極少數研究下之統合分析:以假說檢定為本之點估計及信賴區間

Abstract

隨機效應模型統合分析是目前主流的研究統整方法。然而在極少數研究下的統合分析，目前尚未有最合適的方法。在本論文中，我們假設每篇研究的真實效果服從常態分佈，提出了一套以假說檢定為基礎，得到真實效果平均值的點估計值以及信賴區間的新方法（test-based , TB）。模擬研究顯示當納入統合分析的篇數極少時，傳統的DerSimonian-Laird（DL）方法與Knapp-Hartung結合Paule-Mandel（KHPM）方法都有信賴區間覆蓋率不足的問題。但是本論文的方法不論在哪種情形下，都能維持足夠的信賴區間覆蓋率。當研究的真實效果與研究內的變異量有相關時，DL與KHPM法的點估計有較大的偏差及均方根誤差，其信賴區間覆蓋率不足的問題也更加嚴重。在此情況下，我們方法的點估計值亦有偏差，但偏差量及均方根誤差皆比DL與KHPM法小。我們方法的信賴區間此時為不對稱型，能夠適當彌補點估計的偏差，而保有良好的覆蓋率。我們並提供了真實的統合分析例子來呈現以假說檢定為本的估計方法之優缺點。

Random-effects meta-analysis is one of the mainstream methods for research synthesis. However, there is no suitable method for meta-analysis in the case of very few studies. In this study, we assume the true effect of each study follow a normal distribution, and propose a new method to estimate the mean of the true effects and its confidence interval. The method is based on hypothesis testing and is referred to as the test-based（TB）method. Simulation study shows that both the conventional DerSimonian-Laird（DL）method and the Knapp-Hartung in combination with Paule-Mandel（KHPM）method have the problem of inadequate coverage rates of confidence intervals in the case of very few studies. But, in all scenarios we studied, the proposed TB method can maintain adequate coverage rates of confidence intervals. When the true effect is associated with the within-study variance, the DL and KHPM methods have larger bias and root-mean-square error, and have more serious problem of the undercoverage for the confidence intervals. In this situation, the proposed TB method is also biased, but to lesser extent and with smaller root-mean-square error. The confidence interval of the TB method under this situation is asymmetric. This counteracts the bias in the point estimate and allows the confidence interval to maintain adequate coverage. Real examples are also provided to illustrate the methodology.