Discovering causal relationships from observational data is a fundamental yet challenging task. Invariant causal prediction (ICP, Peters et al., 2016) is a method for causal feature selection which requires data from heterogeneous settings and exploits that causal models are invariant. ICP has been extended to general additive noise models and to nonparametric settings using conditional independence tests. However, the latter often suffer from low power (or poor type I error control) and additive noise models are not suitable for applications in which the response is not measured on a continuous scale, but reflects categories or counts. Here, we develop transformation-model (TRAM) based ICP, allowing for continuous, categorical, count-type, and uninformatively censored responses (these model classes, generally, do not allow for identifiability when there is no exogenous heterogeneity). As an invariance test, we propose TRAM-GCM based on the expected conditional covariance between environments and score residuals with uniform asymptotic level guarantees. For the special case of linear shift TRAMs, we also consider TRAM-Wald, which tests invariance based on the Wald statistic. We provide an open-source R package 'tramicp' and evaluate our approach on simulated data and in a case study investigating causal features of survival in critically ill patients.

翻译：从观测数据中发现因果关系是一项基础但具有挑战性的任务。不变因果预测（ICP，Peters等，2016）是一种因果特征选择方法，它需要来自异质性环境的数据，并利用因果模型不变性的特点。ICP已通过条件独立性检验扩展到一般加性噪声模型和非参数设置。然而，后者往往存在统计功效低（或第一类错误控制较差）的问题，且加性噪声模型不适用于响应变量非连续尺度测量、而是反映类别或计数数据的应用场景。本文我们开发了基于变换模型（TRAM）的ICP方法，可处理连续型、类别型、计数型以及非信息删失型响应变量（这些模型类别在缺乏外生异质性时通常无法识别）。作为不变性检验，我们提出基于环境与得分残差之间的期望条件协方差的TRAM-GCM方法，具有渐近一致的检验水平保证。针对线性移位TRAM的特殊情形，我们还提出基于Wald统计量检验不变性的TRAM-Wald方法。我们提供了开源R包'tramicp'，并在模拟数据以及探究危重症患者生存因果特征的案例研究中评估了该方法。