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Fully nonparametric estimation of the marginal survival function based on case-control clustered data. (English) Zbl 1444.62117
The paper proposes and characterizes a refined nonparametric estimator of the marginal survival function of the onset-time (with possibly right-censored age) of some disease which is observed in a target population. The case-control-family statistical frame is considered. This kind of statistical study, previously developed by M. Gorfine et al. [“A fully nonparametric estimator of the marginal survival function based on case-control clustered age-at-onset data”, Biostatistics 18, No. 1, 76–90 (2017; doi:10.1093/biostatistics/kxw032)], involves observations on case-probands (sick individuals) and control-probands (individuals without the disease). The sampling of probands is followed by subsequent samplings of relatives for each case and control proband, with an ascertainment of information about the dependence of the outcomes. The consistency of the fully nonparametric proposed estimator is proved by a suitable asymptotic study. The proofs of the main theoretical results are really difficult. Practical implementation details, comparative simulation study and concrete biological application of the proposed method complete this work.
62N02 Estimation in survival analysis and censored data
62G20 Asymptotic properties of nonparametric inference
62G07 Density estimation
62H12 Estimation in multivariate analysis
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[1] Andersen, P. K., and Gill, R. D. (1982). Cox’s regression model for counting processes: a large sample study., Annals of Statistics 10 1100-1120. · Zbl 0526.62026
[2] Beran, R. (1981). Nonparametric regression with randomly censored survival data. Technical Report, University of California at, Berkeley.
[3] Chatterjee, N., Kalaylioglu, Z., Shih, J. H., and Gail, M. (2006). Case-control and case-only designs with genotype and family history data: estimating relative risk, residual familial aggregation and cumulative risk., Biometrics 62 36-48. · Zbl 1099.62126
[4] Dabrowska, D. M. (1987). Non-parametric regression with censored survival time data., Scandinavian Journal of Statistics 14 181-197. · Zbl 0641.62024
[5] Doksum, K. A., Jiang, J., Sun, B. and Wang, S. (2017). Nearest neighbor estimates of regression., Computational Statistics and Data Analysis 110 64-74. · Zbl 1466.62059
[6] Dudley, R. M. (1999)., Uniform Central Limit Theorems. Cambridge University Press, Cambridge. · Zbl 0951.60033
[7] Fan, J., and Gijbels, I. (1996)., Local Polynomial Modelling and Its Applications. Chapman and Hall, London. · Zbl 0873.62037
[8] Giné, E., and Guillou, A. (2002). Rates of strong consistency for multivariate kernel density estimators., Annales de l’Institut Henri Poincaré (B) Probability and Statistics 38 907-922.
[9] Gorfine, M., Bordo, N., and Hsu, L. (2017). A fully nonparametric estimator of the marginal survival function based on case-control clustered age-at-onset data., Biostatistics 18 76-90.
[10] Schuster, E. F. (1969). Estimation of a probability density function and its derivatives., Annals of Mathematical Statistics 40 1187-1195. · Zbl 0212.21703
[11] Shih, J. H., and Chatterjee, N. (2002). Analysis of survival data from case-control family studies., Biometrics 58 502-509. · Zbl 1210.62204
[12] Stanford, J. L., Wicklund, K. G., McKnight, B., Daling, J. R., and Brawer, M. K. (1999). Vasectomy and risk of prostate cancer., Cancer Epidemiology Biomarkers and Prevention 8 881-886.
[13] van der Vaart, A (1998)., Asymptotic Statistics. Cambridge University Press, Cambridge. · Zbl 0910.62001
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