多重中介因子模型之樣本數計算

Sample Size Calculations for the Multiple Mediation Model

戴安順(An-Shun Tai) ； 林詩紋(Shr-Wen Lin) ； 林聖軒(Sheng-Hsuan Lin)

《中國統計學報》 58卷3期 (2020/09) Pp. 199-220

摘要

因果中介模型被廣泛應用在管理學、社會心理學與公共衛生等領域的因果機制探索中，且許多估計中介效應的方法已被開發。然而，在實驗設計時，中介分析時所需樣本數的議題尚未被完整的探討。在現有文獻中，僅有針對單一中介因子模型進行討論。因此，本文根據Lin在2019提出的廣義版多重中介因子模型，探討多重中介因子模型的樣本數推論方式。本文藉由傳統因果中介估計法與G-computation，提出兩種方法來得出樣本數與檢定力的關係式，分別為廣義Sobel法與蒙地卡羅法。廣義Sobel法建立在線性迴歸模型設定下，可得出樣本數與檢定力之數學關係式；蒙地卡羅法則可適用於廣義線性模型且可容許交互作用項，全面性探討樣本數與檢定力之關係式。兩方法各有其優缺點。最後，本文藉由模擬資料，在兩有序中介因子羅吉斯迴歸模型之下，提供了因果中介效應的樣本數計算，並討論兩方法間的差異。

關鍵字

因果推論 ； 因果中介分析 ； G-computation ； 檢定力與樣本數分析

並列摘要

Causal mediation analysis has been widely used to investigate causal mechanisms in many fields, such as economics, psychology, and epidemiology. Many statistical methodologies have been proposed for the estimation of mediation effects. However, there is a lack of literature on the issue of sample size calculation in causal mediation analysis, especially in the case of multiple mediators. Therefore, this study based on the generalized model for causal mediation analysis with multiple mediators proposed by Lin in 2019 to develop two approaches for sample size determination: generalized Sobel's method and Monte Carlo method. Given a regression model setting, the generalized Sobel's method can be used to derive a mathematical relation between the sample size and the power for multiple mediators. By contrast, the Monte Carlo method refers to G-computation, which is a popular computational approach in causal inference study. The Monte Carlo method directly calculates the powers under different sample sizes comprehensively, and by doing so, we can reveal the relation between sample size and power. We provide a simulation study to compare two proposed methods under a logistic regression model with two ordered mediators. Moreover, the simulation study also helps us in understanding the required sample size to achieve a specific statistical power.

並列關鍵字

Causal inference ； Causal mediation analysis ； G-computation ； Power and sample size calculation

參考文獻

Huang, Y.T. and Cai, T. (2015). Mediation analysis for survival data using semiparametric probit models. Biometrics.

Imai, K., Keele, L., Tingley, D. and Yamamoto, T. (2010). Causal mediation analysis using R. In Advances in social science research using R. New York, Springer. pages 129-154.

Lin, S.-H. (2019). Generalized interventional approach for causal mediation analysis with causally ordered multiple mediators. Harvard University Biostatistics Working Paper Series: Working Paper 217

Lin, S.-H. and Vanderweele, T. (2017). Interventional Approach for Path-Specific Effects. Journal of Causal Inference, 5(1), pages 1-10 .

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