Geodesic
Checking proportional rates in the two-sample transformation model
Kybernetika, Tome 45 (2009) no. 2, pp. 261-278 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Transformation models for two samples of censored data are considered. Main examples are the proportional hazards and proportional odds model. The key assumption of these models is that the ratio of transformation rates (e. g., hazard rates or odds rates) is constant in time. A~method of verification of this proportionality assumption is developed. The proposed procedure is based on the idea of Neyman's smooth test and its data-driven version. The method is suitable for detecting monotonic as well as nonmonotonic ratios of rates.
Transformation models for two samples of censored data are considered. Main examples are the proportional hazards and proportional odds model. The key assumption of these models is that the ratio of transformation rates (e. g., hazard rates or odds rates) is constant in time. A~method of verification of this proportionality assumption is developed. The proposed procedure is based on the idea of Neyman's smooth test and its data-driven version. The method is suitable for detecting monotonic as well as nonmonotonic ratios of rates.
Classification : 62N01, 62N02, 62N03, 65C60
Keywords: Neyman's smooth test; proportional hazards; proportional odds; survival analysis; transformation model; two-sample test 
@article{KYB_2009_45_2_a4,
     author = {Kraus, David},
     title = {Checking proportional rates in the two-sample transformation model},
     journal = {Kybernetika},
     pages = {261--278},
     year = {2009},
     volume = {45},
     number = {2},
     mrnumber = {2518151},
     zbl = {1165.62072},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2009_45_2_a4/}
}
TY  - JOUR
AU  - Kraus, David
TI  - Checking proportional rates in the two-sample transformation model
JO  - Kybernetika
PY  - 2009
SP  - 261
EP  - 278
VL  - 45
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/KYB_2009_45_2_a4/
LA  - en
ID  - KYB_2009_45_2_a4
ER  - 
%0 Journal Article
%A Kraus, David
%T Checking proportional rates in the two-sample transformation model
%J Kybernetika
%D 2009
%P 261-278
%V 45
%N 2
%U http://geodesic.mathdoc.fr/item/KYB_2009_45_2_a4/
%G en
%F KYB_2009_45_2_a4
Kraus, David. Checking proportional rates in the two-sample transformation model. Kybernetika, Tome 45 (2009) no. 2, pp. 261-278. http://geodesic.mathdoc.fr/item/KYB_2009_45_2_a4/

[1] P. K. Andersen, O. Borgan, R. D. Gill, and N. Keiding: Statistical Models Based on Counting Processes. Springer, New York 1993. | MR

[2] P. K. Andersen and R. D. Gill: Cox’s regression model for counting processes: a large sample study. Ann. Statist. 10 (1982), 1100–1120. | MR

[3] V. Bagdonavičius and M. Nikulin: Generalized proportional hazards model based on modified partial likelihood. Lifetime Data Anal. 5 (1999), 329–350. | MR

[4] V. Bagdonavičius and N. Nikulin: On goodness-of-fit for the linear transformation and frailty models. Statist. Probab. Lett. 47 (2000), 177–188. | MR

[5] V. Bagdonavičius and M. Nikulin: Accelerated life models. Modeling and Statistical Analysis. Chapman & Hall/CRC, Boca Raton 2001.

[6] K. Chen, Z. Jin, and Z. Ying: Semiparametric analysis of transformation models with censored data. Biometrika 89 (2002), 659–668. | MR

[7] D. Collett: Modelling Survival Data in Medical Research. Chapman & Hall/CRC, Boca Raton 2003. | MR

[8] D. M. Dabrowska and K. A. Doksum: Estimation and testing in a two-sample generalized odds-rate model. J. Amer. Statist. Assoc. 83 (19í8), 744–749. | MR

[9] J.-Y. Dauxois and S. N. U. A. Kirmani: Testing the proportional odds model under random censoring. Biometrika 90 (2003), 913–922. | MR

[10] T. R. Fleming and D. P. Harrington: Counting Processes and Survival Analysis. Wiley, New York 1991. | MR

[11] R. D. Gill and M. Schumacher: A simple test of the proportional hazards assumption. Biometrika 74 (1987), 289–300.

[12] D. Kraus: Data-driven smooth tests of the proportional hazards assumption. Lifetime Data Anal. 13 (2007), 1–16. | MR | Zbl

[13] T. Ledwina: Data-driven version of Neyman’s smooth test of fit. J. Amer. Statist. Assoc. 89 (1994), 1000–1005. | MR | Zbl

[14] D. Y. Lin, L. J. Wei, and Z. Ying: Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika 80 (1993), 557–572. | MR

[15] T. Martinussen and T. H. Scheike: Dynamic Regression Models for Survival Data. Springer, New York 2006. | MR

[16] S. A. Murphy, A. J. Rossini, and A. W. van der Vaart: Maximum likelihood estimation in the proportional odds model. J. Amer. Statist. Assoc. 92 (1997), 968–976. | MR

[17] J. C. W. Rayner and D. J. Best: Smooth Tests of Goodness of Fit. Oxford University Press, New York 1989. | MR

[18] D. Sengupta, A. Bhattacharjee, and B. Rajeev: Testing for the proportionality of hazards in two samples against the increasing cumulative hazard ratio alternative. Scand. J. Statist. 25 (1998), 637–647. | MR

[19] C. A. Struthers and J. D. Kalbfleisch: Misspecified proportional hazard models. Biometrika 73 (1986), 363–369. | MR

[20] A. W. van der Vaart and J. A. Wellner: Weak Convergence and Empirical Processes. With Applications to Statistics. Springer, New York 1996. | MR

[21] L. J. Wei: Testing goodness of fit for proportional hazards model with censored observations. J. Amer. Statist. Assoc. 79 (1984), 649–652. | MR | Zbl