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. Bibliography: 20 titles.
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References
P. Andersen, O. Borgan, R. Gill, and N. Keiding, Statistical Models Based on Counting Processes, Springer, NewYork (1993).
V. Bagdonavičius and M. Nikulin, Accelerated Life Models: Modeling and Statistical Analysis, Chapmanand Hall/CRC, Boca Raton (2002).
V. Bagdonavičius, M. Hafdi, and M.Nikulin," Analysis of survival data with cross-effects of survival functions," Biostatistics, 5, 415–425 (2004).
D. R. Cox," Regression models and life tables," J. R. Statist. Soc., B 34, 187–220 (1972).
P. Grambsch and T. M. Therneau," Proportional hazards tests and diagnostics based on weighted residuals," Biometrika, 8, 515–526 (1994).
P. Greenwood and M. Nikulin, A Guide to Chi-squares Testing, John Wiley and Sons Inc., New York (1996).
D. W. Hosmer and S. Lemeshow, Applied Survival Analysis: Regression Modeling of Time to Event Data, John Wiley and Sons Inc., New York (1998).
D. W. Hosmer, S. Lemeshow, and S. May, Applied Survival Analysis: Regression Modeling of Time to Event Data, John Wiley and Sons Inc., New York (2008).
C. Huber-Carol, V. Solev, and F. Vonta," Interval censored and truncated data: rate of convergence of NPMLE of the density," J. Statist. Planning and Inference (toappear).
C. Huber-Carol, V. Solev, and F. Vonta," Estimation of density for arbitrary censored and truncated data," in: M. S. Nikulin, D. Commenges, and C. Huber-Carol (eds), Probability, Statistics, and Modelling in Public Health, Springer, New York (2006), pp. 246–265.
C. Huber and F. Vonta," A semiparametric model for interval censored and truncated data," Zap. Nauchn. Semin. POMI, 363, 139–150 (2009).
J. P. Klein and M. L. Moeshberger, Survival Analysis. Tehniques for Censored and Truncated Data, Springer, New York (2003).
D. G. Kleinbaum and M. Klein, Survival Analysis, Springer, New York (2005).
D. Y. Lin. "Goodness-of-fit analysis for the Cox regression model based on a class of parameter estimators," JASA, 86, 725–728 (1991).
T. Moreau, J. O'Quigley, and M. Mesbah," A global goodness-of-fit statistic for the proportional hazards model," Biometrics, 34, 212–218 (1985).
N. J. Nagelkerke, J. Oosting, and A. A. Hart," A simple test for goodness of fit of Cox's proportional hazards model," Biometrika, 40, 483–486 (1984).
C. Quantin, T. Moreau, B. Asselain, and J. Lelouh," A regression model for testing the proportional hazards hypothesis," Biometrika, 52, 874–885 (1996).
V. Solev, "Estimation of density on censored data," in: M. S. Nikulinetal (eds.), Advances in Degradation Models. Applications to Industry, Medicine, and Finance, Birkhauser, Boston (2009), pp. 369–380.
D. Stablein and I. Koutrouvelis, "A two sample test sensitive to crossing hazards in uncensored and singly censored data," Biometrics, 4, 643–652 (1985).
B. W. Turnbull, "The empirical distribution function with arbitrary grouped, censored, and truncated data," J. Royal Statist. Soc., 38, 290–295 (1976).
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 368, 2009, pp. 7–19.
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Bagdonavičius, V., Levuliené, R. & Nikulin, M.S. Goodness-of-fit criteria for the Cox model from left truncated and right censored data. J Math Sci 167, 436–443 (2010). https://doi.org/10.1007/s10958-010-9929-6
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DOI: https://doi.org/10.1007/s10958-010-9929-6