伽马分布结局下基于目标最大似然估计的因果推断研究

Research on Causal Inference Based on Targeted Maximum Likelihood Estimation for Gamma-Distributed Outcomes

摘要: 传统的因果推断方法(如G计算和逆概率加权)在估计平均处理效应时，往往依赖于结果模型或倾向得分模型的正确设定，当模型被错误指定时可能产生有偏估计，存在稳健性不足的问题。目标最大似然估计通过引入波动参数对初始结果模型进行靶向更新，提高了模型的双重稳健性和估计效率。本文基于伽马分布假设，通过构造结果回归模型和倾向得分模型的得分函数，利用目标最大似然估计方法得到了平均处理效应的估计结果。蒙特卡洛模拟结果表明，在所有模型设定场景下目标最大似然估计均表现稳健，当任一模型正确时保持无偏估计，估计精度随样本量增加而提高。对比于单一的G计算方法，基于目标最大似然估计的估计结果在模型错误设定时具有更小的偏差和更优的均方误差。将所提方法应用于ACTG175艾滋病数据集，估计结果显示联合治疗可显著提升CD4细胞计数，验证了方法的稳健性和实用性。

Abstract: Traditional causal inference methods, such as G-computation and inverse probability weighting, often rely on the correct specification of the outcome model or the propensity score model when estimating average treatment effects. Incorrect model specification may lead to biased estimates and a lack of robustness. Targeted maximum likelihood estimation (TMLE) improves double robustness and estimation efficiency by introducing a fluctuation parameter to update the initial outcome model in a targeted manner. Assuming a gamma distribution, this paper constructs the score functions for both the outcome regression model and the propensity score model, and obtains the estimated average treatment effect using TMLE. Monte Carlo simulation results show that TMLE remains robust across all model specification scenarios, maintaining unbiased estimates when either model is correctly specified, and estimation accuracy improves as the sample size increases. Compared with the standalone G-computation method, TMLE yields smaller bias and superior mean squared error under model misspecification. Applying the proposed method to the ACTG175 AIDS dataset, the estimation results indicate that combination therapy significantly increases CD4 cell counts, validating the robustness and practicality of the method.