遞迴雙變量 Probit 模型在二元工具變項統合分析之應用：以硬脊膜外麻醉對剖腹產之影響為例

Abstract

在醫學與流行病學的因果推論中，隨機對照試驗雖被視為黃金標準，但實務上常受限於受試者不遵循醫囑及倫理限制，導致傳統意向性治療分析（ITT）難以精確評估實際治療的生物機制。工具變數（Instrumental Variable, IV）方法雖可利用隨機分派作為工具來解決內生性問題，但現有的工具變數統合分析（Meta-IV）文獻多聚焦於連續型變數，缺乏針對工具變數、暴露與結果變數皆為二元（Binary Z-X-Y）且僅能取得匯總資料（Aggregate Data, AD）情境下的系統性分析框架。本研究旨在填補此方法學缺口，探討在該架構下如何建構適當的統計模型以維持估計的一致性。 本研究採用遞迴雙變量Probit模型（Recursive Bivariate Probit Model, RBPM）作為核心估計方法，該模型允許暴露與結果方程式的誤差項存在相關性，進而校正由未測量干擾因子所導致的內生性偏誤。研究程序包含模擬研究與實證資料分析兩部分。首先，透過蒙地卡羅模擬（Monte Carlo Simulation）在不同樣本數（N=1000, 3000, 5000）下比較 RBPM 與傳統Probit 模型的表現；其次，利用Zhou等人（2021）關於「硬脊膜外麻醉是否增加剖腹產風險」的臨床試驗匯總資料，透過2×2×2列聯表結構將其還原為個體層級資料（IPD），並應用RBPM檢驗內生性及估計真實因果效應。 模擬結果顯示，在存在未觀測干擾因子的情境下，忽略內生性的傳統模型會產生嚴重的高估偏誤，而RBPM則能有效還原真實的因果效應，且隨著樣本數增加，其估計精確度顯著提升。在實證分析方面，RBPM檢定結果顯示暴露與結果模型的誤差項存在顯著正相關（ρ=0.060），證實了內生性的存在，意即傾向選擇麻醉的產婦本身即具有較高的剖腹產潛在風險。然而，在校正此內生性偏誤後，研究發現實際接受硬脊膜外麻醉對於剖腹產的發生率並無統計上顯著的因果影響（p = 0.126）。 本研究結論指出，過去部分文獻認為麻醉會增加剖腹產風險的結論，可能源於未能妥善處理內生性所導致的選擇性偏誤。本研究透過RBPM模型證實了在二元變數架構下檢驗與校正內生性的必要性，並釐清了臨床上的爭議。此方法學嘗試展示了在特定條件下從匯總資料還原個體資料的可行性，為未來發展適用於更廣泛變數型態的工具變數統合分析統一框架提供了重要的實證基礎。

While Randomized Controlled Trials (RCTs) are regarded as the gold standard for causal inference in medicine and epidemiology, practical constraints such as subject noncompliance and ethical limitations often hinder traditional Intention-to-Treat (ITT) analysis from accurately evaluating the biological mechanisms of the actual treatment. Although Instrumental Variable (IV) methods can utilize random assignment as an instrument to address endogeneity, existing literature on IV meta-analysis (Meta-IV) predominantly focuses on continuous variables. There is a notable lack of a systematic analytical framework for scenarios where the instrument, exposure, and outcome are all binary (Binary Z-X-Y) and only Aggregate Data (AD) is available. This study aims to bridge this methodological gap by exploring the construction of appropriate statistical models within this framework to ensure consistent estimation. The Recursive Bivariate Probit Model (RBPM) was adopted as the core estimation method. This model allows for correlation between the error terms of the exposure and outcome equations, thereby correcting for endogeneity bias arising from unmeasured confounders. The research procedure comprised a simulation study and an empirical analysis. First, Monte Carlo simulations were conducted to compare the performance of RBPM with traditional Probit models across varying sample sizes (N = 1000, 3000, 5000). Second, utilizing aggregate clinical trial data from Zhou et al. (2021) regarding whether epidural analgesia increases the risk of cesarean section, the data was reconstructed into Individual Participant Data (IPD) via a 2 × 2 × 2 contingency table structure. RBPM was then applied to test for endogeneity and estimate the true causal effect. Simulation results demonstrated that in the presence of unobserved confounders, traditional models that ignore endogeneity yield severe overestimation bias. In contrast, RBPM effectively recovered the true causal effect, with estimation precision improving significantly as sample size increased. In the empirical analysis, RBPM results indicated a significant positive correlation (ρ = 0.060) between the error terms of the exposure and outcome models, confirming the presence of endogeneity. This implies that parturients who are inclined to choose epidural analgesia inherently possess a higher latent risk of cesarean section. However, after correcting for this endogeneity bias, the study found no statistically significant causal effect of receiving epidural analgesia on the incidence of cesarean sections (p = 0.126). The study concludes that previous findings suggesting anesthesia increases the risk of cesarean section may stem from selection bias resulting from a failure to adequately address endogeneity. By utilizing the RBPM, this study confirmed the necessity of testing for and correcting endogeneity within a binary variable framework, thereby clarifying clinical controversies. This methodological endeavor demonstrates the feasibility of reconstructing individual-level data from aggregate data under specific conditions, providing a substantial empirical foundation for the future development of a unified framework for instrumental variable meta-analysis applicable to a broader range of variable types.