Abstract
Directed acyclic graphs (DAGs) play a large role in the modern approach to causal inference. DAGs describe the relationship between measurements taken at various discrete times including the effect of interventions. The causal mechanisms, on the other hand, would naturally be assumed to be a continuous process operating over time in a cause–effect fashion. How does such immediate causation, that is causation occurring over very short time intervals, relate to DAGs constructed from discrete observations? We introduce a time-continuous model and simulate discrete observations in order to judge the relationship between the DAG and the immediate causal model. We find that there is no clear relationship; indeed the Bayesian network described by the DAG may not relate to the causal model. Typically, discrete observations of a process will obscure the conditional dependencies that are represented in the underlying mechanistic model of the process. It is therefore doubtful whether DAGs are always suited to describe causal relationships unless time is explicitly considered in the model. We relate the issues to mechanistic modeling by using the concept of local (in)dependence. An example using data from the Swiss HIV Cohort Study is presented.
Highlights
Causal inference has become a topic of major importance in statistics
There is no doubt that causal Directed acyclic graphs (DAGs) are very useful for understanding various types of biases, such as selection bias and confounding
In this article, we have shown that the view of DAGs as a strict representation of causal relationships can be problematic
Summary
Causal inference has become a topic of major importance in statistics. There is a large body of literature on causal modeling in the statistical and epidemiological literature. We see the emergence of fields such as systems biology which aim at understanding biological mechanisms, for example, with the purpose of suggesting useful medical treatments. Medications are often suggested on the basis of mechanistic reasoning, for example, the angiogenesis inhibitors which inhibit the growth of blood vessels. These have been proposed as a treatment against cancer, depriving the tumor of nutrition. The statistical analysis comes from clinical trials which in this case have been somewhat disappointing some angiogenesis inhibitors are in use. The statistical analysis comes from clinical trials which in this case have been somewhat disappointing some angiogenesis inhibitors are in use. 1 The mechanistic thinking can be seen in other fields, such as social science and economics
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