一般性出版偏誤模型

A Generalized Publication Bias Model

羅森梭和魯賓於1978年提出一個在整合性分析中估計未發表論文數的方法－失敗安全數（FSN），史卡構於2000年時曾經為文討論過這個方法。他認為該方法的核心前提與出版偏誤的定義相違背，因此，該方法不可能是正確的。這個論點雖然其他學者也提出過（Darlington, 1980; Elsahoff, 1978; Iyengar & Greenhouse, 1988; Thomas, 1985），不過，史卡構以一個簡單的兩參數模型說明了羅森梭和魯賓的估計在現實情況中可以多離譜。史卡構的結果係建立在決策變項為一平均數為零的常態分配這個前提上。在此前提下，未發表和已發表論文數的比例只有在這個參數面的一小塊區域中會是大的。本研究延伸史卡構先前的結果，進一步說明（一）將連續變項的機率密度代以不連續變項的機率密度可以大幅簡化史卡構的推導，使第一類型錯誤的概率α和stepsizeβ之間的關係可以明確地陳述；（二）這樣的結果並不需要對母群體的次數分佈型態做任何假設；（三）單尾和雙尾拒絕區的差異變得不再重要；（四）這個無母數的方法可以立刻泛推至兩個以上的區間，涵蓋較廣的選擇函數。

Scargle (2000) has discussed Rosenthal and Rubin's (1978) fail-safe number"（FSN) method for estimating the number of unpublished studies in meta-analysis. He concluded that this FSN cannot possibly be correct because a central assumption the authors used conflicts with the very definition of publication bias. While this point has been made by others before (Darlington, 1980; Elsahoff, 1978; Iyengar & Greenhouse, 1988; Thomas, 1985), Scargle showed, by way of a simple 2- parameter model, how far off Rosenthal and Rubin's estimate can be in practice. However, his results relied on the assumption that the decision variable is normally distributed with zero mean. In this case the ratio of unpublished to published papers is large only in a tiny region of the parameter plane. Building on these results, we now show that (1) replacing densities with probability masses greatly simplifies Scargle's derivations and permits an explicit statement of the relation between the probability α of Type I errors and the step-size β; (2) this result does not require any distribution assumptions; (3) the distinction between 1- sided and 2- sided rejection regions becomes immaterial; (4) this distribution-free approach leads to an immediate generalization to partitions involving more than two intervals, and thus covers more general selection functions.