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Kernel regression for cause-specific hazard models with nonparametric covariate functions. (English) Zbl 07739684

Summary: We study the local kernel pseudo-partial likelihood approach for the cause-specific hazard model with nonparametric covariate functions. The derivative of the covariate function is estimated first, and the estimator of the nonparametric covariate function is then derived by integrating the derivative estimator. The consistency and pointwise asymptotic normality of the local kernel estimator for the interested failure types are obtained. Moreover, numerical studies show that the proposed kernel estimator performs well under a finite sample size. And we compare the local kernel estimator with the regression B-splines estimator. We also apply the proposed method to analyse the kidney and renal pelvis cancer data with composite endpoints.

MSC:

62G05 Nonparametric estimation
62G08 Nonparametric regression and quantile regression

Software:

cmprsk
Full Text: DOI

References:

[1] Andersen, P. K.; Gill, R. D., Cox’s Regression Model for Counting Processes: A Large Sample Study, The Annals of Statistics, 10, 1100-1120 (1982) · Zbl 0526.62026
[2] Austin, P. C.; Fine, J. P., Accounting for Competing Risks in Randomized Controlled Trials: A Review and Recommendations for Improvement, Statistics in Medicine, 36, 1203-1209 (2017)
[3] Bakoyannis, G.; Yu, M.; Yiannoutsos, C. T., Semiparametric Regression on Cumulative Incidence Function with Interval-Censored Competing Risks Data, Statistics in Medicine, 36, 3683-3707 (2017)
[4] Belot, A.; Abrahamowicz, M.; Remontet, L.; Giorgi, R., Flexible Modeling of Competing Risks in Survival Analysis, Statistics in Medicine, 29, 2453-2468 (2010)
[5] Bender, R.; Augustin, T.; Blettner, M., Generating Survival Times to Simulate Cox Proportional Hazards Models, Statistics in Medicine, 24, 1713-1723 (2005)
[6] Beyersmann, J.; Latouche, A.; Buchholz, A.; Schumacher, M., Simulating Competing Risks Data in Survival Analysis, Statistics in Medicine, 28, 956-971 (2009)
[7] Cai, Z.; Fan, J.; Li, R., Efficient Estimation and Inferences for Varying-Coefficient Models, Journal of the American Statistical Association, 95, 888-902 (2000) · Zbl 0999.62052
[8] Fan, J.; Gijbels, I.; King, M., Local Likelihood and Local Partial Likelihood in Hazard Regression, The Annals of Statistics, 25, 1661-1690 (1997) · Zbl 0890.62023
[9] Fine, J. P.; Gray, R. J., A Proportional Hazards Model for the Subdistribution of a Competing Risk, Journal of the American Statistical Association, 94, 496-509 (1999) · Zbl 0999.62077
[10] Gaynor, J. J.; Feuer, E. J.; Tan, C. C.; Wu, D. H.; Brennan, M. F., On the Use of Cause-Specific Failure and Conditional Failure Probabilities: Examples From Clinical Oncology Data, Journal of the American Statistical Association, 88, 400-409 (1993) · Zbl 0775.62297
[11] Gaynor, J. J.; Moon, J. I.; Kato, T.; Sageshima, J.; Tryphonopoulos, P.; Nishida, S.; Selvaggi, G.; Levi, D. M.; Island, E. R.; Weppler, D.; Ciancio, G.; Burke, G. W.I.; Ruiz, P.; Tzakis, A. G., Parametric Cause-Specific Hazard Modeling with Nonproportional Covariate Effects: A Case Study Using Liver Transplant Data, Statistics in Biopharmaceutical Research, 2, 133-142 (2010)
