目前已有許多統計方法考量於期中分析時，使用短期臨床試驗指標協助評估長期臨床試驗指標的有效性，然而這些研究並無估計兩種臨床試驗指標之相關性。因此本研究發展一於期中分析時，若長期與短期臨床試驗指標之樣本相關性夠高，則納入短期臨床試驗指標之資訊，以協助長期臨床試驗指標之有效性評估方法。透過模擬研究證實我們所提出的統計方法在不同的參數組合之下，大致可以有效控制期中分析之型一錯誤率，並且也調查了樣本數與檢定力之間的關係。最後我們對整篇研究進行討論及總結，並提出未來可能延伸的方向。

Several statistical methods have been developed using the short-term endpoint in interim analysis to help assess the long-term endpoint. However, these studies have not estimated the correlation between the two endpoints. Therefore, we propose a study such that, if the sample correlation between the two endpoints is high enough, the information of the short-term endpoint will be included in the assessment of the long-term endpoint. Simulation confirms that the proposed statistical method controls the Type I error rate roughly under different combinations of parameters components, while we also investigate the relationship between power and sample size. Finally, we have discussion for the proposed method and future works are pointed out.

CONTENTS	IV
CONTEMTS OF TABLE	V
CONTEMTS OF FIGURE	VI
1	INTRODUCTION	1
2	THE PROPOSED METHOD	3
2.1	STATISTICAL MODEL	3
2.2	INTERIM ANALYSES	6
3.	SIMULATION	12
3.1	COMPARISON WITH MARSCHNER AND BECKER[2] METHOD	12
3.2	TYPE I ERROR STUDY	17
3.3	POWER STUDY	22
4.	DISCUSSION	27
APPENDIX	30
REFERENCES	32


CONTEMTS OF TABLE

TABLE 1. DISTRIBUTION OF THE RESPONSES BY THE BINARY OUTCOMES FOR LONG-TERM AND SHORT-TERM ENDPOINTS.	5
TABLE 2. A COMPARISON OF THE EMPIRICAL TYPE I ERROR RATE OF THE PROPOSED METHOD WITH THE MB METHOD.	15
TABLE 3. SIMULATION RESULT OF THE CONTROL OF THE TYPE I ERROR RATE FOR THE INTERIM ANALYSIS WHEN ,  , WHERE  .	18
TABLE 4. SIMULATION RESULT OF THE CONTROL OF THE TYPE I ERROR RATE FOR THE INTERIM ANALYSIS WHEN ,  , WHERE  .	19
TABLE 5. SIMULATION RESULT OF THE CONTROL OF THE TYPE I ERROR RATE FOR THE INTERIM ANALYSIS WHEN ,  , WHERE  .	20
TABLE 6. SIMULATION RESULT OF THE DIFFERENCE BETWEEN THE EMPIRICAL POWER AND THEORETICAL POWER OF THE PROPOSED METHOD WHEN FIXED  ,  ,  ,  .	23
TABLE 7. SIMULATION RESULT OF THE DIFFERENCE BETWEEN THE EMPIRICAL POWER AND THEORETICAL POWER OF THE PROPOSED METHOD WHEN FIXED  ,    .	24


CONTEMTS OF FIGURE
FIGURE 1. DECISION FLOWCHART FOR INTERIM ANALYSIS BASED ON THE PROPOSED METHOD.	11
FIGURE 2.HISTOGRAMS OF THE EMPIRICAL TYPE I ERROR RATE OF THE PROPOSED METHOD AND MB METHOD.	16
FIGURE 3. HISTOGRAM OF EMPIRICAL TYPE I ERROR RATE BASE ON DIFFERENT SAMPLE SIZES FOR THE PROPOSED METHOD.	21
FIGURE 4. THE EMPIRICAL POWER CURVE AND THEORETICAL POWER CURVE WITH DIFFERENT CORRELATION AND GREEN CURVES ARE EMPIRICAL POWER CURVES AND BLUE CURVES ARE THE THEORETICAL POWER CURVES AND FIXED  AND   BY THE PROPOSED METHOD.	25
FIGURE 5. THE EMPIRICAL POWER CURVE AND THEORETICAL POWER CURVE WITH DIFFERENT CORRELATION AND GREEN CURVES ARE EMPIRICAL POWER CURVES AND BLUE CURVES ARE THE THEORETICAL POWER CURVES AND FIXED  AND   BY THE PROPOSED METHOD.	26

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