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Hazard models with varying coefficients for multivariate failure time data. (English) Zbl 1114.62104
Summary: Statistical estimation and inference for marginal hazard models with varying coefficients for multivariate failure time data are important subjects in survival analysis. A local pseudo-partial likelihood procedure is proposed for estimating the unknown coefficient functions. A weighted average estimator is also proposed in an attempt to improve the efficiency of the estimator. The consistency and asymptotic normality of the proposed estimators are established and standard error formulas for the estimated coefficients are derived and empirically tested. To reduce the computational burden of the maximum local pseudo-partial likelihood estimator, a simple and useful one-step estimator is proposed. Statistical properties of the one-step estimator are established and simulation studies are conducted to compare the performance of the one-step estimator to that of the maximum local pseudo-partial likelihood estimator. The results show that the one-step estimator can save computational cost without compromising performance both asymptotically and empirically and that an optimal weighted average estimator is more efficient than the maximum local pseudo-partial likelihood estimator. A data set from the Busselton Population Health Surveys is analyzed to illustrate our proposed methodology.

62N02 Estimation in survival analysis and censored data
62H12 Estimation in multivariate analysis
62G20 Asymptotic properties of nonparametric inference
62G08 Nonparametric regression and quantile regression
65C60 Computational problems in statistics (MSC2010)
62P10 Applications of statistics to biology and medical sciences; meta analysis
62G05 Nonparametric estimation
62N01 Censored data models
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