前後測隨機控制試驗，為常用以評估介入成效的設計，依試驗單位又可分別為個體與集群。若忽略群集中可能的相關，會使推論錯誤的機會增加。在此目的於比較前後測群集隨機試驗下的三種標準平均差估計。

蒙地卡羅模擬法在此是用於比較三種標準平均差估計的相對效力。，三種估計為以後測差異、前後測改變量差異，與利用共變異數分析調整前測下的後測差異所組成的標準平均差。在此以SAS 9.1版以建立前後測群集試驗資料，並假設資料來自一重複測量混合模型。

研究中的三種效果量估計皆為不偏估計，但在混合共變異數分析下，將調整前測當成共變量納入調整的後測差異，所組成的標準平均差其估計效力相對較高。而在改變量差異組成的標準平均之下，其理論分布與採樣分布不符。並且研究發現以總變異建立的效果量估計，在群集資料中當群中相關性低於0.2時，個體與群集效果量估計皆為不偏，但大於0.2後個體效果量估計會出現估計偏誤。

Pretest-posttest randomized control design is a common approach for evaluation of intervention effects. The units of randomization are clusters not individuals for intervention delivered at group levels. Ignoring the intra-cluster correlation may lead to erroneous inferences about the intervention effects. This study aims to compare three estimators of standardized mean difference (SMD) for data obtained from pretest posttest cluster randomized control trials.

A Monte-Carlo simulation study was performed to compare the relative efficiencies of three estimators of SMD using posttest means, change score means or adjusted means in the analysis of covariance with pretest score as a covariate estimators of SMD. The generation of pseudo data uses SAS 9.1 under the assumption that the pretest and posttest scores follow the mixed repeated measure analysis of variance model.

Although these three estimators appeared to be unbiased, using adjusted means in the analysis of covariance with pretest score as a covariate estimator of SMD seemed to have the highest efficiency. The theoretical and observed sampling variations were generally comparable but the theoretical sampling variation for the estimator using the change score appeared to be less reliable. In addition, if intra-cluster correlation is more then 0.2, the effect size estimators under individual will be biased.

摘要 III
ABSTRACT IV
致謝 V
目錄 VII
表目錄 IX
圖目錄 X

第一章：緒論 1
第一節：研究背景 1
第二節：研究目的 4

第二章：前後測群集隨機控制試驗下的介入效果 5
第一節: 以後測差異建立的效果估計 6
第二節: 以前後測改變量差異建立的效果估計 8
第三節: 以共變數調整前測下，後測差異建立的效果估計 10

第三章：前後測群集隨機控制試下的驗效果量估計 12
第一節：前後測群集隨機控制試驗下的效果量定義 12
第二節：前後測群集隨機控制試驗下的效果量估計 13
3.2.1 兩組後測差異所建立的的效果量估計 13
3.2.2. 兩組前後測改變量差異所建立的的效果量估計 14
3.2.3. 調整前測下兩組後測差異所建立的的效果量估計 14

第四章：材料與方法 17
第一節：資料模擬的設計 17
第二節：模擬資料的參數設計 18

第五章:研究結果 20
第一節：效果量估計的比較 20
第二節：效果量估計的資料應用與不全時的探討 22
1. 群集分析下的群集效果量估計 22
2. 抽樣單位與分析單位不符 24

第六章：研究結論與討論 27
第一節：結論 27
第二節：討論 27
第三節：研究限制與建議 29

參考文獻 31
[附錄一] 三種分析模型的變異數分析表 51
[附錄二] 效果量估計的採樣分佈 56
[附錄三] 程式補充 60

表目錄

表一 資料模擬的參數設計 33
表二 三種效果量估計期望值與參數的誤差比例 34
表四 不同相關性下三種效果量估計的期望值、變異數與相對有效性
(d=0.2；N=10；M=50、150) 40
表五 不同相關性下三種效果量估計的期望值、變異數與相對有效性
(d=0.5；N=10；M=50、150) 41
表六 不同相關性下三種效果量估計的期望值、變異數與相對有效性
(d=0.8；N=10；M=50、150) 42
表七 三種個體效果量估計期望值與參數的誤差比例 43
表八 三種效果量估計個體與群集觀察變異的誤差比例 46


