Summary: | 碩士 === 東海大學 === 統計學系 === 101 === Medical studies for drug development are frequently conducted to evaluate the treatment effects of a drug, where subjects or patients are randomly allocated to receive different treatment groups of the drug and a control. For right-censored survival data, it is usually interested in comparing the difference between two survival functions at a fixed time point rather than comparing the entire survival curves, when the survival functions are crossing. Moreover, in practice, a treatment effect may fades as time progresses. Even for the patients with the same covariates, not only might their survival times be different, but their individual survival functions could also be different. To account for variability due to unobserved individual-level factors, therefore, in this thesis, we extend the method of Jeong et al. (2003) and consider construct the simultaneous confidence interval for the difference of several survival functions under a gamma frailty model for randomly right-censored survival data. The associated coverage probability and the interval will be investigated via a simulation study. The implementation of the confidence interval will be illustrated using a real data set.
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