Goodness-of-fit for the Cox model from left truncated and right censored data
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 7-19 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We propose a test for the proportional hazards (Cox) model which is oriented against wide classes of alternatives including monotone hazard ratios and crossings of survival functions and can be used when data are left truncated and right censored. The limit distribution of the test statistics is derived. The results are applied for statistical analysis of classical data considered by Stablein and Koutrouvelis [19], Klein and Moeschberger [12], Hosmer and Lemeshow [7], Hosmer, Lemeshow and May [8]. Bibl. – 20 titles.
@article{ZNSL_2009_368_a1,
     author = {V. Bagdonavi\v{c}ius and R. Levulien\'e and M. S. Nikulin},
     title = {Goodness-of-fit for the {Cox} model from left truncated and right censored data},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {7--19},
     year = {2009},
     volume = {368},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a1/}
}
TY  - JOUR
AU  - V. Bagdonavičius
AU  - R. Levuliené
AU  - M. S. Nikulin
TI  - Goodness-of-fit for the Cox model from left truncated and right censored data
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2009
SP  - 7
EP  - 19
VL  - 368
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a1/
LA  - en
ID  - ZNSL_2009_368_a1
ER  - 
%0 Journal Article
%A V. Bagdonavičius
%A R. Levuliené
%A M. S. Nikulin
%T Goodness-of-fit for the Cox model from left truncated and right censored data
%J Zapiski Nauchnykh Seminarov POMI
%D 2009
%P 7-19
%V 368
%U http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a1/
%G en
%F ZNSL_2009_368_a1
V. Bagdonavičius; R. Levuliené; M. S. Nikulin. Goodness-of-fit for the Cox model from left truncated and right censored data. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 7-19. http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a1/

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

[2] V. Bagdonavičius, M. Nikulin, Accelerated Life Models: Modeling and Statistical Analysis, Chapman and Hall/CRC, Boca Raton, 2002

[3] V. Bagdonavičius, M. Hafdi, M. Nikulin, “Analysis of survival data with cross-effects of survival functions”, Biostatistics, 5 (2004), 415–425 | DOI | Zbl

[4] D. R. Cox, “Regression models and life tables”, J. Roy. Statist. Soc. Ser. B, 34 (1972), 187–220 | MR | Zbl

[5] P. Grambsch, T. M. Therneau, “Proportional hazards tests and diagnostics based on weighted residials”, Biometrika, 81:3 (1994), 515–526 | DOI | MR | Zbl

[6] P. Greenwood, M. Nikulin, A guide to chi-sqaures testing, Wiley, New York, 1996 | MR | Zbl

[7] D. W. Hosmer, S. Lemeshow, Applied Survival Analysis: Regression Modeling of Time to Event Data, Wiley, New York, 1998 | MR

[8] D. W. Hosmer, S. Lemeshow, S. May, Applied Survival Analysis: Regression Modeling of Time to Event Data, Wiley, New York, 2008 | MR | Zbl

[9] C. Huber-Carol, V. Solev, F. Vonta, “Interval censored and truncated data: rate of convergence of NPMLE of the density”, J. Statist. Plann. Inference, 139:5 (2009), 1734–1749 | DOI | MR

[10] C. Huber-Carol, V. Solev, F. Vonta, “Estimation of density for arbitrary censored and truncated data”, Probability, Statistics and Modelling in Public Health, eds. Nikulin M. S., Commenges D., Huber-Carol C., Springer, New York, 2006, 246–265 | DOI | MR

[11] C. Huber, F. Vonta, “A semiparametric model for interval censored and truncated data”, Zapiski nauchn. semin. POMI, 363, 2009, 139–150 | MR | Zbl

[12] J. P. Klein, M. L. Moeschberger, Survival analysis. Techniques for Censored and Truncated Data, Springer, New York, 2003

[13] D. G. Kleinbaum, M. Klein, Survival Analysis, Springer, New York, 2005 | Zbl

[14] D. Y. Lin, “Goodness of fit analysis for the Cox regression model based on a class of parameter estimators”, JASA, 86 (1991), 725–728 | DOI | MR | Zbl

[15] T. Moreau, J. O'Quigley, M. Mesbah, “A global goodness-of-fit statistic for the proportional hazards model”, Biometrics, 34 (1985), 212–218 | MR

[16] N. J. Nagelkerke, J. Oosting, A. A. Hart, “A simple test for goodness of fit of Cox's proportional hazards model”, Biometrika, 40 (1984), 483–486 | DOI

[17] C. Quantin, T. Moreau, B. Asselain, J. Lelouch, “A regression model for testing the proportional hazards hypothesis”, Biometrika, 52 (1996), 874–885 | DOI | MR | Zbl

[18] V. Solev, “Estimation of Density on Censored Data”, Advances in degradation models. Applications to Industry, Medicine and Finance, eds. Nikulin M., Limnios N., Balakrishnan N., Huber C., Kahle W., Birkhäuser, Boston, 2009, 369–380 | MR

[19] D. Stablein, I. Koutrouvelis, “A two sample test sensitive to crossing hazards in uncensored and singly censored data”, Biometrics, 41 (1985), 643–652 | DOI | MR | Zbl

[20] B. W. Turnbull, “The empirical distribution function with arbitrary grouped, censored and truncated data”, J. Roy. Statist. Soc. Ser. B, 38 (1976), 290–295 | MR | Zbl