圖目錄

圖一 後測分析下效果量估計與調整前測分析下效果量估計在不同參
數條件下的相對估計效力比較 49
圖二 改變量分析下效果量估計與調整前測分析下效果量估計在不同 參數條件下的相對估計效力比較 49
圖三 三種個體效果量估計在不同群集大小及相關性下的估計誤差 50

Cohen, J. W. (1988). Statistical power analysis for the behavioral sciences (2nd Edition ed.). New Jersey: Hillsdale.
Cooper, H. M., & Lemke, K. M. (1991). On the role of meta-analysis in personality and social psychology. Personality and Social Psychology Bulletin 17, 245-251.
DerSimonian, R., & Laird, N. (1986). Meta-analysis in clinical trials. Controlled clinical trials, 7, 177-188.
Donner, A., & Klar, N. (2002). Issues in the meta-analysis of cluster randomized trials. Statistics in Medicine, 21.
Donner, A., Piaggio, G., & Villar, J. (2001). Statistical methods for the meta-analysis of cluster randomization trials. Statistics in Medicine Research, 10, 325-338.
Gilbody, S., Bower, P., Torgerson, D., & Richards, D. (2008). Cluster randomized trials produced similar results to individually randomized trials in meta-analysis of enhanced care for depression. Journal of Clinical Epidemiology, 61, 160-168.
Glaster, R. R. (2002). Accuracy of effect size calculation method for repeated method. Psychology, The University of Memphis. Doctor of Philosophy Degree: 155.
Gotzsche, P. C., & Hrobjartsson, A. (2007). Data extraction errors in meta-analyses. The use standardized mean differences Journal of the American Medical Association, 298(4), 430-437.
Hedges, L. V. (2007a). Correcting a significance test for clustering. Journal of Educational & Behavioral Statistics, 32(2), 151-179.
Hedges, L. V. (2007b). Effect sizes in cluster-randomized designs. Journal of Educational & Behavioral Statistics, 32(4), 341-370.
Hedges, L. V., & Hedberg, E. C. (2007). Intraclass correlation value for planning group-randomized trials in education. Educational Evaluation and Policy Analysis, 29(1), 60-87.
Janega, J. B., Murray, D. M., & Varnell, S. P. (2002). Assessing intervention effects in a school-based nutrition intervention trial: which analytic model is most powerful? Health Education & Behavior, 31(6), 756-774.
Laopaiboon, M. (2003). Meta-analyses involving cluster randomization trials: a review of published literature in health care. Statistics in Medicine 12, 515-530.
Morris, S. B. (2007). Estimating effect sizes from pretest-posttest-control group designs [Electronic Version]. Organizational Research Methods, doi:10.1177/1094428106291059. Retrieved July 23.
Morris, S. B., & DeShon, R. P. (2002). Combining effect size estimates in meta-analysis with repeated measures and independent-groups designs. Psychological Methods, 7(1), 105-125.
Murray, D. M. (1998). Design and analysis of group-randomized trials. New York: Oxford press
Murray, D. M., Hannan, P. J., Wolfinge, R. D., Baker, W. L., & Dwyer, J. H. (1998). Analysis of data from group-randomized trials with repeat observations on the same groups. Statistics in Medicine, 17(14), 1581-1600.
Villar, J., Mackey, M. E., Carroli, G., & Donner, A. (2001). Meta-analyses in systematic reviews of randomized controlled trials in perinatal medicine: comparison of fixed and random effect models. Statistics in Medicine, 20, 3635-3647.
Wang, M. C., & Bushman, B. J. (1999). Integrating results-Through meta-analytic review using SAS soft ware Cary,NC: SAS Institute Inc.
White, I. R., & Thomas, J. (2005). Standardized mean differences in individually-randomized and cluster-randomized trials, with applications to meta-analysis. Clinical Trials, 2, 141-151.
Yang, L., & Tsiatis, A. A. (2001). Efficiency study of estimator for a treatment effect in a pretest-posttest trial. The american statistician, 55(4), 312-321.
Zwi, K., Woolfenden, S., & Wheeler, D. (2007). School-based education programmes for the prevention of child sexual abse(Review).