  There are well-established methods for identifying the causal effect of a
time-varying treatment applied at discrete time points. However, in the real
world, many treatments are continuous or have a finer time scale than the one
used for measurement or analysis. While researchers have investigated the
discrepancies between estimates under varying discretization scales using
simulations and empirical data, it is still unclear how the choice of
discretization scale affects causal inference. To address this gap, we present
a framework to understand how discretization scales impact the properties of
causal inferences about the effect of a time-varying treatment. We introduce
the concept of "identification bias", which is the difference between the
causal estimand for a continuous-time treatment and the purported estimand of a
discretized version of the treatment. We show that this bias can persist even
with an infinite number of longitudinal treatment-outcome trajectories. We
specifically examine the identification problem in a class of linear stochastic
continuous-time data-generating processes and demonstrate the identification
bias of the g-formula in this context. Our findings indicate that
discretization bias can significantly impact empirical analysis, especially
when there are limited repeated measurements. Therefore, we recommend that
researchers carefully consider the choice of discretization scale and perform
sensitivity analysis to address this bias. We also propose a simple and
heuristic quantitative measure for sensitivity concerning discretization and
suggest that researchers report this measure along with point and interval
estimates in their work. By doing so, researchers can better understand and
address the potential impact of discretization bias on causal inference.
