Causal directed acyclic graph (DAG) application in exposure-response analyses
Authors: Xu Siyan , Lu Jiarui 
Published: February 2025

Objectives: Exposure-response (ER) analyses estimate the relationship between drug dosage or pharmacokinetics (PK) and clinical outcomes or biomarker. While deriving a causal ER relationship from randomized trials with varying exposure levels is often unfeasible, comprehending this causality is crucial for informed decision-making. A lack of understanding of the causal dynamics between exposure and response can result in erroneous analyses. To minimize bias, it is essential to articulate the research question clearly, account for potential confounders, and ensure sufficient data collection. Initiating this process with a well-constructed causal diagram can provide a clear roadmap.Methods: In causal DAG, nodes symbolize variables, while directed edges denote causal influences. 'A -- > B' implies that a change in A causes a change in B. To elucidate the research question, particularly when it involves an intercurrent event, it is beneficial to incorporate all pertinent covariates, irrespective of their measurability, that might influence an ER analysis. Here, DAG serves as a visual summary of prior beliefs or knowledge, encompassing fundamental elements like forks, mediators, and colliders.Moreover, DAGs estimated from data can be considered. The PC algorithm (Kalisch 2007) is a common method to estimate the causal structure. It performs a sequence of conditional independence tests at pre-specified type-I error rate to identify all colliders within the graph. The direction of remaining edges is determined through a set of orientation rules. The PC algorithm is extended to latent PC algorithms (Cai 2022) for mixed data types. Constraints can be specified to reflect the temporal order of the variables. It is important to note that DAGs derived from algorithms must reflect the scientific comprehension of the data generation process and are not solely reliant on algorithmic output.Results: We implemented the causal DAG approach in two practical scenarios. The DAG facilitated a clearer understanding of the research question, enabling us to delineate both direct and indirect pathways from exposure (dose) to response (survival). Notably, the presence of a time-varying covariate along these paths prompted an in-depth investigation into its temporal dynamics and the challenges of data scarcity. Additionally, in a separate instance, the employment of an algorithm-derived DAG revealed the underlying causal framework, highlighting the conditional independence given the baseline variables. This enhanced our comprehension of the causal relationships within the data, guiding more informed analytical decisions.Conclusions: The causal DAG is instrumental in clarifying the research question, understanding the causal structure and confounders, and identifying variables that may have gaps in data collection. It is strongly advised to consider the causal DAG prior to conducting ER analyses to ensure a robust and comprehensive evaluation.Citations: [1] Cai, Z., Xi, D., Zhu, X., & Li, R. (2022). Causal discoveries for high dimensional mixed data. Statistics in Medicine, 41(24), 4924-4940.[2] Kalisch, M., & Bühlman, P. (2007). Estimating high-dimensional directed acyclic graphs with the PC-algorithm. Journal of Machine Learning Research, 8(3).