1997). A stochastic model for the analysis of bivariate longitudinal AIDS data. Biometrics 53, 542-555.
26. Wu, H. and Liang, H. (2004). Backfitting random varying-coefficient models with time-dependent smoothing covariates. Scandinavian Journal of Statistics 31, 3-19.
27. Yao, F., Müller, H.-G., and Wang, J.-L. (2005a). Functional data analysis for sparse longitudinal data. Journal of the American Statistical Association 100, 577-590.
28. Yao, F., Müller, H.-G., and Wang, J.-L. (2005b). Functional linear regression analysis for longitudinal data. The Annals of Statistics 33, 2873-2903.