[12] Gray, R. J., A Class of K-Sample Tests for Comparing the Cumulative Incidence of a Competing Risk, The Annals of Statistics, 16, 1141-1154 (1988) · Zbl 0649.62040
[13] Gray, R. J., Flexible Methods for Analyzing Survival Data Using Splines, With Application to Breast Cancer Prognosis, Journal of the American Statistical Association, 87, 942-951 (1992)
[14] Härdle, W., Applied Nonparametric Regression, 19 (1990), Cambridge: Cambridge University Press, Cambridge · Zbl 0714.62030
[15] Härdle, W.; Müller, M., Smoothing and Regression, Multivariate and Semiparametric Kernel Regression, 357-391 (2000), New York: John Wiley & Sons,, New York · Zbl 0979.62023
[16] Hastie, T.; Tibshirani, R., Generalized Additive Models (1990), New York: Chapman and Hall, New York · Zbl 0747.62061
[17] Kalbfleisch, J. D.; Prentice, R. L., The Statistical Analysis of Failure Time Data (2011), Hoboken: John Wiley & Sons, Ltd, Hoboken · Zbl 0504.62096
[18] Lambert, P. C.; Wilkes, S. R.; Crowther, M. J., Flexible Parametric Modelling of the Cause-Specific Cumulative Incidence Function, Statistics in Medicine, 36, 1429-1446 (2017)
[19] Lau, B.; Cole, S. R.; Gange, S. J., Competing Risk Regression Models for Epidemiologic Data, American Journal of Epidemiology, 170, 244-256 (2009)
[20] O’Sullivan, F., Nonparametric Estimation of Relative Risk Using Splines and Cross-Validation, SIAM Journal on Scientific and Statistical Computing, 9, 531-542 (1988) · Zbl 0688.65084
[21] Pollard, D., Convergence of Stochastic Processes (1984), New York: Springer-Verlag, New York · Zbl 0544.60045
[22] Prentice, R. L.; Kalbfleisch, J. D.; Peterson, A. V.; Flournoy, N. T.; Breslow, N. E., The Analysis of Failure Times in the Presence of Competing Risks, Biometrics, 34, 541-554 (1979) · Zbl 0392.62088
[23] Putter, H.; Fiocco, M.; Geskus, R. B., Competing Risks and Multi-State Models, Statistics in Medicine, 26, 2389-2430 (2007)
[24] Qi, X.; Yu, Z., Kernel Regression for Cause-Specific Hazard Models with Time-Dependent Coefficients, Computational Statistics, 38, 263-283 (2023) · Zbl 07696209
[25] Ren, X.; Li, S.; Shen, C.; Yu, Z., Linear and Nonlinear Variable Selection in Competing Risks Data, Statistics in Medicine, 37, 2134-2147 (2018)
[26] Rice, J. A.; Silverman, B. W., Estimating the Mean and Covariance Structure Nonparametrically When the Data are Curves, Journal of the Royal Statistical Society. Series B: Methodological, 53, 233-243 (1991) · Zbl 0800.62214
[27] Suzukawa, A.; Taneichi, N., Semiparametric Estimation Based on Parametric Modeling of the Cause-Specific Hazard Ratios in Competing Risks, Journal of Multivariate Analysis, 87, 80-100 (2003) · Zbl 1030.62082
[28] Tibshirani, R.; Hastie, T., Local Likelihood Estimation, Journal of the American Statistical Association, 82, 559-567 (1987) · Zbl 0626.62041
[29] Verweij, P. J.M.; Van Houwelingen, H. C., Cross-Validation in Survival Analysis, Statistics in Medicine, 12, 2305-2314 (1993)
[30] Wanner, C.; Krane, V.; März, W.; Olschewski, M.; Mann, J. F.; Ruf, G.; Ritz, E., Atorvastatin in Patients with Type 2 Diabetes Mellitus Undergoing Hemodialysis, New England Journal of Medicine, 353, 238-248 (2005)
[31] Yu, Z.; Lin, X., Nonparametric Regression Using Local Kernel Estimating Equations for Correlated Failure Time Data, Biometrika, 95, 123-137 (2008) · Zbl 1437.62667
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