Towards a Holistic Understanding of Selection Bias for Causal Effect Identification

Selection bias is pervasive in observational studies. For example, large scale biobanks data can exhibit ``healthy volunteer bias'' when respondents are healthier and of higher socio-economic status than the population they are meant to represent. Recovering causal effects from such sub-population is an important problem in causal inference, as estimating average treatment effects (ATE) from selected populations can result in a severely biased estimate of the ATE from the whole population. In this paper, we investigate the identifiability of the ATE under selection bias. We provide necessary and sufficient conditions for ATE identifiability, leveraging weak assumptions on probability classes to characterize propensity score and selection probability, which are weaker assumptions than those required by existing general identification frameworks. Compared to previous works, our results extend existing graphical identifiability criteria and offer a more comprehensive understanding of causal effect identification with strictly weaker conditions in the presence of selection bias.

The data we collected are often biase due to "healthy voluntary bias", e.g. people who are healthier and with higher education are more inclined to participate in data collection. This paper provides the condition on the data distribution where one can uniquely calculate causal effect of a treatment when we only have biased dataset. We also provide an estimation method. This clarifies when and how we can deal with selection bias.