| 摘要(英) |
In this thesis, we are concerned about the meta-analysis of bivariate semi-competing risks data, where one event time is a competing risk for another event time. Meta-analysis is a statistical method that collects data from different independent studies and concludes research results. Rondeau et al. (2015) proposed the joint frailty model for the meta-analysis of semi-competing risks data, where frailty is applied for heterogeneity between different studies. The model they proposed is an extension of the Cox proportional hazard model, in which the assumption of conditional independence between two event times given frailty is imposed. Emura et al. (2017a) used the copula function to relax the conditional independence assumption of the joint frailty model, and proposed the joint frailty-copula model. The baseline hazard functions in the joint frailty-copula model are estimated non-parametrically by splines. In this thesis, we propose the Weibull distribution for baseline hazard functions and the gamma distribution for frailty in the joint frailty-copula model. We show that the Weibull model constitutes a conjugate model for the gamma frailty distribution, and that the Weibull models give explicit expressions for the marginal moments, survival functions, quantiles, and mean residual lifetimes. These mathematical properties are not possible to derive under the spline models. In the point estimation part, the maximum likelihood estimation method is used to estimate the unknown parameters in the model, and its computer programs are developed. In the part of the interval estimation, two different methods for constructing the standard error and confidence intervals are proposed and their performances are compared. We conduct simulation studies to examine the accuracy of the proposed methods. Finally, we use an ovarian cancer patient data to illustrate the proposed method. |
| 參考文獻 |
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