結果依賴採樣設計在很多研究中已被證實是具有成本效益的抽樣方式。若同一位實驗對象有多於兩個觀測值，則存在無法忽略的相關性。給出不正確的相關矩陣類型結構的假設，可能影響估計值的準確性。因此，本研究的目標是考慮多個實作相關矩陣結構，依據多維度依賴採樣設計所得到的長期追蹤資料，如何找到有效的參數估計。我們的模擬試驗已證實在不同的相關矩陣下，多維度依賴採樣下的估計值皆比簡單抽樣的估計值更有效率。我們計算 AIC 和 BIC 的值來當作我們選擇合適的相關矩陣的指標。最後，我們使用此模型去分析關於牙齒修復的資料。

Outcome-dependent sampling (ODS) scheme has been shown to be a cost-effective scheme in a lot of large-cohort studies. A multivariate outcome-dependent sampling (MODS) design is a further generalization for longitudinal data collected under the ODS scheme. For multivariate responses, the correlation between the responses from the same subject cannot be neglected. Misspecified working correlation structures may lead to erroneous conclusions. In this study, we consider an ODS design for multivariate longitudinal or clustered data and model under various types of the working correlation structure. A semiparametric empirical likelihood approach is developed for the proposed design under several commonly-used working correlation structures. Simulation studies show that the proposed estimator is more efficient than the estimator from a simple random sample of the same sample size. We then used AIC and BIC to obtain the appropriate correlation matrix. We also apply our proposed approach to the dental restoration data.

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