  In many stochastic service systems, decision-makers find themselves making a
sequence of decisions, with the number of decisions being unpredictable. To
enhance these decisions, it is crucial to uncover the causal impact these
decisions have through careful analysis of observational data from the system.
However, these decisions are not made independently, as they are shaped by
previous decisions and outcomes. This phenomenon is called sequential bias and
violates a key assumption in causal inference that one person's decision does
not interfere with the potential outcomes of another. To address this issue, we
establish a connection between sequential bias and the subfield of causal
inference known as dynamic treatment regimes. We expand these frameworks to
account for the random number of decisions by modeling the decision-making
process as a marked point process. Consequently, we can define and identify
causal effects to quantify sequential bias. Moreover, we propose estimators and
explore their properties, including double robustness and semiparametric
efficiency. In a case study of 27,831 encounters with a large academic
emergency department, we use our approach to demonstrate that the decision to
route a patient to an area for low acuity patients has a significant impact on
the care of future patients.
