Causal Attribution Analysis for Continuous Outcomes

Previous studies have extensively addressed the attribution problem for binary outcome variables. However, in many practical scenarios, the outcome variable is continuous, and simply binarizing it may result in information loss or biased conclusions. To address this issue, we propose a series of posterior causal estimands for retrospectively evaluating multiple correlated causes from a continuous outcome. These estimands include posterior intervention effects, posterior total causal effects, and posterior natural direct effects. Under assumptions of sequential ignorability, monotonicity, and perfect positive rank, we show that the posterior causal estimands of interest are identifiable and present the corresponding identification equations. We also provide a simple but effective estimation procedure and establish asymptotic properties of the proposed estimators. An artificial hypertension example and a real developmental toxicity dataset are employed to illustrate our method.

In many research fields, scholars aim to understand what causes certain outcomes. Previous studies have mostly focused on binary outcomes, for example, whether lung cancer is caused by smoking. However, in real-world settings, many important outcomes, such as blood pressure or income, are measured on a continuous scale. Simplifying these outcomes into binary categories can obscure meaningful patterns and potentially lead to misleading conclusions.To better address such situations, our study introduces a new way to identify which factors are likely responsible for continuous outcomes. Our approach allows researchers to evaluate how different causes, especially those that may be related to each other, jointly affect a result. It also helps determine whether the effect came directly from a cause or through more complex paths.We show that, under reasonable assumptions, this method can yield reliable retrospective causal inferences. To illustrate the proposed method, we apply it to a simulated example of hypertension.