對於增進估計的效益，多階段取樣實驗是其中一種方式。本研究考慮對於存活數據資料採用兩階段機率依賴採樣設計，其中第一階段為簡單隨機採樣，第二階段為機率依賴採樣。此方法目的為在有限的經費或是資源中選取更有資訊的樣本。模擬研究的估計結果會與相同樣本數的簡單隨機採樣以及結果依賴採樣的估計做比較。模擬結果顯示，兩階段機率依賴採樣的設計方法的估計結果比其他兩種估計方法具有更好的性質。此外我們也發展出在固定樣本數的情況下，兩階段機率依賴採樣的最佳設計。最後，我們使用研究的結果去分析巴瑟爾頓健康研究。

It has been shown that multiphased designs is one of the approaches to enhance study efficiency. In this thesis, we consider a two-phase probability dependent sampling scheme for failure time data. Where one selects a simple random sample at the first phase and targets more informative subjects based on a certain probability at the second phase. Simulation studies show that the proposed estimator performed the two competitive estimators, one from a simple random sample of the same sample size and the other from the outcome-dependent sampling design. We also develop the optimal allocation of the subsamples for the two-phase probability dependent sampling scheme under the fixed sample size. We then apply our proposed design and estimator to the Busseltion Health Study.

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