事件時間資料之差異中的差異分析：反事實存活曲線與限制平均存活時間估計

Abstract

在政策評估與準實驗研究中，差異中的差異分析法常被用來比較處理組與對照組在政策前後的結果變化。然而，當研究結果為事件時間資料時，資料通常具有右設限與吸收狀態的特性，個體一旦發生事件即離開風險集合，使傳統以平均結果為基礎的差異中的差異分析法不易直接適用。本研究旨在探討事件時間資料下的政策效果估計問題，並以反事實存活曲線與限制平均存活時間作為主要分析架構。 本研究提出加權反事實累積風險建構法。此方法先以傾向分數反比加權調整處理組與對照組在共變數上的差異，再透過加權 Nelson--Aalen 估計量估計兩組的累積風險函數。接著，利用政策前期估計處理組與對照組之固定對數風險差異，建構處理組在未受政策介入情境下的反事實存活曲線。最終以處理組在事實世界與反事實世界下的限制平均存活時間差異，衡量政策使事件平均延後或提前發生的效果。 本研究透過 Weibull 與 Gompertz 基礎風險設定進行模擬分析，並與 Cox 比例風險模型下的差異中的差異分析法及存續時間差異中的差異分析法比較。結果顯示本研究方法在多數情境下具有較小的平均偏誤，並能較穩定地重建處理組的反事實存活曲線；但在樣本數較小且共變數不平衡較明顯時，仍可能因加權程序而提高估計變異。實際資料應用方面，本研究分別分析出獄者財務協助與首次再逮捕時間，以及 ACA Medicaid 擴張政策與低收入非高齡成人取得 Medicaid 等待時間之關係。結論呈現本研究方法能將事件時間政策效果轉換為平均時間差，提供較單一風險比更直觀的政策解釋。

In policy evaluation and quasi-experimental studies, the difference-in-differences (DiD) framework is widely used to compare outcome changes between treated and control groups before and after an intervention. However, when the outcome of interest is time-to-event, standard mean-based DiD methods cannot be directly applied due to right censoring and absorbing states, as individuals leave the risk set once an event occurs. To address this challenge, this study investigates policy effect estimation for time-to-event outcomes by developing an analytical framework based on counterfactual survival curves and restricted mean survival time (RMST). Specifically, we propose a weighted counterfactual cumulative hazard construction approach. The method first employs inverse probability of treatment weighting (IPTW) based on propensity scores to adjust for baseline covariate imbalances between the treated and control groups. It then estimates group-specific cumulative hazard functions using a weighted Nelson–Aalen estimator. Utilizing the pre-policy period, a fixed log-hazard difference between the treated and control groups is estimated and used to construct the counterfactual survival curve for the treated group in the absence of the policy. The final policy effect is quantified by the RMST difference between the factual and counterfactual survival curves, representing the average delay or acceleration in event occurrence induced by the policy. Simulation studies are conducted under Weibull and Gompertz baseline hazard configurations to evaluate the proposed method against two benchmarks: a Cox proportional hazards DiD model and a Duration DiD model. The results demonstrate that the proposed method yields smaller mean bias in most scenarios and more stably reconstructs the counterfactual survival curve for the treated group. However, in small sample sizes with pronounced covariate imbalances, the weighting procedure may increase estimation variability. For empirical validation, this study analyzes two applications: the relationship between financial aid for released prisoners and time to first rearrest, and the impact of the ACA Medicaid expansion on the waiting time to Medicaid acquisition among low-income, non-elderly adults. The findings indicate that the proposed method successfully expresses policy effects for time-to-event outcomes as average time differences, providing a more interpretable and policy-relevant measure than a traditional single hazard ratio.