Spline-based accelerated failure time model.
accelerated failure time model
model misspecification
simulations
spline-based method
survival analysis
Journal
Statistics in medicine
ISSN: 1097-0258
Titre abrégé: Stat Med
Pays: England
ID NLM: 8215016
Informations de publication
Date de publication:
30 01 2021
30 01 2021
Historique:
received:
17
06
2019
revised:
05
08
2020
accepted:
06
10
2020
pubmed:
27
10
2020
medline:
22
6
2021
entrez:
26
10
2020
Statut:
ppublish
Résumé
The accelerated failure time (AFT) model has been suggested as an alternative to the Cox proportional hazards model. However, a parametric AFT model requires the specification of an appropriate distribution for the event time, which is often difficult to identify in real-life studies and may limit applications. A semiparametric AFT model was developed by Komárek et al based on smoothed error distribution that does not require such specification. In this article, we develop a spline-based AFT model that also does not require specification of the parametric family of event time distribution. The baseline hazard function is modeled by regression B-splines, allowing for the estimation of a variety of smooth and flexible shapes. In comprehensive simulations, we validate the performance of our approach and compare with the results from parametric AFT models and the approach of Komárek. Both the proposed spline-based AFT model and the approach of Komárek provided unbiased estimates of covariate effects and survival curves for a variety of scenarios in which the event time followed different distributions, including both simple and complex cases. Spline-based estimates of the baseline hazard showed also a satisfactory numerical stability. As expected, the baseline hazard and survival probabilities estimated by the misspecified parametric AFT models deviated from the truth. We illustrated the application of the proposed model in a study of colon cancer.
Types de publication
Journal Article
Research Support, Non-U.S. Gov't
Langues
eng
Sous-ensembles de citation
IM
Pagination
481-497Commentaires et corrections
Type : CommentIn
Informations de copyright
© 2020 John Wiley & Sons Ltd.
Références
Cox DR. Regression models and life-tables. J R Stat Soc B Methodol. 1972;34(2):187-202.
Hernán MA. The hazards of Hazard ratios. Epidemiology. 2010;21(1):13-15. https://doi.org/10.1097/EDE.0b013e3181c1ea43.
Wynant W, Abrahamowicz M. Flexible estimation of survival curves conditional on non-linear and time-dependent predictor effects. Stat Med. 2016;35(4):553-565.
Warwick J, Tabàr L, Vitak B, Duffy SW. Time-dependent effects on survival in breast carcinoma. Cancer. 2004;100(7):1331-1336.
Gagnon B, Abrahamowicz M, Xiao Y, Beauchamp ME. Flexible modeling improves assessment of prognostic value of C-reactive protein in advanced non-small cell lung cancer. Br J Cancer. 2010;102(7):1113-1122. https://www.nature.com/articles/6605603.
Quantin C, Abrahamowicz M, Moreau T, et al. Variation over time of the effects of prognostic factors in a population-based study of colon cancer: comparison of Statistical Models. Am J Epidemiol. 1999;150(11):1188-1200. https://doi.org/10.1093/oxfordjournals.aje.a009945.
Wei LJ. The accelerated failure time model: a useful alternative to the cox regression model in survival analysis. Stat Med. 1992;11(14-15):1871-1879. https://doi.org/10.1002/sim.4780111409.
Fleming TR, Lin DY. Survival analysis in clinical trials: past developments and future directions. Biometrics. 2000;56(4):971-983.
Orbe J, Ferreira E, Núñez-Antón V. Comparing proportional hazards and accelerated failure time models for survival analysis. Stat Med. 2002;21(22):3493-3510.
Kalbfleisch JD, Prentice RL. The statistical analysis of failure time data. Vol 360. New Jersey, NJ: John Wiley & Sons; 2011.
Klein JP, Moeschberger ML. Survival analysis. Techniques for Censored and Truncated Data. 2nd ed. New York, NY: Springer-Verlag; 2003. https://www.springer.com/gp/book/9780387953991 Accessed March 2, 2019.
Statistical Models LJF. Methods for Lifetime Data. Vol 362. New Jersey, NJ: John Wiley & Sons; 2011.
Hutton JL, Monaghan PF. Choice of parametric accelerated life and proportional hazards models for survival data: asymptotic results.
Li Y-H, Klein JP, Moeschberger ML. Effects of model misspecification in estimating covariate effects in survival analysis for small sample sizes. Comput Stat Data Anal. 1996;22(2):177-192. https://doi.org/10.1016/0167-9473(96)88029-7.
Collett D. Modelling Survival Data in Medical Research. Bristol, England: Chapman & Hall/CRC; 1993.
George B, Seals S, Aban I. Survival analysis and regression models. J Nucl Cardiol. 2014;21(4):686-694. https://doi.org/10.1007/s12350-014-9908-2.
Mahboubi A, Abrahamowicz M, Giorgi R, Binquet C, Bonithon-Kopp C, Quantin C. Flexible modeling of the effects of continuous prognostic factors in relative survival. Stat Med. 2011;30(12):1351-1365. https://doi.org/10.1002/sim.4208.
Buckley J, James I. Linear regression with censored data. Biometrika. 1979;66(3):429-436. https://doi.org/10.1093/biomet/66.3.429.
Lai TL, Ying Z. Large sample theory of a modified Buckley-James estimator for regression Analysis with censored data. Ann Stat. 1991;19(3):1370-1402.
Ritov Y. Estimation in a linear regression model with censored data. Ann Stat. 1990;18(1):303-328.
Jones MP. A class of semiparametric regressions for the accelerated failure time model. Biometrika. 1997;84(1):73-84. https://doi.org/10.1093/biomet/84.1.73.
Tsiatis AA. Estimating regression parameters using linear rank tests for censored data. Ann Stat. 1990;18(1):354-372.
