Cox regression models with functional covariates for survival data

Statistical Modelling

Volumn 15, Issue 3, 2015, Pages 256-278

  Gellar, Jonathan E ^a   Colantuoni, Elizabeth ^a   Needham, Dale M ^b   Crainiceanu, Ciprian M ^a  

^a JOHNS HOPKINS BLOOMBERG SCHOOL OF PUBLIC HEALTH   (United States)

^b JOHNS HOPKINS UNIVERSITY SCHOOL OF MEDICINE   (United States)

Author keywords

Cox proportional hazards model; functional data analysis; intensive care unit; nonparametric statistics; Survival analysis

Indexed keywords

EID: 84930386213     PISSN: 1471082X     EISSN: 14770342     Source Type: Journal    
DOI: 10.1177/1471082X14565526     Document Type: Article

References (59)

1. Belitz C,Brezger A,Kneib T,Lang S,Umlauf N.BayesX: Software for Bayesian inference in structured additive regression models. 2013;:
2. Bender R,Augustin T,Blettner M.Generating survival times to simulate Cox proportional hazards models.Statistics in medicine. 2005;24:1713-23
3. J Buckley,James I.Biometrika. 1979;66:429-36
4. K Burnham,Anderson DModel selection and multimodel inference: a practical information-theoretic approach. New York:: Springer Verlag; 2002:
5. Cai T,RJ Hyndman,MP Wand.Mixed model-based hazard estimation.Journal of Computational and Graphical Statistics. 2002;11:784-98
6. T Cai,RA Betensky.Hazard regression for interval-censored data with penalized spline.Biometrics. 2003;59:570-79
7. Cardot H,F Ferraty,Sarda P.Spline estimators for the functional linear model.Statistica Sinica. 2003;13:571-91
8. H Cardot,Sarda P.Estimation in generalized linear models for functional data via penalized likelihood.Journal of Multivariate Analysis. 2005;92:24-41
9. Cardot H,F Ferraty,Sarda P.Statistics & Probability Letters. 1999;45:11-22
10. Charlson ME,Pompei P,KL Ales,MacKenzie CR.A new method of classifying prognostic comorbidity in longitudinal stu- dies: development and validation.Journal Of Chronic Diseases. 1987;:373-83
11. J Chiou,Müller H.Modeling hazard rates as functional data for the analysis of cohort lifetables and mortality forecasting.Journal of the American Statistical Association. 2009;104:572-85
12. Cox D.Regression models and lifetables.Journal of the Royal Statistical Society. Series B (Methodological). 1972;34:187-220
13. Crainiceanu CM,Staicu AM,S Ray,Punjabi N.Bootstrap-based inference on the difference in the means of two correlated functional processes.Statistics in medicine. 2012a;31:3223-40
14. CrainiceanuCReissPGoldsmithJHuangLHuoLScheiplFGrevenSHarezlakJKunduMZhaoY (2012b) Refund: regression with functional data, R package version 0.1–6.
15. PHC Eilers,BD Marx.Flexible smoothing with B-splines and penalties.Statistical Science. 1996;11:89-121
16. Ferraty FRecent advances in functional data analysis and related topics. Berlin: Springer Verlag; 2011:
17. F Ferraty,Vieu PNonparametric functional data analysis: Theory and practice. New York:: Springer Verlag; 2006:
18. GellarJEColantuoniEDMNeedhamCMCrainiceanu (2014) Variable-domain functional regression for modeling ICU data. Journal of the American Statistical Association, 109(508), 1425–39. 10.1080/01621459.2014.940044http://biostats.bepress.com/jhubiostat/paper261.
19. Goldsmith J,Bobb J,Crainiceanu CM,B Caffo,Reich D.Penalized functional regression.Journal of Computational and Graphical Statistics. 2011;20:830-51
20. P Grambsch,Therneau T. Proportional hazards tests and diagnostics based on weighted residuals.Biometrika. 1994;81:515-26
21. Gray R.Flexible methods for analyzing survival data using splines, with applications to breast cancer prognosis.Journal of the American Statistical Association. 1992;87:942-51
22. J Harezlak,TW RandolphRecent advances in functional data analysis and related topics. Heidelberg: Springer Verlag; 2011:161-67.
23. Harrell FE,KL Lee,DB Mark.Multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors.Statistics in Medicine. 1996;15:361-87
24. Hurvich CM,JS Simonoff,CL Tsai.Smoothing parameter selection in nonparametric regression using an improved akaike information criterion.Journal of the Royal Statistical Society. Series B (Methodological). 1998;60:271-93
25. Ibrahim JG,H Chu,LM Chen.Basic concepts and methods for joint models of longitudinal and survival data.Journal of clinical oncology: official journal of the American Society of Clinical Oncology. 2010;28:2796-801
26. GM James.Generalized linear models with functional predictors.Journal of the Royal Statistical Society: Series B (Statistical Methodology). 2002;64:411-32
27. James GM,J Wang,Zhu J.Functional linear regression thats interpretable.The Annals of Statistics. 2009;37:2083-108
28. T Kneib,Fhrmeir L.A mixed model approach for geoadditive hazard regression.Scandinavian Journal of Statistics. 2007;34:207-28
29. B Marx,Eilers P.Generalized linear regression on sampled signals and curves: A P-spline approach.Technometrics. 1999;41:1-13
