辛普森悖論於流行病學與統計學層面之整合性探討

Abstract

研究背景：辛普森悖論自1951年被提出後，相關現象已反覆在現實生活被觀察到。其在流行病學被稱之干擾效應，而在統計學被稱為相關性翻轉，此兩者在各學科間之連結卻甚少被探討。 研究目的：本論文目的在提出一個系統性和整合性的方法架構，去統整各種分析方法，用於處理辛普森悖論在科學研究中之相關現象。 研究方法：首先探討流行病學中用於因果推論中處理干擾效應之方法，包括描述流行病學之標準化以及分析流行病學之分層分析和迴歸模型。接著討論統計學之相關性翻轉和流行病學之分析方法間之連結。文中提出一個系統性的檢查列表，用於評估符合辛普森悖論之統計條件。此外，本論文之創新處在於發展出一個分析架構，用於連結流行病學之年齡標準化和分層分析以及統計學存活分析模型之等比例風險假設。此外，我們利用邏輯迴歸模型和Cox等比例風險迴歸模型發展出符合辛 普森悖論之統計條件。此一整合性方法提供一個系統性檢查辛普森悖 論現象的分析架構。 研究結果：文中利用口腔癌發生率和大腸直腸癌死亡率之實際數據，以年齡標準化之方法分析描述性統計中之干擾效應和相關性翻轉之程度。接著使用分層分析和邏輯迴歸分析去比較分層分析各分層之罹癌風險勝算比及多變數迴歸模型和馬可夫蒙地卡羅模擬之貝氏分析之斜率值，進一步檢查干擾效應和相關性翻轉之程度。透過比較各種方法之分析結果，進一步發展出符合辛普森悖論之統計條件。同時也應用Cox等比 例風險迴歸模型去評估和其他方法分析結果之差異。 結論：本論文提出一個整合性的分析架構和檢查條件用於量化及處理流行病學和統計學研究中可能存在的辛普森悖論現象。

Background: Simpson’s paradox proposed since 1951 has been often seen in real life but its link between epidemiology in terms of confounding effect and statistics in terms of association reversal has been rarely explored. Aims: This thesis aims to propose a systematic and integrative approach to consolidate various solutions into a unified framework for dealing with the phenomenon in relation to Simpson’s paradox. Methods: Epidemiological approaches pertaining to Simpson’s paradox were first proposed to deal with causal effects perturbed by confounding factors. They include covariate-specific standardization on descriptive epidemiology and stratification or regression models on analytical epidemiology. Integrative aspects of Simpson Paradox are then proposed to link these epidemiological methods to the corresponding phenomenon often called association reversal in the language of statistics. A systematic check-up list is developed to assess the criteria for meeting Simpson’s paradox beginning with probability area method. The novelty here is to develop a common structure with Simpson’s paradox underpinning that renders epidemiological approaches such as age-standardization or stratification commensurate with statistical proportional hazards premise or constant intercept used in survival models. The logistic regression and Cox proportional hazards regression models are further used to develop the criteria for meeting Simpson’s paradox. This integrative statistical approach provides a systematic check for an instance of Simpson’s paradox. Results: Age-standardization supported by empirical data is first demonstrated to show confounding and association reversal for descriptive epidemiology by using the empirical data of oral cancer and colorectal cancer. Risk stratification and logistic regression models are further applied to examine the degree of confounding effect and reversal association by comparing the crude with stratum-specific odds ratio or comparing common slope with adjusted slopes after considering confounding factors. We compared these results with our developed criteria for meeting Simpson’s paradox. We also applied Cox proportional hazards regression models and Bayesian analysis with Markov Chain Monte Carlo simulations to estimate the results in comparison with those in age-standardization, risk stratification, and logistic regression models. The results of the developed check criteria for Simpson’s paradox is also compared with those estimated from Cox proportional hazards regression model. Conclusion: An integrative framework and checklist criteria for both epidemiology and statistics is developed to quantitatively assess the criteria of Simpson’s paradox.