Motivated by studies investigating causal effects in survival analysis, we propose a transformation model to quantify the impact of a binary treatment on a time-to-event outcome. The approach is based on a flexible linear transformation structural model that links a monotone function of the time-to-event with the propensity for treatment through a bivariate Gaussian distribution. The model equations are specified as functions of additive predictors, allowing the impacts of observed confounders to be accounted for flexibly. Furthermore, the effect of the instrumental variable may be regularized through a ridge penalty, while interactions between the treatment and modifier variables can be incorporated into the model to acknowledge potential variations in treatment effects across different subgroups. The baseline survival function is estimated in a flexible manner using monotonic P-splines, while unobserved confounding is captured through the dependence parameter of the bivariate Gaussian. The proposal naturally provides an intuitive causal measure of interest, the survival average treatment effect. Parameter estimation is achieved via a computationally efficient and stable penalized maximum likelihood estimation approach and intervals constructed using the related inferential results. We revisit a dataset from the Illinois Reemployment Bonus Experiment to estimate the causal effect of a cash bonus on unemployment duration, unveiling new insights. The modeling framework is incorporated into the R package GJRM, enabling researchers and practitioners to fit the proposed causal survival model and obtain easy-to-interpret numerical and visual summaries.

翻译：受生存分析中因果效应研究的启发，本文提出一种转换模型用于量化二元处理对生存时间结果的影响。该方法基于灵活的线性转换结构模型，通过二元高斯分布将生存时间的单调函数与处理倾向性相关联。模型方程被设定为加性预测变量的函数，从而能够灵活地校正已观测混杂因素的影响。此外，工具变量的效应可通过岭惩罚进行正则化处理，同时处理变量与修饰变量间的交互作用可纳入模型，以识别不同亚组间治疗效应的潜在异质性。基线生存函数采用单调P样条进行灵活估计，而未观测混杂则通过二元高斯分布的相依参数予以捕捉。该方案自然地提供了直观的因果度量指标——生存平均处理效应。参数估计通过计算高效且稳定的惩罚最大似然估计方法实现，并利用相关推断结果构建置信区间。我们重新分析了伊利诺伊州再就业奖金实验数据集，以估计现金奖金对失业持续时间的因果效应，揭示了新的研究发现。该建模框架已集成至R软件包GJRM中，使研究者和实践者能够拟合所提出的因果生存模型，并获得易于解读的数值与可视化结果摘要。