30. P McCullagh,JA NelderGeneralized linear models. Boca Raton:: Chapman & Hall/CRC; 1989:
31. McLeanMWHookerGStaicuA.-M.FScheiplRuppertD (2013) Functional generalized additive models. Journal of Computational and Graphical Statistics, 23, 249–69, 130322113058003. ISSN 1061-8600. doi: 10.1080/10618600.2012.729985. http://www.tandfonline.com/doi/abs/10.1080/10618600.2012.729985.
32. R Miller,Halpern J.Regression with censored data.Biometrika. 1982;69:521-31
33. Müller H-G,Stadtmüller U.Generalized functional linear models.The Annals of Statistics. 2005;33:774-805
34. Müller H,Zhang Y.Time-varying functional regression for predicting remaining lifetime distributions from longitudinal trajectories.Biometrics. 2005;61:1064-75
35. NeedhamDMDennisonCRDowdyDWMendez-TellezPaCieslaNDesaiSVSevranskyJShanholtzCScharfsteinDHerridgeMSPJPronovost (2006) Study protocol: The improving care of acute lung injury patients (ICAP) study. Critical care (London, England), 10, R9. ISSN 1466-609X. doi: 10.1186/cc3948. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1550857&tool=pmcentrez&rendertype=abstract.
36. O'sullivan F,BS Yandell,WJJ Raynor.Automatic smoothing of regression functions in generalized linear models.Journal of the American Statistical Association. 1986;81:96-103
37. O'Sullivan F.Nonparametric estimation of relative risk using splines and cross-validation.SIAM Journal on Scientific and Statistical Computing. 1988;9:531-42
38. R Development Core Team (2011) R: a language and environment for statistical computing. ISSN 16000706. http://www.r-project.org.
39. JO Ramsay,Silverman BFunctional data analysis. New York: Springer; 2005:
40. Ramsay JO,Hooker G,Graves SFunctional data analysis with R and MATLAB. New York:: Springer Verlag; 2009:
41. PT Reiss,RT Ogden.Functional principal component regression and functional partial least squares.Journal of the American Statistical Association. 2007;102:984-96
42. RizopoulosD (2012) Joint models for longitudinal and time-to-event data: With applications in R. Boca Raton, FL: Chapman & Hall/CRC. http://books.google.com/books?hl=en&lr=&id=xotIpb2duaMC&oi=fnd&pg=PP1&dq=Joint+Models+for+Longitudinal+and+Time-to-Event+Data:+With+Applications+in+R&ots=ODo7KlbUmd&sig=fsARbJp2SJbuUxcWx_GOjRUHrUQ.
43. Ruppert D,MP Wand,RJ CarrollSemiparametric regression. New York:: Cambridge University Press; 2003:
44. J Schmee,Hahn G.A simple method for regression analysis with censored data.Technometrics. 1979;21:417-32
45. ShinoharaRCrainiceanuCBCaffoReichD (2011) Longitudinal analysis of spatiotemporal processes: a case study of dynamic contrast-enhanced magnetic resonance imaging in multiple sclerosis. Technical Report September 2011. http://biostats.bepress.com/jhubiostat/paper231/.
46. J Staniswalis,Lee J.Nonpametric regression analysis of longitudinal data.Journal of the American Statistical Association. 1998;93:1403-18
47. Strasak A,Lang S,T Kneib,Brant L.Use of penalized splines in extended Cox-type additive hazard regression to flexibly estimate the effect of time-varying serum uric acid on risk of cancer incidence: a prospective, population-based study in 78,850 men.Annals of Epidemiology. 2009;19:15-24
48. Swihart BJ,Caffo B,James BD,Strand M,BS Schwartz,NM Punjabi.Lasagna plots: a saucy alternative to spaghetti plots.Epidemiology (Cambridge, Mass.). 2010;21:621-25
49. TM Therneau.Coxme: Mixed Effects Cox Models.R package version 2.2-3. http://CRAN.R-project.org/package=coxme. 2012;:
50. TM Therneau.A package for survival analysis in S.R package version 2.37-7. http://CRAN.R-project.org/package=survival. 2014;:
51. TM Therneau,PM Grambsch.Penalized Cox models and frailty.Technical report, Division of Biostatistics. Mayo Clinic; Rochester, MN. 1998;:1-58
52. Therneau TM,PM Grambsch,VS Pankratz.Penalized survival models and frailty.Journal of Computational and Graphical Statistics. 2003;12:156-75
53. A Tsiatis,Davidian M.Joint modeling of longitudinal and time-to-event data: an overview.Statistica Sinica. 2004;14:809-34
54. van Houwelingen H,Putter HDynamic prediction in clinical survival analysis. Boca Raton, FL: Chapman & Hall/CRC; 2012:
55. PJ Verweij,Van Houwelingen HC.Cross-validation in survival analysis.Statistics in medicine. 1993;12:2305-14
56. P Verweij,HV Houwelingen.Penalized likelihood in Cox regression.Statistics in Medicine. 1994;13:2427-36
57. Yao F,Müller H-G,Clifford AJ,Dueker SR,Follett J,Lin Y,Buchholz Ba,JS Vogel.Shrinkage estimation for functional principal component scores with application to the population kinetics of plasma folate.Biometrics. 2003;59:676-85
58. M Zambon,Vincent J-L.Mortality rates for patients with acute lung injury/ARDS have decreased over time.Chest. 2008;133:1120-27
59. D Zucker,Karr A.Nonparametric survival analysis with time-dependent covariate effects: a penalized partial likelihood approach.The Annals of Statistics. 1990;18:329-53