摘要(英) |
In the survival analysis, when we use the misspecified model to fit the survival data, it often affects the parameter estimates of the survival model, and this even leads to produce different results of significance from covariates on the hazard function, if we compare with the result of using the correct model to fit the survival data. Therefore, through statistical simulation under the time-independent covariate of survival model and the time-dependent covariate of survival model, we use Cox model, AFT model, and extended hazard model to fit the survival data, and we have interest in the effects of misspecification of regression parameters between Cox and AFT model. Our approach is to use extended hazard model to discuss the effect of misspecification between Cox and AFT model mainly, because the extended hazard model is a more generalized model, which includes the features of Cox model and AFT model. In the real data analysis, we analyze Stanford heart transplant data from Miller (1981), and the Taiwan AIDS data. We use Cox model and AFT model to analyzed these data, and to observe the degree of influence from the covariate on the hazard function.
|
參考文獻 |
[1] Andersen, P. K. and Borgan, Q. and Gill, R. D. and Keiding, N. (1993). Statistical Models Based On Counting Processes. Springer: New York.
[2] Andersen, P. K. and Gill, R. D. (1982). Cox's regression model for counting processes: a large sample study. The Annals of Statistics 10: 1100-1120.
[3] Bretagnolle, J. and Huber-Carol, C. (1985). Sous-estimation des contrastes due à I’oubli de variables pertinentes dans le modèle de Cox pour les durées de survie avec censure. C.R. Acad. Sc Paris, t. 300, Série I 11:359-362.
[4] Buckley, J. and James, I. (1979). Linear regression with censored data. Biometrika 66: 429-436.
[5] Chen, Y. Q. and Jewell, N. P. (2001). On a general class of semiparametric hazards regression models. Biometrika 88: 687-702.
[6] Ciampi, A. and Etezadi-Amoli, J. (1985). A general model for testing the proportional hazards and the accelerated failure time hypothesis in the analysis of censored survival data with covariates. Communication in Statistics-Theory and Methods 14: 651-667.
[7] Cox, D. R. (1975). Partial likelihood. Biometrika 62: 269-276.
[8] Crowley, J. and Hu, M. (1976). Covariance analysis of heart transplant survival data. Journal of the American Statistical Association 72: 27-36.
[9] Etezadi-Amoli, J. and Ciampi, A. (1987). Extended hazard regression for censored survival data with covariates: A spline approximation for the baseline hazard function. Biometrics 43: 181-192.
[10] Gehan, E. A. (1965). A generalized Wilcoxon test for comparing arbitrary single censored samples. Biometrika 52: 203-223.
[11] Hutton, J. L. and Monaghan, P. F. (2002). Choice of parametric accelerated life and proportional hazards models for survival data: Asymptotic results. Lifetime Data Analysis 8: 375-393.
[12] Jones, M. C. (1990). The performance of kernel density functions in kernel distribution function estimation. Statistics & Probability 9: 129-132.
[13] Jones, M. C. and Sheather, S. J. (1991). Using non-stochastic terms to advantage in kernel-based estimation of integrated squared density derivatives. Statistics & Probability 11: 511-514.
[14] Latouche, A. and Boisson, V. and Chevret, S. and Porcher, R. (2007). Misspecified regression model for the subdistribution hazard of a competing risk. Statistics in Medicine 26: 965-974.
[15] Lin, D. Y. and Ying, Z. (1995). Semiparametric inference for the accelerated life model with time-dependent covariates. Journal of Statistical Planning and Inference 44: 47-63.
[16] Lin, D. Y. and Ying, Z. (1997). Additive regression models for survival data. In Proceedings of the First Seattle Symposium in Biostatistics: Survival Analysis. Springer: New York.
[17] Lu, W. (2010). Efficient estimation for an accelerated failure time model with a cure fraction. Statistica Sinica 20: 661-674.
[18] Miller, R. G. (1976). Least squares regression with censored data. Biometrika 63: 449-464.
[19] Miller, R. G. (1981). Survival Analysis. New York: Wiley.
[20] Nelder, J. A. and Mead, R. (1965). A simplex method for function minimization. The Computer Journal 7: 308-313.
[21] O’Neill, T. J. (1986). Inconsistency of the misspecified proportional hazards model. Statistics & Probability 4: 219-222.
[22] Solomon, P. J. (1984). Effect of misspecification of regression models in the analysis of survival data. Biometrika 71: 291-298.
[23] Struthers, C. A. and Kalbfleisch, J. D. (1986). Misspecified proportional hazard models. Biometrika 73: 363-369.
[24] Tseng, Y. K. and Shu, K. N. (2011). Efficient estimation for a semiparametric extended hazards model. Communications in Statistics-Simulation and Computation 40: 258-273.
[25] Tsiatis, A. A. (1981). A large sample study of Cox's regression model. The Annals of Statistics 9: 93-108.
[26] Zeng, D. and Lin, D. Y. (2007). Efficient estimation for the accelerated failure time model. Journal of the American Statistical Association 102: 1387-1396.
|