Considering a study described by Hernán and Robins in 'Causal Inference: What If'. I had a rough idea of the selection bias that could arise in this study, but I encountered some difficulties when I tried to use causal graphs to represent the relationships between variables.
- Suppose an investigator conducted a randomized experiment to answer the causal question 'does one’s looking up to the sky make other pedestrians look up too?' She found a strong association between her looking up and other pedestrians’ looking up. Does this association reflect a causal effect? Well, by definition of randomized experiment, confounding bias is not expected in this study. However, there was another potential problem: The analysis included only those pedestrians that, after having been part of the experiment, gave consent for their data to be used. Shy pedestrians (those less likely to look up anyway) and pedestrians in front of whom the investigator looked up (who felt tricked) were less likely to participate. Thus participating individuals in front of whom the investigator looked up (a reason to decline participation) are less likely to be shy (an additional reason to decline participation) and therefore more likely to lookup.
Fan Chao It is a type of study design that is used to collect evidence of a cause and effect relationship between two or more variables, where one or more variables are dependent and the others are independent.
This tutorial might help further: https://www.youtube.com/watch?v=3PdIR4P107k
Qamar Ul Islam Thank you for your comment! But what I would like to know is how to express the relationship between these variables in a causal diagram. For example, the structure of a typical selection bias could be represented by a causal diagram as follows, which depicts dichotomous treatment X, outcome Y, and their common effect A.
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