本論文使用CD4 細胞數以及病毒載量與測量時間來找出愛滋病患的CD4 細胞數和病毒載量與時間之間的關係。在許多生物測量或各領域的資料，常會有檢測極限的觀測限制，也因為長期追蹤資料中，人為的測量誤差或生物體本身的差異，使得我們對生物指標的觀測產生偏差；因此，本研究同時使用檢測極限之設限與線性混合效應模型來解決上述的問題，並探討使用雞尾酒療法與無使用雞尾酒療法對愛滋病患之CD4 細胞數以及病毒載量的關係差異，以及用各種找出生物指標與時間的方法做比較，並用EM演算法計算考慮檢測極限下的資料的參數估計。
關鍵字：測量極限、EM演算法、長期追蹤共變數。

In this study, we are interested to investigate the relationship among CD4 counts, viral load and measurement time of AIDS patients. In many medical and biological studies, limitation of detection in observations exists. A famous example is the viral load of HIV. Consequently, we simultaneously use limitation of detection and linear mixed effected model to solve the problem. We also find the difference of the CD4 counts and viral load between patients who are given treatment of HAART and non-HAART. The estimating procedure is based on likelihood approach by considering the limitation detection as censoring. Simulations and data example demonstrate the usefulness of the proposed likelihood approach.

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