Wei L-J, Ying Z, Lin DY. Linear regression analysis of censored survival data based on rank tests. Biometrika. 1990;77(4):845-851.
Huang J, Ma S, Xie H. Least absolute deviations estimation for the accelerated failure time model. Stat Sin. 2007;4:1533-1548.
Ying Z, Jung S-H, Wei L-J. Survival analysis with median regression models. J Am Stat Assoc. 1995;90(429):178-184.
Yang S. Censored median regression using weighted empirical survival and hazard functions. J Am Stat Assoc. 1999;94(445):137-145.
Ciampi A, Etezadi-Amoli J. A general model for testing the proportional hazards and the accelerated failure time hypotheses in the analysis of censored survival data with covariates. Commun Stat Theory Methods. 1985;14(3):651-667.
Etezadi-Amoli J, Ciampi A. Extended Hazard regression for censored Survival data with covariates: a spline approximation for the baseline Hazard function. Biometrics. 1987;43(1):181-192. https://doi.org/10.2307/2531958.
Komárek A, Lesaffre E, Hilton JF. Accelerated failure time model for arbitrarily censored data with smoothed error distribution. J Comput Graph Stat. 2005;14(3):726-745.
Komárek A. SmoothSurv: Survival Regression with Smoothed Error Distribution; 2018. https://CRAN.R-project.org/package=smoothSurv. Accessed April 15, 2019.
Ramsay JO. Monotone regression splines in action. Statistical Science. 1988;3(4):425-441.
Durrleman S, Simon R. Flexible regression models with cubic splines. Stat Med. 1989;8(5):551-561.
Senthilselvan A. Penalized likelihood estimation of hazard and intensity functions. J R Stat Soc B Methodol. 1987;49(2):170-174.
Abrahamowicz M, Clampl A, Ramsay JO. Nonparametric density estimation for censored survival data: Regression-spline approach. Can J Stat. 1992;20(2):171-185.
Wynant W, Abrahamowicz M. Validation of the alternating conditional estimation algorithm for estimation of flexible extensions of Cox's proportional hazards model with nonlinear constraints on the parameters. Biom J. 2016;58(6):1445-1464.
Therneau T A Package for Survival Analysis in S; 2015. https://CRAN.R-project.org/package=survival. Accessed October 21, 2018.
Moertel CG, Fleming TR, Macdonald JS, et al. Levamisole and fluorouracil for adjuvant therapy of resected colon carcinoma. N Engl J Med. 1990;322(6):352-358. https://doi.org/10.1056/NEJM199002083220602.
Moertel CG, Fleming TR, Macdonald JS, et al. Fluorouracil plus levamisole as effective adjuvant therapy after resection of stage III colon carcinoma: a final report. Ann Intern Med. 1995;122(5):321-326.
Cox DR, Snell EJ. A general definition of residuals. J R Stat Soc B Methodol. 1968;30(2):248-265.
Holtz TH, Sternberg M, Kammerer S, et al. Time to sputum culture conversion in multidrug-resistant tuberculosis: predictors and relationship to treatment outcome. Ann Intern Med. 2006;144(9):650-659.
Kim S-M, Park J, Kim SH, et al. Factors associated with the time to next attack in neuromyelitis optica: accelerated failure time models with random effects. PLoS ONE. 2013;8(12):e82325.
Montini E, Cesana D, Schmidt M, et al. The genotoxic potential of retroviral vectors is strongly modulated by vector design and integration site selection in a mouse model of HSC gene therapy. J Clin Invest. 2009;119(4):964-975.
Marko NF, Weil RJ, Schroeder JL, Lang FF, Suki D, Sawaya RE. Extent of resection of glioblastoma revisited: personalized Survival Modeling facilitates more accurate Survival prediction and supports a maximum-safe-resection approach to surgery. J Clin Oncol. 2014;32(8):774-782. https://doi.org/10.1200/JCO.2013.51.8886.
Kooperberg C, Stone CJ, Truong YK. Hazard regression. J Am Stat Assoc. 1995;90(429):78-94.
Hastie T, Tibshirani R. Varying-coefficient models. J R Stat Soc B Methodol. 1993;55(4):757-779.
Abrahamowicz M, MacKenzie TA. Joint estimation of time-dependent and non-linear effects of continuous covariates on survival. Stat Med. 2007;26(2):392-408.
Royston P, Parmar MK. Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Stat Med. 2002;21(15):2175-2197.
Orbe J, Ferreira E, Núñez-Antón V. Censored partial regression. Biostatistics. 2003;4(1):109-121.
Xue H, Lam KF, Cowling BJ, de WF. Semi-parametric accelerated failure time regression analysis with application to interval-censored HIV/AIDS data. Stat Med. 2006;25(22):3850-3863. https://doi.org/10.1002/sim.2486.
Zou Y, Zhang J, Qin G. A semiparametric accelerated failure time partial linear model and its application to breast cancer. Comput Stat Data Anal. 2011;55(3):1479-1487.
Yu L, Peace KE. Spline nonparametric quasi-likelihood regression within the frame of the accelerated failure time model. Comput Stat Data Anal. 2012;56(9):2675-2687.
Cai Z, Sun Y. Local linear estimation for time-dependent coefficients in Cox's regression Models. Scand J Stat. 2003;30(1):93-111. https://doi.org/10.1111/1467-9469.00320.
Zucker DM, Karr AF. Nonparametric survival analysis with time-dependent covariate effects: a penalized partial likelihood approach. Ann Stat. 1990;18(1):329-353.
Crowther MJ, Lambert PC. A general framework for parametric survival analysis. Stat Med. 2014;33(30):5280-5297. https://doi.org/10.1002/sim.6300.