後設分析──貝氏方法在混合效果模式上的應用

Meta-analysis: A Bayesian Method for the Mixed-Effect Models

後設分析（Meta-analysis）主要在將個別獨立研究結果以組合的觀點進行系統性的評估與檢視。在研究實例中，心理學效果量指標值通常為Hedges（1981）之標準化平均差異效果量，醫學效果量指標值多為Odds Ratio（OR），而管理學文獻大都以相關係數為效果量指標值。本研究從文獻間不同的資料蒐集方法、資料屬性及不同的效果量指標值加以探討及分析，期使研究結果更為可信。在混合效果模式（mixed-effect model）下，本研究採古典方法與貝氏（Bayesian）方法估計參數，並比較模式之配適（model-data fit）。古典方法主要介紹加權最小平方法（WLS），貝氏方法主要介紹蒙地卡羅法（MCMC）。WLS取其應用上簡單易行，估計時以SAS/IML程式進行。貝氏MCMC取其在複雜階層模式中卻能直接抽樣的便利性，並以WinBUGS軟體進行。研究發現：文獻間存在異質性變異時，WLS（random model）與MCMC（random model）的參數估計結果近似，但與固定效果模式下之參數估計結果則明顯不同；反之，當文獻間存在同質性變異時，則古典方法和貝氏方法的參數估計結果幾乎相同。

Meta-analysis refers to methods for combining the results of independent studies into effectiveness of medical treatments， or into the impact of environmental or other health risks， and so form a prior evidence base for planning new studies or interventions. Two alternative approaches (classical and Bayesian) provide different estimates for a random effects model. In classical approach， the true effect sizes under study are taken from a larger population of effect sizes. In Bayesian analysis， the observed data is used to modify the prior beliefs， with the updated knowledge summarized in a posterior density. The classical method， such as weighted least square estimation， present an alternative to Markov Chain Monte Carlo (MCMC) method， which provides some promise for parameter estimation with complex models. MCMC may have advantages in handling issues which occur in meta-analysis， such as choice between fixed-effects vs. random-effects models， robust inference for small studies or non Normal effects. The resulting MCMC (fixed model)、WLS (random model) and MCMC (random model) parameter estimates were comparable.