Biometrika Advance Access originally published online on August 5, 2007
Biometrika 2007 94(4):861-872; doi:10.1093/biomet/asm054
Articles |
Aalen Additive Hazards Change-Point Model
Department of Natural Sciences, The Royal Veterinary and Agricultural University, Thorvaldsensvej 40, DK-1871 Frederiksberg C, Denmark torbenm{at}dina.kvl.dk
Department of Biostatistics, University of Copenhagen, Øster Farimagsgade 5 opg. B, 1014 Copenhagen K, Denmark ts{at}biostat.ku.dk
Received for publication 1 February 2006. Revision received 1 January 2007.
We study a test comparing the full Aalen additive hazards model and the change-point model, and suggest how to estimate the parameters of the change-point model. We also study a test for no change-point effect. Both tests are provided with large sample properties and a resampling method is applied to obtain p-values. The finite-sample properties of the proposed inference procedures and estimators are assessed through a simulation study. The methods are further applied to a dataset concerning myocardial infarction.
Key Words: Aalen's additive model Change-point Counting process Hazard model Survival data Time-varying effect
References
-
Aalen O. O. A model for non-parametric regression analysis of counting processes. In: Lecture Notes in Statistics-2: Mathematical Statistics and Probability Theory—Klonecki W., Kozek A., Rosinski J., eds. (1980) New York: Springer-Verlag. 1–25.
Andersen P. K., Borgan Ø., Gill R., Keiding N. Statistical Models Based on Counting Processes (1993) New York: Springer-Verlag.
Andersen P. K., Gill R. D. Cox's regression model for counting processes: A large sample study. Ann. Statist. (1982) 10:1100–20.[CrossRef]
Chang I.-S., Chen C.-H., Hsiung C. A. Estimation in change-point hazard rate models with random censorship. In: Change-Point Problems—Carlstein E., Muller H.-G., Siegmund D., eds. (1994) Hayward, CA: Institute of Mathematical Statistics. 78–92. IMS Lecture Notes-Monograph series.
Chen Y. Q., Wang M.-C. Additive hazards models with latent treatment effectiveness lag time. Biometrika (2002) 89:917–31.
Davies R. B. Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika (1977) 64:247–54.
Henderson R. A problem with the likelihood ratio test for a change-point hazard rate model. Biometrika (1990) 77:835–43.
Jensen G. V., Torp-Pedersen C., Hildebrandt P., Kober L., Nielsen F. E., Melchior T., Joen T., Andersen P. K. Does in-hospital ventricular fibrillation affect prognosis after myocardial infarction? Eur. Heart J. (1997) 18:919–24.
Lin D. Y., Wei L. J., Ying Z. Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika (1993) 80:557–72.
Lin D. Y., Ying Z. Semiparametric analysis of the additive risk model. Biometrika (1994) 81:61–71.
Luo X. The asymptotic distribution of mle of treatment lag threshold. J. Statist. Plan. Infer. (1996) 53:33–61.[CrossRef]
Luo X., Turnbull B. W., Clark L. C. Likelihood ratio tests for changepoint with survival data. Biometrika (1997) 84:555–65.
Martinussen T., Scheike T. H. Dynamic Regression Models for Survival Data (2006) New York: Springer-Verlag.
Martinussen T., Scheike T. H., Skovgaard I. M. Efficient estimation of fixed and time-varying covariate effects in multiplicative intensity models. Scand. J. Statist. (2002) 28:57–74.
Matthews D. E., Farewell V. T. On testing for a constant hazard against a change-point alternative. Biometrics (1982) 38:463–8.[CrossRef][Web of Science][Medline]
Matthews D. E., Farewell V. T., Pyke R. Asymptotic score processes and tests for constant hazard against a change-point alternative. Ann. Statist. (1985) 13:583–91.[CrossRef]
McKeague I. W., Sasieni P. D. A partly parametric additive risk model. Biometrika (1994) 81:501–14.
Pons O. Estimation in a Cox regression model with a change-point according to a threshold in a covariate. Ann. Statist. (2003) 31:442–63.[CrossRef]
Ramlau-Hansen H. Smoothing counting process intensities by means of kernel functions. Ann. Statist. (1983) 11:453–66.[CrossRef]
Spiekerman C. F., Lin D. Y. Marginal regression models for multivariate failure time data. J. Am. Statist. Assoc. (1998) 93:1164–75.[CrossRef][Web of Science]
van der Vaart A. W., Wellner J. A. Weak Convergence and Empirical Processes: With Applications to Statistics (1996) New York: Springer-Verlag.
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