在生物醫學研究的過程中經常收集到與時間有關的長期追蹤共變數，一般最常使用Cox比例風險模型推估時間相依共變數與存活時間過程的關聯性。傳統使用Cox（1972）的部分概似法估計參數，但前提是必須有所有研究對象的完整共變數資訊及無測量誤差，才能達到準確地估計。為了減少部分概似法參數估計上的偏差，採用Wulfsohn（1997）聯合模型能有效地同時運用長期追蹤資料與存活資訊作分析。本研究之目的是比較部分概似法與聯合模型對共變數是與時間有關之下，其參數估計值之變化情況，以利於實例分析中提供根據資料的型態選擇有效率又準確的估計方法。本篇以模擬不同的共變數歷史與存活資料，得到若資料是時間固定（每位研究對象按時回診），使用程式效率高的部分概似法即可有良好的估計結果。然而，隨著共變數資料遺失比例愈高（研究對象測量時間參差不齊），部分概似法所估計的參數偏差愈大，則必須使用估計過程較為繁雜的聯合模型估計其參數，以有效減少偏差。最後，藉由地中海果蠅資料驗證部分概似法與聯合模型所估計的參數之變化。 Time-dependent covariates along with survival information are very common to be collected at same time in many medical research. It is very popular to use Cox proportional hazards model when studying the relationship between time-dependent covariates and the survival time. Cox(1972) propose a method called partial likelihood to estimate model parameters. To obtain unbiased and efficient estimates, we need to know complete information of the covariate history for all individuals and time-dependent covariates without measurement error. Therefore, failure to settle measurement error on the observed covariates and handle incompleteness of time-dependent covariates can cause the estimation to be biased. In order to reduce the bias of the parameter estimate based on partial likelihood, Wulfsohn(1997) successfully develope a joint modeling approach, which employs efficiently longitudinal and survival information at the same time. The purpose of this research is to compare the estimation betweem partial likelihood and joint modeling approach when time-dependent covariates present. We undertake the simulation studies to investigate the properties of the estimation according to various percentage of missing covariate. The simulation results show that partial likelihood is appropriate when individual is examined on schedule. Otherwise, we suggest to use joint modeling. Finally, an example of medfly data is analyzed to demonstrate the properties of the estimation based on partial likelihood and joint modeling approach.
