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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.
MSC:
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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References:
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